diff --git a/docs/_build/doctrees/environment.pickle b/docs/_build/doctrees/environment.pickle
index 618d92a..14affea 100644
Binary files a/docs/_build/doctrees/environment.pickle and b/docs/_build/doctrees/environment.pickle differ
diff --git a/docs/_build/html/searchindex.js b/docs/_build/html/searchindex.js
index c752ae4..396b4a4 100644
--- a/docs/_build/html/searchindex.js
+++ b/docs/_build/html/searchindex.js
@@ -1 +1 @@
-Search.setIndex({docnames:["api/api","api/datatypes/datatypes","api/datatypes/demand_source","api/datatypes/disruption_process","api/datatypes/policy","api/datatypes/supply_chain_network","api/datatypes/supply_chain_node","api/meio/gsm_helpers","api/meio/gsm_serial","api/meio/gsm_tree","api/meio/meio","api/meio/meio_general","api/meio/ssm_serial","api/other/helpers","api/other/instances","api/other/loss_functions","api/other/optimization","api/other/other","api/seio/eoq","api/seio/finite_horizon","api/seio/newsvendor","api/seio/rq","api/seio/seio","api/seio/ss","api/seio/supply_uncertainty","api/seio/wagner_whitin","api/simulation/sim","api/simulation/sim_io","api/simulation/simulation","index","install","tutorial/tutorial","tutorial/tutorial_meio","tutorial/tutorial_seio","tutorial/tutorial_sim","tutorial/tutorial_su"],envversion:{"sphinx.domains.c":2,"sphinx.domains.changeset":1,"sphinx.domains.citation":1,"sphinx.domains.cpp":5,"sphinx.domains.index":1,"sphinx.domains.javascript":2,"sphinx.domains.math":2,"sphinx.domains.python":3,"sphinx.domains.rst":2,"sphinx.domains.std":2,"sphinx.ext.viewcode":1,sphinx:56},filenames:["api/api.rst","api/datatypes/datatypes.rst","api/datatypes/demand_source.rst","api/datatypes/disruption_process.rst","api/datatypes/policy.rst","api/datatypes/supply_chain_network.rst","api/datatypes/supply_chain_node.rst","api/meio/gsm_helpers.rst","api/meio/gsm_serial.rst","api/meio/gsm_tree.rst","api/meio/meio.rst","api/meio/meio_general.rst","api/meio/ssm_serial.rst","api/other/helpers.rst","api/other/instances.rst","api/other/loss_functions.rst","api/other/optimization.rst","api/other/other.rst","api/seio/eoq.rst","api/seio/finite_horizon.rst","api/seio/newsvendor.rst","api/seio/rq.rst","api/seio/seio.rst","api/seio/ss.rst","api/seio/supply_uncertainty.rst","api/seio/wagner_whitin.rst","api/simulation/sim.rst","api/simulation/sim_io.rst","api/simulation/simulation.rst","index.rst","install.rst","tutorial/tutorial.rst","tutorial/tutorial_meio.rst","tutorial/tutorial_seio.rst","tutorial/tutorial_sim.rst","tutorial/tutorial_su.rst"],objects:{"stockpyl.demand_source":[[2,1,1,"","DemandSource"]],"stockpyl.demand_source.DemandSource":[[2,2,1,"","cdf"],[2,3,1,"","demand_distribution"],[2,4,1,"","demand_list"],[2,2,1,"","from_dict"],[2,2,1,"","generate_demand"],[2,4,1,"","hi"],[2,2,1,"","initialize"],[2,2,1,"","lead_time_demand_distribution"],[2,4,1,"","lo"],[2,4,1,"","mean"],[2,4,1,"","probabilities"],[2,4,1,"","round_to_int"],[2,4,1,"","standard_deviation"],[2,2,1,"","to_dict"],[2,4,1,"","type"],[2,2,1,"","validate_parameters"]],"stockpyl.disruption_process":[[3,1,1,"","DisruptionProcess"]],"stockpyl.disruption_process.DisruptionProcess":[[3,4,1,"","disrupted"],[3,4,1,"","disruption_probability"],[3,4,1,"","disruption_state_list"],[3,4,1,"","disruption_type"],[3,2,1,"","from_dict"],[3,2,1,"","initialize"],[3,4,1,"","random_process_type"],[3,4,1,"","recovery_probability"],[3,2,1,"","steady_state_probabilities"],[3,2,1,"","to_dict"],[3,2,1,"","update_disruption_state"],[3,2,1,"","validate_parameters"]],"stockpyl.eoq":[[18,5,1,"","economic_order_quantity"],[18,5,1,"","economic_order_quantity_with_backorders"],[18,5,1,"","economic_production_quantity"],[18,5,1,"","joint_replenishment_problem_silver_heuristic"]],"stockpyl.finite_horizon":[[19,5,1,"","finite_horizon_dp"],[19,5,1,"","myopic_bounds"]],"stockpyl.gsm_helpers":[[7,5,1,"","cst_to_base_stock_levels"],[7,5,1,"","inbound_cst"],[7,5,1,"","net_lead_time"],[7,5,1,"","safety_stock_levels"],[7,5,1,"","solution_cost_from_base_stock_levels"],[7,5,1,"","solution_cost_from_cst"]],"stockpyl.gsm_serial":[[8,5,1,"","optimize_committed_service_times"]],"stockpyl.gsm_tree":[[9,5,1,"","gsm_to_ssm"],[9,5,1,"","is_correctly_labeled"],[9,5,1,"","optimize_committed_service_times"],[9,5,1,"","preprocess_tree"],[9,5,1,"","relabel_nodes"]],"stockpyl.helpers":[[13,5,1,"","build_node_data_dict"],[13,5,1,"","change_dict_key"],[13,5,1,"","check_iterable_sizes"],[13,5,1,"","convolve_many"],[13,5,1,"","dict_match"],[13,5,1,"","ensure_dict_for_nodes"],[13,5,1,"","ensure_list_for_nodes"],[13,5,1,"","ensure_list_for_time_periods"],[13,5,1,"","find_nearest"],[13,5,1,"","irwin_hall_cdf"],[13,5,1,"","is_continuous_distribution"],[13,5,1,"","is_discrete_distribution"],[13,5,1,"","is_integer"],[13,5,1,"","is_iterable"],[13,5,1,"","is_list"],[13,5,1,"","min_of_dict"],[13,5,1,"","round_dict_values"],[13,5,1,"","sort_dict_by_keys"],[13,5,1,"","sum_of_continuous_uniforms_distribution"],[13,5,1,"","sum_of_discrete_uniforms_distribution"],[13,5,1,"","sum_of_discrete_uniforms_pmf"],[13,5,1,"","sum_of_discretes_distribution"]],"stockpyl.instances":[[14,5,1,"","load_instance"],[14,5,1,"","save_instance"]],"stockpyl.loss_functions":[[15,5,1,"","continuous_loss"],[15,5,1,"","continuous_second_loss"],[15,5,1,"","discrete_loss"],[15,5,1,"","discrete_second_loss"],[15,5,1,"","exponential_loss"],[15,5,1,"","exponential_second_loss"],[15,5,1,"","gamma_loss"],[15,5,1,"","gamma_second_loss"],[15,5,1,"","geometric_loss"],[15,5,1,"","geometric_second_loss"],[15,5,1,"","lognormal_loss"],[15,5,1,"","negative_binomial_loss"],[15,5,1,"","negative_binomial_second_loss"],[15,5,1,"","normal_loss"],[15,5,1,"","normal_second_loss"],[15,5,1,"","poisson_loss"],[15,5,1,"","poisson_second_loss"],[15,5,1,"","standard_normal_loss"],[15,5,1,"","standard_normal_second_loss"],[15,5,1,"","uniform_loss"],[15,5,1,"","uniform_second_loss"]],"stockpyl.meio_general":[[11,5,1,"","meio_by_coordinate_descent"],[11,5,1,"","meio_by_enumeration"],[11,5,1,"","truncate_and_discretize"]],"stockpyl.newsvendor":[[20,5,1,"","myopic"],[20,5,1,"","myopic_cost"],[20,5,1,"","newsvendor_continuous"],[20,5,1,"","newsvendor_discrete"],[20,5,1,"","newsvendor_normal"],[20,5,1,"","newsvendor_normal_cost"],[20,5,1,"","newsvendor_normal_explicit"],[20,5,1,"","newsvendor_poisson"],[20,5,1,"","newsvendor_poisson_cost"],[20,5,1,"","newsvendor_poisson_explicit"],[20,5,1,"","set_myopic_cost_to"]],"stockpyl.optimization":[[16,5,1,"","golden_section_search"]],"stockpyl.policy":[[4,1,1,"","Policy"]],"stockpyl.policy.Policy":[[4,4,1,"","base_stock_level"],[4,2,1,"","from_dict"],[4,2,1,"","get_order_quantity"],[4,2,1,"","initialize"],[4,4,1,"","node"],[4,4,1,"","order_quantity"],[4,4,1,"","order_up_to_level"],[4,4,1,"","reorder_point"],[4,2,1,"","to_dict"],[4,4,1,"","type"],[4,2,1,"","validate_parameters"]],"stockpyl.rq":[[21,5,1,"","r_q_cost"],[21,5,1,"","r_q_cost_poisson"],[21,5,1,"","r_q_eil_approximation"],[21,5,1,"","r_q_eoqb_approximation"],[21,5,1,"","r_q_eoqss_approximation"],[21,5,1,"","r_q_loss_function_approximation"],[21,5,1,"","r_q_optimal_r_for_q"],[21,5,1,"","r_q_poisson_exact"]],"stockpyl.sim":[[26,5,1,"","close"],[26,5,1,"","initialize"],[26,5,1,"","run_multiple_trials"],[26,5,1,"","simulation"],[26,5,1,"","step"]],"stockpyl.sim_io":[[27,5,1,"","write_instance_and_states"],[27,5,1,"","write_results"]],"stockpyl.ss":[[23,5,1,"","s_s_cost_discrete"],[23,5,1,"","s_s_discrete_exact"],[23,5,1,"","s_s_power_approximation"]],"stockpyl.ssm_serial":[[12,5,1,"","expected_cost"],[12,5,1,"","expected_holding_cost"],[12,5,1,"","newsvendor_heuristic"],[12,5,1,"","optimize_base_stock_levels"]],"stockpyl.supply_chain_network":[[5,1,1,"","SupplyChainNetwork"],[5,5,1,"","echelon_to_local_base_stock_levels"],[5,5,1,"","local_to_echelon_base_stock_levels"],[5,5,1,"","mwor_system"],[5,5,1,"","network_from_edges"],[5,5,1,"","owmr_system"],[5,5,1,"","serial_system"],[5,5,1,"","single_stage_system"]],"stockpyl.supply_chain_network.SupplyChainNetwork":[[5,2,1,"","add_edge"],[5,2,1,"","add_edges_from_list"],[5,2,1,"","add_node"],[5,2,1,"","add_predecessor"],[5,2,1,"","add_successor"],[5,2,1,"","deep_equal_to"],[5,3,1,"","edges"],[5,2,1,"","from_dict"],[5,2,1,"","get_node_from_index"],[5,2,1,"","has_directed_cycle"],[5,2,1,"","initialize"],[5,4,1,"","max_max_replenishment_time"],[5,2,1,"","networkx_digraph"],[5,3,1,"","node_indices"],[5,3,1,"","nodes"],[5,4,1,"","period"],[5,4,1,"","problem_specific_data"],[5,2,1,"","reindex_nodes"],[5,2,1,"","remove_node"],[5,3,1,"","sink_nodes"],[5,3,1,"","source_nodes"],[5,2,1,"","to_dict"]],"stockpyl.supply_chain_node":[[6,1,1,"","NodeStateVars"],[6,1,1,"","SupplyChainNode"]],"stockpyl.supply_chain_node.NodeStateVars":[[6,3,1,"","backorders"],[6,4,1,"","backorders_by_successor"],[6,2,1,"","deep_equal_to"],[6,4,1,"","demand_cumul"],[6,4,1,"","demand_met_from_stock"],[6,4,1,"","demand_met_from_stock_cumul"],[6,4,1,"","disrupted"],[6,3,1,"","echelon_inventory_level"],[6,2,1,"","echelon_inventory_position"],[6,3,1,"","echelon_on_hand_inventory"],[6,4,1,"","fill_rate"],[6,2,1,"","from_dict"],[6,4,1,"","holding_cost_incurred"],[6,3,1,"","in_transit"],[6,2,1,"","in_transit_from"],[6,4,1,"","in_transit_holding_cost_incurred"],[6,2,1,"","in_transit_to"],[6,4,1,"","inbound_disrupted_items"],[6,3,1,"","inbound_disrupted_items_aggregate"],[6,4,1,"","inbound_order"],[6,4,1,"","inbound_order_pipeline"],[6,4,1,"","inbound_shipment"],[6,4,1,"","inbound_shipment_pipeline"],[6,4,1,"","inventory_level"],[6,2,1,"","inventory_position"],[6,4,1,"","node"],[6,3,1,"","on_hand"],[6,3,1,"","on_order"],[6,4,1,"","on_order_by_predecessor"],[6,4,1,"","order_quantity"],[6,4,1,"","outbound_disrupted_items"],[6,4,1,"","outbound_shipment"],[6,4,1,"","period"],[6,3,1,"","raw_material_aggregate"],[6,4,1,"","raw_material_inventory"],[6,2,1,"","reindex_state_variables"],[6,4,1,"","revenue_earned"],[6,4,1,"","stockout_cost_incurred"],[6,2,1,"","to_dict"],[6,4,1,"","total_cost_incurred"]],"stockpyl.supply_chain_node.SupplyChainNode":[[6,2,1,"","add_predecessor"],[6,2,1,"","add_successor"],[6,3,1,"","ancestors"],[6,2,1,"","deep_equal_to"],[6,4,1,"","demand_source"],[6,3,1,"","derived_demand_mean"],[6,3,1,"","derived_demand_standard_deviation"],[6,3,1,"","descendants"],[6,3,1,"","disrupted"],[6,4,1,"","disruption_process"],[6,4,1,"","echelon_holding_cost"],[6,3,1,"","equivalent_lead_time"],[6,3,1,"","forward_echelon_lead_time"],[6,2,1,"","from_dict"],[6,2,1,"","get_one_predecessor"],[6,2,1,"","get_one_successor"],[6,3,1,"","holding_cost"],[6,4,1,"","in_transit_holding_cost"],[6,4,1,"","initial_inventory_level"],[6,4,1,"","initial_orders"],[6,2,1,"","initialize"],[6,4,1,"","inventory_policy"],[6,4,1,"","lead_time"],[6,4,1,"","local_holding_cost"],[6,4,1,"","local_holding_cost_function"],[6,3,1,"","neighbor_indices"],[6,3,1,"","neighbors"],[6,4,1,"","network"],[6,4,1,"","order_lead_time"],[6,2,1,"","predecessor_indices"],[6,2,1,"","predecessors"],[6,4,1,"","problem_specific_data"],[6,4,1,"","purchase_cost"],[6,2,1,"","reindex_all_state_variables"],[6,2,1,"","remove_predecessor"],[6,2,1,"","remove_successor"],[6,4,1,"","revenue"],[6,4,1,"","shipment_lead_time"],[6,4,1,"","state_vars"],[6,3,1,"","state_vars_current"],[6,4,1,"","stockout_cost"],[6,4,1,"","stockout_cost_function"],[6,2,1,"","successor_indices"],[6,2,1,"","successors"],[6,4,1,"","supply_type"],[6,2,1,"","to_dict"]],"stockpyl.supply_uncertainty":[[24,5,1,"","eoq_with_additive_yield_uncertainty"],[24,5,1,"","eoq_with_disruptions"],[24,5,1,"","eoq_with_disruptions_cost"],[24,5,1,"","eoq_with_multiplicative_yield_uncertainty"],[24,5,1,"","newsvendor_with_additive_yield_uncertainty"],[24,5,1,"","newsvendor_with_disruptions"]],"stockpyl.wagner_whitin":[[25,5,1,"","wagner_whitin"]],stockpyl:[[2,0,0,"-","demand_source"],[3,0,0,"-","disruption_process"],[18,0,0,"-","eoq"],[19,0,0,"-","finite_horizon"],[7,0,0,"-","gsm_helpers"],[8,0,0,"-","gsm_serial"],[9,0,0,"-","gsm_tree"],[13,0,0,"-","helpers"],[14,0,0,"-","instances"],[15,0,0,"-","loss_functions"],[11,0,0,"-","meio_general"],[20,0,0,"-","newsvendor"],[16,0,0,"-","optimization"],[4,0,0,"-","policy"],[21,0,0,"-","rq"],[26,0,0,"-","sim"],[27,0,0,"-","sim_io"],[23,0,0,"-","ss"],[12,0,0,"-","ssm_serial"],[5,0,0,"-","supply_chain_network"],[6,0,0,"-","supply_chain_node"],[24,0,0,"-","supply_uncertainty"],[25,0,0,"-","wagner_whitin"]]},objnames:{"0":["py","module","Python module"],"1":["py","class","Python class"],"2":["py","method","Python method"],"3":["py","property","Python property"],"4":["py","attribute","Python attribute"],"5":["py","function","Python function"]},objtypes:{"0":"py:module","1":"py:class","2":"py:method","3":"py:property","4":"py:attribute","5":"py:function"},terms:{"0":[3,5,6,7,8,9,11,12,13,14,15,18,19,20,21,23,24,25,26,29,32,33,34,35],"00":[7,33],"0000":34,"000000001":24,"0000005374905":16,"0001":11,"001353352589297054":15,"0013533528323661267":15,"002394806823354":[20,33],"007":13,"007824431159359786":15,"008646647165633875":15,"01":[11,14],"010958904109589041":14,"012332294949644":[12,32],"013533528103402742":15,"013533528323661264":15,"01880706693657111":15,"0198":[24,35],"02":[14,19,34],"027434723327854":[12,32],"03":14,"031731173050459915":15,"034111561471642":[23,33],"04":[14,24,34,35],"0430622009569378":18,"04552796208651397":15,"0467800264368":[18,21,29,33],"0479999999999743":15,"048":15,"04837003438256":33,"0485760000000004":15,"0485760000000006":15,"05":[12,14,16],"052":13,"05773502691896258":14,"06":[14,21,24,35],"063":23,"0631099655841":32,"0689302470355":24,"07114627035178":33,"07116250928294":21,"08":[5,6,14],"08333333333333333":14,"09":13,"0936537653899085":15,"09365376538990855":15,"09891883213067":20,"0s":13,"0th":[13,19,25],"1":[3,4,5,6,7,8,9,11,12,13,14,15,16,18,19,20,21,23,24,25,26,27,29,32,33,34,35],"10":[2,7,11,13,14,15,23,29,32,33,34],"100":[11,12,14,19,21,29,32,33,34],"1000":[11,12,14,29,34],"10000":34,"1000000":[14,24,35],"10108087745232":15,"102":15,"1020":33,"103":[8,21],"103164454170876":[18,33],"104":34,"10522318598177341":15,"1067":[19,20],"107":[21,24,33,34],"108":24,"1083":[19,20],"11":[12,14,32,34],"110":[14,19,29,33],"1100":14,"111":[19,29,33],"113":8,"11353352830366131":15,"115":14,"116":23,"12":[12,14,15,20,21,32,33,34],"120":[14,18,25,29,33],"1200":[14,24],"121":24,"122195054841043":15,"125":14,"12500":14,"126":[19,21,29,33],"128":[21,33],"129":[21,24],"12914":[24,35],"13":[12,14,15,16,34],"1300":[14,18,21,24,29,33,35],"13086":[24,35],"132":24,"13263":24,"133":[19,29,33],"13426":24,"135":14,"1380":[25,29,33],"14":[14,15,19,20,24,34,35],"140":14,"1400":14,"14085904245475275":14,"142":14,"1421":34,"1426":[12,34],"1432417118889":[24,35],"1443":[12,34],"1443484":35,"15":[11,14,15,24,34,35],"150":[14,21,25,29,33],"1500":14,"15000":[14,24,35],"1500000":35,"15000000":14,"15328525645054":29,"155":24,"1558":19,"156131552870387":20,"15945901616041":12,"16":[12,14,20,21,34],"160":[14,18,33],"16169098594":[24,35],"167124183311998e":12,"16794575837224":29,"1683073521514889":15,"1689463285519":29,"17":[14,15,20,21,34],"170":14,"1700":18,"171":14,"173":[24,35],"1736":14,"174":24,"175":14,"176":[7,9],"1765":[14,20],"177":[7,9],"1780":14,"18":[14,15,20,21,23,24,29,33,34],"180":14,"1800":14,"182":13,"182500":14,"183":23,"1833333":[24,35],"183979125298336":18,"18500":[14,24,35],"19":[14,15,34],"190":[14,21,33],"191":19,"19102133030678":33,"1912":14,"192":14,"192z":23,"194304":33,"194304000000002":15,"19461695647407":[23,33],"1953":[21,33],"1960":[12,29,32],"1963":[21,33],"1966":[19,20],"1976":[14,18,33],"198":33,"1984":[23,33],"1989":[6,14],"1991":[8,23,24,32,33,35],"1992":[21,33],"1994":[12,24,29,32,34,35],"1996":[12,32],"1998":14,"1e":[5,6,13,16,21],"2":[3,5,7,8,9,11,12,13,14,15,16,18,19,20,21,23,24,25,26,29,32,33,34,35],"20":[14,15,18,19,21,29,32,33,34],"200":14,"2000":[6,7,9,14,15,19,20,24,29,32,34,35],"20000":14,"200000":35,"2003":[7,9,12,14,34],"2014":[24,35],"2017":14,"2019":[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],"20243187688158":33,"2080":14,"20800":14,"21":[14,21,34],"210":[25,29,33],"213":[21,33],"21428571428571427":14,"21449789525488":32,"21486028212500707":15,"22":[12,14,15,24,32,34],"220":14,"2222222222222222":15,"223748044859164":33,"225":[14,18,21,24,29,33,35],"2250":14,"226":29,"227":29,"23":[15,24,34],"230246":[24,35],"24":[8,14,20,24,34],"25":[3,14,24,29,34,35],"250000":35,"25317":35,"254477":[24,35],"2591674214654":34,"259837154163556":34,"26":34,"26036848597217":19,"26119040852187103":34,"264":34,"27":[7,14,15,18,20,21,24,34],"270":[14,33],"27039814681794644":34,"27335621540425":34,"2737":24,"275":14,"277916867529369":[7,9,29,32],"28":[14,15,21,24,34],"280288386513346":15,"2831":34,"28364973888106326":15,"28687665608078":33,"29":[14,18,20,21],"29017010980579":[23,33],"29236193":13,"295":20,"29720380302459":34,"2_l":23,"2d":24,"2e":24,"2h":24,"2k":[18,21],"2kd":24,"2l":23,"2nd":[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],"2p":24,"2r":15,"3":[3,7,8,9,12,13,14,15,18,19,20,21,24,25,29,32,33,34,35],"30":[14,15,20,23,33,34],"300":[14,18,21,33],"3000":14,"300000":24,"3023987673176":33,"304":[18,21,29,33],"308":[21,33],"309493362512628":[18,33],"31":[7,14,15,18,34],"310":18,"3132203403":35,"318":[21,33],"31910867996449":34,"32":[12,14,15,18,34],"326192933063429":15,"326459980156931":15,"32645998015693145":15,"327":13,"328":[21,33],"33":[14,15,18,20,33,34],"3333333333333333":15,"3333333335":[24,35],"33491040676202":32,"3369965715624":[21,33],"34":[15,29,34],"34000":14,"342":13,"344790717086":24,"3453768":13,"345527962086514":15,"35":[7,14,20],"35613154776623":20,"36":[14,15,34],"36000":14,"3600000000000003":14,"365":14,"36782387894158":19,"37":[12,14,15,20,32,34],"37046881882":[24,35],"38":[15,21,24,34],"38000":14,"39":[23,25],"394684658734164":20,"4":[7,9,11,12,13,14,15,18,19,20,21,23,24,25,29,32,33,34],"40":[12,14,15,20,21,23,29,32,33,34],"400":14,"4000":14,"41":[7,15,20,24,34],"41052550594829":[18,29,33],"4142135623730951":7,"42":[15,29,32,34],"42277610622506":33,"4272799263067":21,"428":14,"43":[12,14,34],"44":29,"4400":14,"44254351324322":20,"445":14,"447304632028364":15,"4491421980451":[21,33],"4494897427831783":7,"4497316":35,"45":[7,14,34],"45114022285196":21,"457":15,"46":[2,32,34],"46000":14,"46130342316":[24,35],"46826882694954":15,"47":[12,14,32,34],"475":12,"475292852532866":34,"48":[14,21,32,34],"49":[12,14,20,34],"490":12,"490880975286938":[12,32],"494":23,"5":[4,7,9,11,12,13,14,15,16,18,19,20,21,23,24,25,29,32,33,34,35],"50":[2,13,14,18,19,20,23,29,33,34],"500":[14,25,29,33],"500000":[14,24,35],"506":23,"51":34,"5135882931757045":32,"5144388073261155":[12,32],"5176095282584723":15,"5176095282584724":15,"519":33,"52":4,"53":[14,33],"55":34,"5544912009711833":15,"558":14,"56":[14,20,29,33],"57":[14,34],"570106945770941":20,"5701069457709416":20,"5710":24,"5737801203754":[21,33],"58":20,"580":14,"59":14,"5901810768729":[21,33],"590296024616343":20,"5e6":24,"6":[7,8,9,11,12,13,14,15,19,20,21,23,24,29,32,33,34],"60":[4,14,20],"600":[14,18,33],"60395592743389":[20,29,33],"61530461":13,"618":[12,23,34],"62":[14,20,32,34],"6200":14,"622":23,"6249999":[24,35],"625":12,"6250000":24,"626":18,"6266448071368":20,"63":2,"634032391786285":[12,32],"635971381157268":15,"63781442427097":[21,33],"638":[12,34],"64":14,"640":[25,29,33],"65":34,"650":14,"651659697082211":15,"654":23,"656":14,"66":[18,19],"66022942788436":19,"661338147750939e":12,"665":23,"668653127136345":[12,32],"67":[15,34],"68":[7,9,18,29,33],"680099140842174":[12,32],"682411764618777":20,"69":14,"6946467384012":19,"69602421013684":29,"69842911":13,"7":[4,13,14,15,19,20,21,23,29,32,33,34],"70":[14,20,23,25,29,33,34],"700":24,"700237234889784":[12,32],"71":[20,23,34],"7197116134866537":15,"7257":14,"726131552870388":20,"73":14,"730":14,"74":[23,33,34],"74000":35,"7499999999999999":3,"75":[23,24,35],"75000":[14,24,35],"75000000":14,"75370030596123":2,"758375187638261":32,"76":14,"760000000000001":14,"762":32,"765139717874998":15,"7683073521514903":15,"7692307692307693":34,"77":23,"770562822512":24,"772":[24,35],"773":[24,35],"7777777777777777":15,"78":[21,33],"78222812913":[24,35],"78528000921442":34,"78711738886236":24,"789138050714946":34,"79":[14,34],"797235211809178":[20,33],"8":[7,9,13,14,15,18,19,20,21,23,24,29,30,32,33,34,35],"80":[13,14,23,25,29,33,34],"800":14,"8000":[24,34],"8050847457627118":34,"805695999999998":15,"80614234644133":24,"808":21,"8084945889684":18,"8110739983106":[24,35],"81255515896464":18,"813":21,"82":34,"8284271247461903":[8,32],"83":[7,9],"83200":14,"8333":[24,35],"8333333333333334":[14,34],"837":[18,33],"84":14,"840":[14,18,33],"848340302917789":15,"84861989932769":20,"85":[14,34],"850319828088736":20,"8544026261366":[18,33],"86000":14,"8670634479628":[21,33],"8695652173913043":34,"87":[14,19,21,33,34],"877804945158942":15,"880":14,"8823529411764706":34,"887604785075":35,"888960377059731e":16,"892036436905893":32,"8989191225476816":15,"9":[7,14,15,18,21,24,25,33,34],"90":[14,25,29,33],"900":14,"9000":[14,24,35],"90365729191992":32,"90625":34,"91":24,"9100":14,"9152542372881356":34,"9166666666666666":34,"9183673469387755":34,"92":[14,33],"920":14,"9200000000000004":14,"9210526315789473":34,"92136355097325":18,"92358063314975":[21,33],"9264705882352942":34,"9285714285714286":34,"93":14,"9310527835":35,"93248526934437":29,"9342105263157895":34,"93hall_distribut":13,"94":14,"940":[25,29,33],"9411764705882353":34,"947368421053":24,"9484536082474226":34,"95":[14,21,34],"95000257319708":[24,35],"9519230769230769":34,"9555555555555556":34,"957229385175":[24,35],"97044213580244":[21,33],"973":23,"98":[14,20],"9803921568627451":34,"99":[13,14,34],"9906261152138731":34,"994095842987605":32,"995771265226075":32,"997499999":[24,35],"997605188935892":20,"9976051931766445":[20,29,33],"99995914365099":32,"999999999999996":20,"boolean":13,"case":[2,4,5,6,8,9,12,13,14,19,25,27,34],"class":[2,3,4,5,6,15,29,31,34],"default":[2,3,4,5,6,12,13,19,20,26,27,34],"do":[2,3,5,6,9,11,12,13,14,26,34],"final":[19,34],"float":[2,3,4,5,6,7,8,9,11,12,13,15,16,18,19,20,21,23,24,25,26],"function":[2,4,5,6,9,11,12,13,14,15,16,19,20,21,23,24,26,27,29,32,33,35],"import":[7,8,9,14,15,20,24,29,32,33,34,35],"int":[2,3,4,5,6,7,8,9,11,12,13,15,18,19,20,23,25,26,27],"new":[2,3,4,5,6,9,13,14,19,20],"return":[2,3,4,5,6,7,8,9,11,12,13,14,15,16,18,19,20,21,23,24,25,26,33,34,35],"true":[2,3,5,6,9,11,12,13,14,16,20,23,24,26,27,33,34,35],"try":19,"var":[15,24],"while":[6,32],A:[2,3,4,5,6,7,8,11,12,13,14,19,20,21,23,24,27,32,34],And:[29,32,34],As:34,At:34,By:[5,12],For:[2,5,6,7,8,9,10,11,12,13,15,18,19,20,21,22,23,24,25,26,27,28,32,33,34],IS:[27,34],If:[2,3,4,5,6,8,9,11,12,13,14,15,18,19,20,21,23,24,25,26,27,33,34,35],In:[2,5,6,13,19,25,27,32,34,35],Is:6,It:[6,20,29,34],Its:34,No:26,Not:13,Of:34,On:[6,19,20,21],Or:[15,29,32,33],That:[5,6,12,13],The:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,31,34],Then:34,There:32,These:[11,12,14,32,33,34],To:[6,26,30,32,34],_0:12,_1:12,_5:19,_:[12,19,29,33,34],_d:19,_j:[6,12],_pdf:15,_pmf:15,_predecessor:[5,6],_successor:[5,6],_t:[19,20],abbrevi:[14,27],about:[5,23,34],abov:[5,20,27,29,34,35],abs_tol:13,absolut:[13,21],access:32,accord:[3,34],accordingli:3,account:[12,15,19,34],accumul:[3,34],accur:[11,24,32],accuraci:32,across:[19,26],act:19,action:19,acycl:29,ad:[5,19,34],adapt:[13,16],add:[5,6,32],add_edg:5,add_edges_from_list:[5,14],add_nod:[5,14,32],add_predecessor:[5,6,14],add_successor:[5,6,32],addit:[14,24,35],adjac:[6,9],adjust:[4,14,15,19,34],advanc:[29,31],after:[4,19,26,34],again:[19,34],against:19,aggreg:6,ago:34,algorithm:[6,7,8,9,11,12,16,19,21,23,25,29,32,33,34],alia:6,all:[5,6,7,8,9,11,12,13,14,19,26,27,32,34],allow:[2,4,5,32,34],alpha:[3,20,21,24,26,34,35],alreadi:[5,9,14,34],also:[2,5,6,15,29,32,33],altern:[27,32,34,35],although:32,alwai:[6,12,34,35],ambigu:5,among:[5,34],an:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,18,19,20,21,22,23,24,25,26,27,28,29,32,33,34,35],analog:19,analysi:21,ancestor:6,ani:[2,3,4,5,6,7,8,11,12,13,14,19,20,25,26,32,34],anyth:[5,9,14],api:[29,34],appear:[5,12,13,34],appl:[19,20],appli:5,applic:4,approach:[11,32],appropri:[2,3,4],approxim:[11,12,21,23,24,32,33,34,35],ar:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],arbitrari:[11,15,32,33,34,35],argmin:[12,13],argument:[2,3,4,5,6,11,13,15,24,32],aris:34,around:[2,19],arrai:[12,13,14,19,20,25,29,33],arreola:[24,35],arriv:[6,27,34],articl:29,ascend:13,asid:26,assembl:[5,6,14],assembly_3_stag:14,assign:[5,12,29],assum:[3,5,6,8,11,12,13,15,19,20,21,23,25,34,35],assumpt:29,atan:14,attain:[13,18,20,24],attribut:[2,3,4,5,6,9,12,13,32,34],attribute_dict:13,attributeerror:5,atyp:34,automat:[11,12],avail:[11,30,32],averag:[26,29,34],avoid:[5,19],awar:34,b:[5,13,14,15,16,20],back:21,backord:[6,18,21,26,27,33,34],backorders_by_successor:6,balanc:[4,14],bar:[11,15,19,20,24,26],base:[4,5,7,11,12,14,20,24,26,29,32,33,34,35],base_cycle_tim:18,base_stock_level:[4,5,7,11,14,20,24,29,32,33,34],basic:[12,27,29,31,33],beb:[4,14],becaus:[6,19,34],been:[2,3,4,5,6,7,9,15,27,34],befor:[3,4,6,9,13,34],began:34,begin:[2,3,12,19,34],being:[3,6,16,34],below:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],berk:[24,35],berkin:[24,35],bernoulli:15,best:[11,32],best_:[11,32],best_cost:[11,32],beta:[3,15,24,35],between:[6,18,34],beyond:[2,3],binomi:15,bisect:21,bo:[27,34],bool:[2,3,5,6,9,11,12,13,14,16,20,23,24,26,27],both:[13,15,20,21,29,32,33,34,35],bound:[8,12,13,15,16,19,32,34],bring:19,broader:32,brute:[11,32],bs:[4,5,14,29,32,34],buffer:19,bui:20,build:[5,13,14,26,29,32,34],build_node_data_dict:13,build_test_pack:14,built:[14,15,32,34],bullwhip:34,bump:19,c:[7,9,12,13,14,15,19,20,23,25,29,33],c_:20,c_star:[12,29,32],c_t:[20,25],c_ty:20,calcul:[2,3,4,6,7,12,13,15,18,19,20,21,23,24,26,33,34],call:[4,5,6,9,12,13,26,33],camera:14,can:[2,3,5,6,11,12,14,29,32,33,34,35],candid:32,cannot:[3,6,14,15,27,34],categori:34,caveat:6,cd:2,cdf:[2,13,15,20],cdot:[12,13,15,19,20,21,23,24],certain:[32,34],chain:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],chang:[2,3,5,6,12,13],change_dict_kei:13,check:[2,3,4,5,6,13,26],check_iterable_s:13,chen:[12,29,32,34],choos:15,ci:34,circuit_board:14,clark:[12,29,32],classic:29,classmethod:[2,3,4,5,6],clear:34,cliff:21,close:[26,34],closest:13,coars:32,code:[7,8,12,13,14,15,16,18,19,20,21,23,24,25,26,32,33,34,35],coeffici:[6,34],column:[19,27,34],columns_to_print:[27,34],com:13,combin:[11,34],come:13,commit:[7,8,9,29,32],common:34,commonli:34,compar:[5,6,34],comparison:13,complementari:[15,20,24],complet:[6,34],complex:[11,32],compon:11,comput:[21,23],computation:19,condit:[19,20,25],confid:[26,34],connect:5,consecut:[6,9,18],conserv:19,consid:[6,12,16,19,32,34],consist:[5,13,14,24,26,32,34],consistency_check:26,consol:[27,34],constant:8,construct:[5,34],contain:[2,3,4,5,6,7,8,9,11,12,13,14,15,16,18,19,20,21,23,24,25,26,27,29,32,33,34,35],continu:[2,13,15,20,21,33],continuous_loss:[15,24],continuous_second_loss:15,continuousreview:24,control:[32,34],converg:21,convert:[2,3,4,5,6,9,29,32],convex:32,convolut:13,convolv:13,convolve_mani:13,coordin:[11,32],copi:[2,3,4,5,6,9,13],correctli:9,correpond:12,correspond:[5,8,12,13,27,33,34],cost:[6,7,8,9,11,12,14,18,19,20,21,23,24,25,26,27,29,32,33,35],cost_matrix:19,costs_to_go:25,could:19,count:[6,13],cours:34,creat:[2,3,4,5,6,13,14,32],create_if_non:14,creation:34,cst:[7,8,9,29,32],cst_to_base_stock_level:7,csv:[27,34],csv_filenam:27,cumul:[2,6,27,34],current:[2,3,4,5,6,9,20,26,27,34,35],custom:[2,6,8,13,15,23,27],cycl:[5,26,33],d1:13,d2:13,d:[2,12,13,19,20,23,24,25,29,33,34,35],d_i:25,d_j:12,d_k:12,d_num:[12,32],d_rang:19,d_spread:19,d_t:20,d_val:[20,33],data:[0,5,6,8,9,12,13,14,26,27,29,31,32],data_dict:13,dataset:14,date:21,debug:27,decis:[6,26],deck:32,declar:[6,15],decreas:6,deep:[2,3,6],deep_equal_to:[5,6],deepli:[5,6],def:[15,34],default_valu:13,defin:[15,19,20,32],deliv:[6,35],delta:19,demand:[2,4,5,6,7,8,9,12,14,15,18,19,20,21,23,24,25,26,27,29,31,32,33,35],demand_bound_const:[8,9,14,32],demand_cumul:6,demand_distrib:[20,33],demand_distribut:2,demand_hi:23,demand_list:[2,34],demand_mean:[8,12,13,14,19,20,21,23,29,32,33],demand_met_from_stock:6,demand_met_from_stock_cumul:6,demand_pdf:[20,23],demand_pmf:[14,20,23,33],demand_r:[14,18,24,29,33,35],demand_sd:[14,19,20,21,23,29,33],demand_sourc:[0,1,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],demand_standard_devi:[8,12,32],demand_typ:[5,14,29,32,34],demandsourc:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],denot:[19,20,34],depend:[13,19,24],deriv:6,derived_demand_mean:6,derived_demand_standard_devi:6,descend:6,descent:[11,32],describ:[6,8,9,12,23],descript:[12,14,29],descrtipt:14,desir:[13,15,19],detail:[19,34],determin:[5,6,7,9,11,12,13,14,21,23,34],determinist:[2,14,24,34,35],deviat:[2,6,8,12,15,19,20,21,23,24,29,35],df:24,dh:24,dict:[2,3,4,5,6,7,8,9,11,12,13,14,15,20,32,33],dict_match:13,dict_to_chang:13,dictionari:[7,11,13,14,33],differ:[6,15,34,35],digraph:5,dimension:13,direct:[5,6,26,32],directli:[6,26,32,34],discount:[19,20],discount_factor:[14,19,20],discret:[2,11,12,13,14,15,19,20,23,32,33],discrete_loss:[15,24],discrete_second_loss:15,discretization_num:11,discretization_step:11,discuss:[12,19,34],displai:[11,26,29,31],disr:[27,34],disrupt:[3,6,14,24,26,27,29,31],disruption_prob:[3,14,24,34],disruption_process:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],disruption_r:[14,24,35],disruption_state_list:3,disruption_typ:[3,34],disruptionprocess:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],distrbut:20,distrib:15,distribut:[2,5,8,12,13,14,15,19,20,21,23,24,29,32,33,34,35],divid:6,dmf:[27,34],doc:15,docstr:[12,26,34],document:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,30,32,33,34,35],doe:[5,6,9,13,14,19,32,34],don:19,done:19,doubl:19,down:[3,12,13,24,26],download:34,downstream:[5,6,12,34],dp:[3,7,8,9,19,25,32,33],ds:2,due:[6,15,21,27,34],dump:26,dure:[3,6,34],dy:[15,21],dynam:[7,8,9,19,25,29,32,33],e2:13,e:[2,3,4,5,6,12,13,14,15,19,20,24,26,32,33,34],each:[2,3,5,6,7,8,9,11,12,13,14,16,19,21,25,26,27,32,33,34],earlier:34,earn:6,eb:[4,34],echelon:[0,4,5,6,7,8,9,11,12,14,18,19,20,21,23,24,25,26,27,29,31,34,35],echelon_:12,echelon_holding_cost:[6,12,14,29,32],echelon_inventory_level:6,echelon_inventory_posit:6,echelon_inventory_position_adjust:4,echelon_on_hand_inventori:6,echelon_to_local_base_stock_level:[5,29,34],econom:[8,18,24,29,33,35],economic_order_quant:[18,29,33],economic_order_quantity_with_backord:18,economic_production_quant:18,edg:[5,14,32,34],edge_list:5,edit:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],ef:26,effect:[3,34],effici:21,ehrhardt:[23,33],eil:[21,33],eipa:4,either:[5,8,11,12,15,19,20,24,32,33,35],element:[5,13,19,25],els:[14,15],empti:5,en:[6,13,16],encapsul:4,end:[3,6,11,12,13,16,19,27,34],englewood:21,ensur:13,ensure_dict_for_nod:13,ensure_list_for_nod:13,ensure_list_for_time_period:13,entir:[6,19,25],entri:[8,13],enumer:[11,32],eoq:[0,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,19,20,21,22,23,24,25,26,27,28,29,30,31,32,34],eoq_with_additive_yield_uncertainti:[24,35],eoq_with_disrupt:[24,35],eoq_with_disruptions_cost:24,eoq_with_multiplicative_yield_uncertainti:[24,35],eoqb:[14,18,19,21,33],eoqd:[14,24,35],epq:[14,18,33],epsilon:21,eq:23,equal:[5,6,8,11,13,14,16,19,20,33,34],equat:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],equiv:34,equival:[6,26,27,34],equivalent_lead_tim:6,equivalentlli:34,erratum:[7,9],error:[13,26,34],estim:19,etc:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],evalu:[11,12,16,18,20,23,24,32,33],even:[4,5,6,9,14,27,32],event:[29,31],ever:6,everi:[2,9,11,13,18,19,25,34],evid:34,exact:[21,23,32,33,34],exactli:[6,9,12,32,35],exampl:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,30,31,32,33,35],example_3_1:14,example_3_8:14,example_3_9:14,example_4_1:14,example_4_1_network:14,example_4_2:14,example_4_3:14,example_4_4:14,example_4_7:14,example_4_8:14,example_5_1:14,example_5_8:14,example_6_1:[14,32,34],example_6_1_network:32,example_6_3:[8,14,32],example_6_3_network:32,example_6_5:[7,9,14,29,32],example_6_5_network:32,example_9_1:14,example_9_3:14,example_9_4:14,example_9_5:14,example_9_6:14,except:[2,3,4,5,6,12,15,26],exclud:6,execut:[13,19,26,32],exist:[13,14],exogen:34,exp:[15,20,33],expect:[7,8,9,11,12,19,20,21,23,24,29,32,33,34,35],expected_cost:[12,32],expected_holding_cost:12,expens:19,experi:32,explicit:[3,14,20,33],explicitli:[3,34],explor:21,expon:15,exponenti:[15,24],exponential_loss:15,exponential_second_loss:15,express:9,ext:[27,34],extens:29,extern:[2,4,6,7,8,27],external_inbound_cst:[8,9,14,32],external_outbound_cst:[8,9,14,32],f:[2,12,13,15,16,19,20,21,24,29,33,34],f_star:16,f_y:24,face:34,factor:[19,20],fail:[11,26],failur:15,fairer:32,fall:19,fals:[3,5,6,9,11,12,13,14,16,20,23,24,27,34],fast:13,faster:[13,19,32],featur:[29,31],federgruen:[21,23,33],fft:13,field:9,figur:14,figure_6_12:14,figure_6_14:14,file:[14,26,27,34],filenam:27,filepath:[14,27],fill:[5,6,9,13,26,27,34],fill_rat:6,find:[5,20,21,23,32],find_nearest:13,finish:34,finit:[14,19,29,31],finite_horizon:[0,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],finite_horizon_dp:[19,29,33],fire:14,first:[2,3,5,6,12,13,21,26,32,34],fix:[4,18,19,21,23,24,25,29,33,34],fixed_cost:[14,18,19,21,23,24,25,29,33],flexibl:34,follow:[3,5,6,8,12,19,24,27,32,33,34,35],forc:[11,32],force_relabel:9,form:[13,14,32,33],format:[27,34],former:[19,25],forthcom:14,forward:6,forward_echelon_lead_tim:6,fosct:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],found:[5,11,14],foundat:[15,19,20,34],four:34,fourier:13,fourth:19,fq:4,fr:[27,34],frac12:15,frac:[12,15,18,20,21,23,24],fraction:18,from:[2,3,4,5,6,7,8,9,13,14,15,16,19,20,24,25,26,27,29,32,33,35],from_dict:[2,3,4,5,6],from_index:5,frozen:[15,24],fundament:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],further:19,futur:24,fx:16,g:[2,3,4,7,12,14,18,19,20,21,23,24,25,34],g_:12,g_i:[19,20],g_j:12,g_t:[19,20],gamma:[15,19,20],gamma_loss:15,gamma_second_loss:15,gamma_tc_:20,gamma_tk_:19,gather:12,ge:[19,20,24],gener:[2,3,5,12,13,15,19,20,24,26,29,31,34],generate_demand:2,geom:[15,33],geometr:15,geometric_loss:15,geometric_second_loss:15,get:[2,3,6],get_node_from_index:[5,14,32,34],get_one_predecessor:6,get_one_successor:6,get_order_quant:4,give:[15,19,32,33],given:[2,3,4,5,6,7,11,12,13,15,16,18,19,20,21,23,24,25,27,33,34],glaze:14,global:32,go:[25,29,33],golden:[11,16,24],golden_section_search:16,good:[32,34],govern:[3,24],graph:7,grave:[7,9,29,32],greater:[9,19],group:[11,27,34],gsm:[7,8,9,14,29,31],gsm_helper:[0,2,3,4,5,6,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],gsm_serial:[0,2,3,4,5,6,7,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],gsm_to_ssm:9,gsm_tree:[0,2,3,4,5,6,7,8,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],guarante:[7,8,29,32],h:[6,8,12,18,19,20,21,23,24,25,29,33,34,35],h_:18,h_i:12,h_jx:12,h_n:18,h_nm_n:18,h_t:[19,20],h_termin:[29,33],ha:[2,4,5,6,9,12,13,14,15,16,27,29,34],hadlei:[21,33],hall:[13,21],hand:[6,34],handl:13,has_directed_cycl:5,hat:[12,18],have:[2,3,4,5,6,7,8,9,11,13,14,19,27,34,35],hc:[27,34],header:34,held:[6,27,34],helper:[0,2,3,4,5,6,7,8,9,10,11,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],here:[12,14,15,32],heurist:[11,12,18,23,32,33,34,35],hi:[2,13,14,23],hi_heur:34,hi_opt:34,high:[2,11,19],highest:9,hill:[15,19,20,34],histori:27,hn:24,hold:[6,8,9,12,18,19,20,21,23,24,25,27,29,33],holding_cost:[6,12,14,18,19,20,21,23,24,25,29,33,34],holding_cost_incur:6,horizon:[14,19,25,29,31],how:[5,32,34],howev:34,hp:[18,21],hq:[18,21,24],html:15,http:[13,15,16],hyperlink:34,i:[3,4,5,6,12,13,14,15,19,25,27,32,33,34],idea:12,ident:13,idi:[27,34],ifi:13,ignor:[5,6,8,9,11,12,13,14,15,19,20,23,24,25,27],ignore_state_var:14,il:[6,19,27,34],il_t:19,imager_assembl:14,imager_bas:14,immedi:[4,34],implement:[7,8,9,12,16,19,29,32,33],implic:34,improv:11,in_transit:6,in_transit_from:6,in_transit_holding_cost:6,in_transit_holding_cost_incur:6,in_transit_to:6,inaccur:32,inbound:[6,7,8,27,34],inbound_cst:7,inbound_disrupted_item:6,inbound_disrupted_items_aggreg:6,inbound_ord:6,inbound_order_pipelin:6,inbound_ship:6,inbound_shipment_pipelin:6,includ:[4,5,6,9,13,18,21,27,29,33,34],include_extern:6,increas:34,increment:26,incur:[6,27,34],ind:13,independ:[2,9],inderfurth:[8,32],index:[4,5,6,7,8,9,11,12,13,14,19,25,27,29,32,34],indic:[4,5,6,7,8,9,11,12,13,19,26,27,33],individu:[5,8,11,12,18,26,32],individual_fixed_cost:[14,18,33],inform:[32,34],infti:[12,15,24],initi:[2,3,4,5,6,11,19,25,26],initial_inventory_level:[6,14,19,26],initial_ord:[6,14],initial_ship:14,initial_solut:11,input:[9,32,34],instal:29,instanc:[0,2,3,4,5,6,7,8,9,10,11,12,13,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],instance_data:14,instance_descript:14,instance_nam:[14,27],instead:[4,6,12,14,15,32,34],insuffici:34,int_0:15,int_:15,int_r:21,int_x:15,integ:[2,9,12,13,15,19,20,21,23],integr:[13,15],interchang:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],intermedi:6,intern:[6,8,9,24],interpret:34,interv:[11,12,16,18,24,26,34],introduc:23,invalid:19,inventori:[0,4,5,6,7,8,9,11,12,14,15,18,19,20,21,23,24,25,26,27,29,31,35],inventory_level:6,inventory_polici:[5,6,14,29,34],inventory_posit:[4,6],io:[27,34],iopl:[27,34],ip:4,irwin:[13,15,19,20,34],irwin_hall_cdf:13,is_continuous_distribut:13,is_correctly_label:9,is_discrete_distribut:13,is_integ:13,is_iter:13,is_list:13,ispl:[27,34],issu:[14,19,26,32],item:[3,6,12,13,18,19,20,21,23,24,25,27,34],iter:[7,11,13,16,21],iterable_list:13,ithc:[27,34],its:[2,3,5,6,8,11,13,18,20,26,32,33,34],itself:[3,5,6,24],j:[12,19,20,34],joint:[18,33],joint_replenishment_problem_silver_heurist:[18,33],jointli:32,journal:[8,24],jr:[19,20],jrp:[14,18,33],json:[14,27],jsonpickl:14,just:[2,3,12,32,34],k:[5,8,12,13,18,19,21,23,24,25,29,33,35],k_:18,k_n:18,k_t:19,kd:24,keep:3,kei:[5,6,7,8,9,11,12,13,14,15,20],kept:34,keyerror:13,keyword:[2,3,4,5],know:[13,34],known:21,kwarg:[2,3,4,5,6],l2:15,l2_bar:15,l:[2,6,8,12,14,15,20,21,23,33,34],l_bar:15,l_i:6,label:[5,7,9,23,27,34],lambda:[16,18,21,24,32,34],lambda_:18,lambda_n:18,larg:34,larger:[12,13,19],larger_adjacent_nod:9,larger_adjacent_node_is_downstream:9,largest:[5,13,19],last:[5,13],later:[14,30,34],latter:[5,19,25,27],ldot:[8,12,13,19],le:[19,20,25],lead:[2,6,7,9,12,14,19,20,21,23,29,31],lead_tim:[2,6,12,13,14,20,21,32,33,34],lead_time_demand_distribut:2,least:13,left:[12,15,20,21,23,24,25],left_half:20,lemma:24,len:13,length:[2,3,8,13,14,19,23,24,25],less:[6,15,16,19,20],let:13,level:[4,5,6,7,9,11,12,19,20,21,23,24,26,27,29,32,33,34,35],like:[4,6,19,29,32],lim_:12,limit:[12,23],line:11,line_search_tol:11,linear:[12,34],list:[2,3,5,6,7,8,11,12,13,14,18,19,23,25,26,27,32,34],literatur:[11,32,34],ln:15,lo:[2,13,14],lo_heur:34,lo_opt:34,load:[14,29,32,34],load_inst:[7,8,9,14,29,32,34],local:[5,6,7,8,9,16,29,32],local_bsl:7,local_holding_cost:[6,8,13,14,29,32,34],local_holding_cost_funct:[6,34],local_to_echelon_base_stock_level:[5,32],logist:24,lognorm:[14,15,20,33],lognormal_loss:15,longer:[14,29],loss:[15,20,21,24,33],loss_funct:[0,2,3,4,5,6,7,8,9,10,11,12,13,14,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],low:[2,11,19],lower:[12,13,15,16,19,23,32,34],ltd_lower_tail_prob:12,ltd_upper_tail_prob:12,m:[3,21,23,33,34],m_:18,m_i:6,m_n:18,made:[14,34],mai:[5,8,9,11,12,13,19,25,32,33,34],main:27,make:[4,6,13,32,34],manag:[7,9,12,15,19,20,21,23,34],mani:[6,34],manual:[14,34],manufactur:[7,9],markov:[3,34,35],markovian:3,match:[5,13,34],materi:[6,27,34],math:[14,15,19,20,24,33,34,35],mathbb:19,mathrm:12,mathscr:15,matric:19,matrix:19,matter:5,max:[6,13,15,19,34],max_max_replenishment_tim:[5,9],max_replenishment_tim:[5,9],maxim:[20,33],maximum:7,mcgraw:[15,19,20,34],mean:[2,5,6,7,8,12,13,14,15,19,20,21,23,24,25,26,29,32,34,35],mean_cost:[26,34],mean_heur:34,mean_opt:34,measur:[6,26],meio:[5,6,10,11,29,31,34],meio_by_coordinate_desc:[11,32],meio_by_enumer:[11,32],meio_gener:[0,2,3,4,5,6,7,8,9,10,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],member:32,messag:[11,13,16],met:[6,27,34],method:[2,4,5,6,11,15,23,32],middl:27,might:[5,6,13],min:[12,13,15,19],min_:[19,25],min_kei:13,min_of_dict:13,min_valu:13,minim:[16,18,19,20],minimum:[13,16,19],minu:[6,7],miss:[2,3,9,13],mix:[19,25],model:[7,8,12,14,24,29,32,33,34,35],modif:11,modifi:[9,20,25],modul:[0,1,10,22,28,29,32,33,34,35],more:[2,3,4,5,6,7,11,13,24,29,32,34],mosier:[23,33],most:[5,6,12,13,14,19,21,25,26,29],mostli:[27,34],move:34,mu:[2,8,12,14,15,18,19,20,21,23,24,29,33],mu_l:23,much:32,multi:[0,5,6,7,8,9,11,12,14,26,27,29,31,34],multiechelon:[12,34],multipl:[5,13,14,24,33,35],multistag:8,must:[5,6,8,9,11,12,13,15,19,20,23,25,32,34],mwor:5,mwor_system:[5,14],my_dist:15,my_exp:15,my_geom:15,my_nod:32,my_other_nod:32,myopic:[19,20],myopic_bound:19,myopic_cost:20,n1:32,n2:[15,32],n2_bar:15,n:[2,8,12,13,14,15,18,20,21,24,26,29,32,34],n_bar:15,name:[5,6,13,14,27,29,32,34],narrow:32,naval:24,nb:15,nbinom:15,ndarrai:[12,13,19],nearest:[2,12,13,19],necessari:[4,8,12],necessarili:[6,11,32],need:[6,7,9,12,13,34],neg:[6,15,23,27,34],negative_binomial_loss:15,negative_binomial_second_loss:15,neighbor:6,neighbor_indic:6,neither:13,ness:13,net:7,net_demand_mean:9,net_demand_standard_devi:9,net_lead_tim:7,network:[4,5,6,7,8,9,11,12,14,26,27,29,32,34],network_from_edg:[5,14,32,34],networkx:5,networkx_digraph:5,never:34,new_kei:13,new_nam:5,new_tre:9,newsvendor:[0,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,21,22,23,24,25,26,27,28,29,30,31,32,34],newsvendor_continu:[20,33],newsvendor_discret:[20,33],newsvendor_heurist:[12,32,34],newsvendor_norm:[20,29,33],newsvendor_normal_cost:[20,33],newsvendor_normal_explicit:[20,33],newsvendor_poisson:[20,33],newsvendor_poisson_cost:20,newsvendor_poisson_explicit:20,newsvendor_with_additive_yield_uncertainti:[24,35],newsvendor_with_disrupt:[24,35],next:[12,13,20,25,29,33,34],next_order_period:25,nj:21,nlt:7,node:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],node_index:7,node_indic:[5,7,11,13],node_order_in_list:[5,12,13,14,32,34],node_order_in_system:[5,12,14,29,32,34],nodestatevar:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],non:[3,6,13,19,20,23,32,33],none:[2,3,4,5,6,8,9,11,12,13,14,15,18,19,20,23,24,26,27,32,34],nonstationari:14,norm:[14,20,34],normal:[2,8,12,14,15,19,20,21,23,24,29,32,33,35],normal_loss:15,normal_second_loss:15,notat:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],note:[5,6,14,15,24,26,27,29,34],noth:[5,14],now:[32,34],np:[14,15,20],num_nod:[5,8,12,13,14,29,32,34],num_period:[13,14,19,25,26,27,29,34],num_retail:5,num_trial:[26,34],num_warehous:[5,14],number:[5,6,8,11,12,13,14,15,19,21,25,26,27,33,34],numer:[13,14,15,24,32,35],numpi:[14,26],o_i:34,obj_fcn:32,object:[2,3,4,5,6,8,9,11,12,13,14,15,20,24,26,32,33,34,35],objective_funct:[11,32],observ:[2,34],obtain:[4,29],obvious:32,occur:34,odi:[27,34],offload:13,often:34,old:[5,6],old_kei:13,old_to_new_dict:[5,6],oldest:21,omit:[2,3,4,5,11,12,14,27,32],omit_state_var:14,on_hand:6,on_ord:6,on_order_by_predecessor:6,onc:26,one:[2,3,4,5,6,7,9,13,15,21,26,32,34],onli:[2,3,4,5,6,14,24,32,33,34,35],oo:[27,34],op:[3,34],oper:[7,9,21,23],opt_cost:[8,9,29,32],opt_cst:[8,9,29,32],optim:[0,2,3,4,5,6,7,8,9,11,12,13,14,15,17,18,19,20,21,23,24,25,26,27,28,29,30,31,34,35],optimize_base_stock_level:[6,12,29,32,34],optimize_committed_service_tim:[6,8,9,29,32],option:[2,3,4,5,6,8,9,11,12,13,14,15,16,18,20,23,24,25,26,27,33],oq:[27,34],order:[3,4,5,6,12,13,15,18,19,21,23,24,25,26,27,29,33,34,35],order_lead_tim:[6,27,34],order_multipl:18,order_quant:[4,6,18,21,24,25,34],order_up_to_level:[4,19,23],org:[13,15,16],origin:[2,3,6,9,14],original_label:9,os:[27,34],other:[0,4,5,6,9,12,13,14,16,21,26,29,32,33,34],other_nod:32,other_part:14,otherwis:[3,5,6,12,13,14,15,19,20,23,27,34],oul_matrix:19,out:34,outbound:[6,7,8,27,34],outbound_disrupted_item:6,outbound_ship:6,output:[9,11,13,19,25,34],outsid:[12,19],over:[6,16,19,20,26],overag:33,overlap:34,overrid:4,overview:[10,22,28],ow:[27,34],owmr:5,owmr_system:5,own:34,p:[2,6,7,9,12,13,14,15,18,19,20,21,23,24,27,29,33,34,35],p_t:[19,20],p_termin:[29,33],packag:[13,29],package_test_waf:14,page:[7,8,9,10,11,12,18,19,20,21,22,23,24,25,26,27,28,34],pair:13,paper:34,paramet:[2,3,4,5,6,7,8,9,11,12,13,14,15,16,18,19,20,21,23,24,25,26,27,29,32,33,34],parlar:[24,35],part:14,particularli:[11,32],pass:[5,13,32,33,34],path:[6,14,27],paus:[3,34],pd:24,pdf:[15,20],per:[2,3,6,7,8,11,12,16,18,19,20,21,23,24,25,26,29,32,34],perform:[6,9,12,18,19,20,24,26,32],period:[2,3,5,6,7,11,13,14,19,20,23,24,25,26,27,29,32,33,34],periods_to_print:[27,34],peterson:14,phi:[15,20],pi:20,pi_0:24,pi_down:3,pi_n:24,pi_up:3,pip:30,pipelin:[26,27,34],place:[3,4,6,13,27,34],placehold:[5,6],placement:[7,9],plot:12,plu:[6,13,21,33],pm:[19,26,34],pmf:[13,15,20,23,33],pn:[20,21],poi:15,point:[4,16,19,21,23,29,33,34],poisson:[2,14,15,20,21,23,33,34],poisson_loss:15,poisson_second_loss:15,pol:4,polici:[0,1,2,3,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,35],policy_typ:[5,14,32,34],posit:[4,6,19,27,34],possibl:[2,13,19,20,34],power:[23,33],ppf:[14,34],pqx:18,pre:9,precis:29,predecessor:[4,5,6,7,27,34],predecessor_index:[4,6],predecessor_indic:6,predecessor_nod:5,predict:[29,34],prentic:21,preprocess:9,preprocess_tre:[7,9],present:[12,13,14,24],press:21,pretti:[32,34],prevent:34,previou:21,primari:[9,26],primarili:[5,6],princeton:21,principl:32,print:[11,16,27,29,34],print_solut:11,prng:26,probabl:[2,3,12,13,15,19,20,24,33,34],problem:[5,6,7,8,12,14,18,19,20,21,23,24,25,29,31,32],problem_3_1:14,problem_3_22:14,problem_3_27:14,problem_3_29:14,problem_3_2b:14,problem_4_1:14,problem_4_29:14,problem_4_30:14,problem_4_31:14,problem_4_32:14,problem_4_3b:14,problem_4_7b:14,problem_4_8a:14,problem_4_8b:14,problem_5_1:14,problem_5_2:14,problem_5_3:14,problem_6_16:14,problem_6_1:14,problem_6_2a:14,problem_6_2a_adj:14,problem_6_2b:14,problem_6_2b_adj:14,problem_6_7:14,problem_6_8:14,problem_6_9:[7,14],problem_9_4a:14,problem_9_4b:14,problem_9_5:14,problem_9_8:14,problem_specific_data:[5,6],process:[3,6,8,9,34,35],process_waf:14,processing_tim:[6,8,13,14,32],produc:[32,34],product:[6,8,18,24,33,34],production_r:[14,18],profit:[20,33],program:[7,8,9,19,25,29,32,33],progress:[11,26],progress_bar:[11,26,34],proof:[19,20],propag:[2,3,6],properti:[2,5,6,21],provi:23,provid:[2,3,4,5,6,8,9,11,12,13,14,15,19,20,23,24,32,34,35],psi:24,purchas:[14,19,20,25,33],purchase_cost:[6,14,19,20,25,33],purchase_cost_next_p:20,pyke:14,pypi:30,python:[29,30,32],q:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,34,35],q_:19,q_eil:33,q_eoqb:33,q_eoqss:33,q_lf:33,q_n:18,qe:24,qh:21,quad:24,quantiti:[4,6,18,19,21,24,25,27,29,33,34,35],queri:4,quickli:32,quit:[11,32],r:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,34,35],r_eil:33,r_eoqb:33,r_eoqss:33,r_lf:33,r_q_cost:[21,33],r_q_cost_poisson:21,r_q_eil_approxim:[21,33],r_q_eoqb_approxim:[21,33],r_q_eoqss_approxim:[21,33],r_q_loss_function_approxim:[21,33],r_q_optimal_r_for_q:21,r_q_poisson_exact:[21,33],rais:[2,3,4,5,12,13,14,15,19,20,21,23,24,25,26],rand:11,rand_se:[26,29,34],random:[2,3,13,15,26],random_process_typ:[3,34],randomli:35,rang:[2,5,11,12,13,14,19,20,32,33,34],rare:6,rate:[6,15,27,29,34],rather:[4,5,6,13,15,29],raw:[6,27,34],raw_materi:14,raw_material_aggreg:6,raw_material_inventori:6,reach:6,read:[2,5,6],reason:19,recalcul:19,receipt:[3,6,34],receiv:[3,6,27,34],recent:[6,13,26],recoveri:[3,34],recovery_prob:[3,14,24,34],recovery_r:[14,24,35],recurs:[4,5,6],ref:34,refer:[10,22,28,29,30,31,32,33,35],reflect:34,reindex_all_state_vari:6,reindex_nod:5,reindex_state_vari:6,rel:[5,6,11,13,32],rel_tol:[5,6,13],relabel:[7,9],relabel_nod:9,relabeled_tre:9,relat:16,relev:34,reliabl:13,remain:34,remov:[5,6],remove_nod:[5,6],remove_predecessor:6,remove_successor:6,reorder:[4,19,21,23,29,33],reorder_point:[4,19,21,23,34],replac:[6,14],replenish:[18,33],report:34,repres:[2,3,4,5,13,15,25,27,34],represent:[2,3,4,5,6,9],request:27,requir:[2,3,4,5,8,12,13,15,19,20,23,24,27,30,32],require_pres:13,research:[21,23,24],respect:[15,19,20,24,34],restart:[2,3,19],result:[6,15,19,27,29,31,33],retail:[5,14],retrev:14,return_list:13,return_valu:13,reus:16,rev:[27,34],revenu:[6,14,20,27,33,34],revenue_earn:6,revers:34,review:[14,21,23],revis:23,rework:29,rho:18,right:[12,13,15,20,21,23,24,25],rightarrow:12,risa:[24,35],rm:[27,34],rong:14,rong_atan_snyder_figure_1a:14,rong_atan_snyder_figure_1b:14,rong_atan_snyder_figure_1c:14,rosl:[6,14],rosling_figure_1:14,round:[2,12,13,18,19],round_dict_valu:13,round_to_int:[2,5,14],round_typ:[12,13],rout:6,row:[14,27,34],rp:[3,6,27,34],rq:[0,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,22,23,24,25,26,27,28,29,30,32,33,34,35],rule:5,run:[11,26,32],run_multiple_tri:[26,34],rv_continu:[2,13,15,20,24,33,35],rv_discret:[2,13,15,20,24,33,35],rv_frozen:13,s:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,34,35],s_5:19,s_echelon:5,s_heur:[12,32,34],s_heur_loc:34,s_i:34,s_j:12,s_local:5,s_opt:34,s_opt_loc:34,s_overbar:19,s_s_cost_discret:23,s_s_discrete_exact:[23,33],s_s_power_approxim:[23,33],s_spread:19,s_star:[12,29,32],s_star_loc:29,s_t:19,s_underbar:19,safeti:[7,8,9,21,33],safety_stock_level:7,sai:34,salvag:[20,33],salvage_valu:[14,20,33],same:[5,7,11,12,13,14,15,19,25,29,32,34],save:[14,16,27],save_inst:14,sc:[27,34],scalar:[19,25],scale:15,scarf:[12,29,32],scienc:[12,21,23,34],scipi:[2,14,15,20,24,33,34,35],scmo:14,scmo_jrp_ex:14,scmo_jrp_hw_1:14,scmo_jrp_hw_2:14,scmo_jrp_hw_3:14,scmo_ww_hw_c:14,sd:[15,24],search:[11,13,16,21,24,32],search_hi:[11,32],search_lo:[11,32],second:[13,15,21],section:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],section_search:16,see:[5,13,15,32,33],seed:[11,26],self:[4,6,15],sell:[20,33],sem:[26,34],sem_cost:[26,34],sem_heur:34,sem_opt:34,send:34,sens:34,sent:34,sequenc:[29,31],serial:[5,8,11,12,14,29,31,34],serial_3:32,serial_system:[5,12,14,29,32,34],serv:34,servic:[7,8,9,12,29,32],set:[2,3,4,5,6,7,8,11,12,13,16,19,20,23,24,26,27,29,32,34],set_myopic_cost_to:20,sever:[13,32],shang:[12,14,32,34],shang_song_17:14,shang_song_1:14,shang_song_25:14,shang_song_9:14,shape:15,share:18,shared_fixed_cost:[14,18,33],shen:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],shift:13,ship:[3,34],ship_to_final_assembl:14,shipment:[3,6,12,26,27,34],shipment_lead_tim:[6,14,27,29,32,34],shortcut:[27,34],shorter:29,should:[4,5,6,11,13,34],show:34,shown:34,si:7,siam:[19,20],sigma:[2,14,15,19,20,21,23,29,33],sigma_l:23,silver:[14,18,33],silver_jrp:14,sim:[0,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,27,28,29,30,32,33,34,35],sim_io:[0,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,28,29,30,32,33,34,35],sim_num_period:[11,32],sim_num_tri:[11,32],sim_rand_se:[11,32],similar:[13,26,29],similarli:[5,6],simpl:23,simpli:6,simul:[0,5,6,11,26,27,29,31,32],simultan:13,sinc:[6,11,12,14,32,34],singl:[0,5,7,11,14,16,18,19,20,21,23,24,25,29,31,34,35],single_stage_system:[5,14,34],singleton:[2,5,8,11,12,13,19,20,25,32],sink:[5,34],sink_nod:5,size:[13,34],skip:27,slightli:15,slot:[5,12,13],slow:[11,32],slower:32,small:32,smallest:[6,9,13,19,20],smilowitz:14,snippet:32,snyder:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],so:[2,3,6,9,20,32,34],soe:34,sold:20,solut:[7,11,12,18,19,20,21,23,24,32,33,34],solution_cost_from_base_stock_level:7,solution_cost_from_cst:7,solv:[7,11,12,18,19,20,21,23,24,25,29,32,33,35],some:[2,6,18,19,20,25,27,32,33],someth:34,sometim:[4,11,12,32],somewhat:34,song:[12,14,32,34],soon:34,sort:[5,13],sort_dict_by_kei:13,sourc:[2,3,4,5,6,7,8,9,11,12,13,14,15,16,18,19,20,21,23,24,25,26,27,34],source_nod:5,sp:[3,6,27,34],space:[13,19,32],special:13,specif:[5,6,8,12],specifi:[2,3,4,5,7,8,12,13,14,19,32,33,34],speed:[11,32],spp_jrp:14,sqrt:[14,18,21,23,24,34,35],ss:[0,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,24,25,26,27,28,29,30,32,33,34,35],ss_power_approx3:23,ssm:[9,12,14,29,31],ssm_serial:[0,2,3,4,5,6,7,8,9,10,11,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],ssm_tree:9,stack:32,stackoverflow:13,stage:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],standalon:[6,34],standard:[2,6,8,12,15,19,20,21,23,24,26,29,34,35],standard_devi:[2,14,29,32,34],standard_normal_loss:15,standard_normal_second_loss:15,start:[9,11,19,27,34],start_index:9,stat:[2,14,15,20,24,33,34,35],state:[3,4,6,14,19,26,27,34,35],state_var:6,state_vars_curr:6,statist:34,stdout:27,steadi:3,steady_state_prob:3,step:[26,34],still:[32,34],stochast:[12,14,19,21,29,31,32,34],stock:[4,5,6,7,8,9,11,12,14,20,21,24,26,27,29,32,33,34,35],stockout:[6,9,12,18,19,20,21,23,24,27,29,33],stockout_cost:[5,6,9,12,13,14,18,19,20,21,23,24,29,32,33,34],stockout_cost_funct:[6,34],stockout_cost_incur:6,stockout_fract:18,stockpyl:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,32,33,34,35],stockpyl_inst:14,stop:15,store:6,str:[2,3,4,6,13,14,26,27],straightforward:19,strateg:[7,9],string:[2,3,4,6,12,13,26,27,34],structur:[5,7,8,9,14,29,31,32],subclass:13,subject:[3,34],suboptim:19,subtract:[4,19],succesor:[27,34],success:15,successor:[5,6,27,34],successor_indic:6,successor_nod:5,suffici:34,suggest:19,suitabl:13,sum:[2,6,12,13],sum_:[12,15,18,21,23,24,25],sum_i:13,sum_ltd_lower_tail_prob:12,sum_ltd_upper_tail_prob:12,sum_of_continuous_uniforms_distribut:13,sum_of_discrete_uniforms_distribut:13,sum_of_discrete_uniforms_pmf:13,sum_of_discretes_distribut:13,suppli:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33],supplier:[3,4,6,8,24,27,35],supply_chain_network:[0,1,2,3,4,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],supply_chain_nod:[0,1,2,3,4,5,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],supply_typ:[5,6,14,34],supply_uncertainti:[0,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,25,26,27,28,29,30,32,33,34,35],supplychainnetwork:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,31,33,34,35],supplychainnod:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],support:[2,3,4,6,12,13,15,23,26,27,33,34,35],swap:34,system:[5,6,7,8,9,11,12,14,21,26,29,31,34],sytem:34,t:[3,18,19,20,21,24,25,29,33,34],tabl:[14,27,34],tail:12,take:[6,11,13,15,24,34],taken:14,tau:21,tc:[27,34],tell:[2,34],tend:[11,32],term:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],termin:[6,11,16,19,21],terminal_holding_cost:[14,19],terminal_stockout_cost:[14,19],test:[11,13,32],text:[12,15,18,19,20,24],textbook:[14,29],texttt:12,th:[5,8,12,13],than:[4,5,6,9,11,13,15,16,19,20,29,32,33,34],the_dict:[2,3,4,5,6,13],thei:[3,4,5,6,11,12,13,14,19,32,34],them:[3,13,29,32,34],themselv:[5,6],theoret:29,theori:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],thereaft:19,therefor:[2,6,34],theta:[25,29,33],theta_1:19,theta_:[19,25],theta_t:[19,25],thi:[2,3,4,5,6,9,11,12,13,14,15,16,19,21,27,32,34],thorough:21,those:[5,12,34],though:5,through:6,throughout:13,tight:24,tild:12,time:[2,6,7,8,9,12,13,14,18,19,20,21,23,24,25,26,29,31,32,33],tm_n:18,to_dict:[2,3,4,5,6],to_index:5,togeth:[5,13],tol:[11,16,21],toler:[5,6,11,13,16,19,21],too:19,topolog:[11,32],total:[6,19,26,27,29,34],total_cost:[19,29,34],total_cost_incur:6,tp:[3,34],traceback:13,track:3,transform:13,transit:[3,6,27,34],treat:[13,14],tree:[7,9,11,14,29,31],trial:[11,15,26,32],trivial:32,trunc_tol:19,truncat:[11,12,19,32],truncate_and_discret:11,truncated_discretized_valu:11,truncation_hi:[11,32],truncation_lo:[11,32],tupl:[5,24],turn:[12,32],tutori:[7,8,9,10,11,12,18,19,20,21,22,23,24,25,26,27,28,29,34],tutorial_meio:32,two:[5,6,13,15,19,34],type:[0,2,3,4,5,6,7,9,11,12,13,14,20,21,23,24,26,27,29,32,33,34,35],typeerror:13,typic:[2,3,4,5,6,32,34],u:[5,6,13,14,15],uc:2,ud:[2,14],uncertainti:[14,24,29,31,33],undefin:13,under:[12,21,23,29,32,33,34],underag:33,underlin:[6,12,19,20],uniform:[2,13,15,24,35],uniform_loss:[15,24],uniform_second_loss:15,unit:[6,8,12,18,20,21,24,34],univers:21,unless:[5,9,13,24],unlimit:6,unrecogn:27,unreli:6,unsold:20,until:[6,15,34],up:[3,4,12,13,14,19,23,24,29,33],upcom:34,updat:[3,5,6,26,34],update_disruption_st:3,upper:[12,13,15,16,19,23,32],uppper:19,upstream:[5,6,12,34],us:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],use_poisson:[23,33],user:19,usual:25,v3:30,v:20,valid:[5,19,26,34],validate_paramet:[2,3,4],valu:[2,3,4,5,6,7,8,9,11,12,13,14,15,16,19,20,21,23,24,25,27,33,34],valueerror:[2,5,12,13,14,15,19,20,21,23,24,25,26],var_nam:13,vari:33,variabl:[2,4,6,13,14,15,26,27,34],variant:[18,20,33],variat:19,varieti:34,variou:34,vector:19,veinott:[19,20],verbos:[11,16],veri:[32,34],version:[15,20,33],via:6,vs:13,w:26,wa:[6,9,14,27,34],wagner:[14,25,29,31],wagner_whitin:[0,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,26,27,28,29,30,32,33,34,35],wai:[6,8,15,32],want:33,warehous:[5,14],warn:[14,19,26],we:[6,14,15,19,29,32,33,34],weight:12,well:[3,6,11,20,27,32],were:34,wf:26,what:[26,29],when:[3,5,6,11,12,13,16,19,21,27,32,34],where:[4,5,6,13,15,18,19,20,21,23,24,34],whether:[5,6,9,13,26,34],which:[2,4,5,6,7,8,9,11,12,13,14,15,19,20,24,25,26,27,32,33,34],whitin:[14,21,25,29,31],whose:[5,6,13,33,34],wide:21,width:[11,16],wiki:[13,16],wikipedia:[13,16],willem:[7,9,29,32],wish:[19,32],within:[5,16,21],without:[11,12,13,19,33],word:13,work:[6,13],wors:[32,34],worth:34,would:[32,34],wrapper:[2,12],write:[14,27],write_csv:27,write_instance_and_st:27,write_result:[27,34],x:[2,12,13,15,16,18,19,24,34],x_1:[13,19],x_2:13,x_3:13,x_4:13,x_:19,x_i:13,x_n:13,x_new:13,x_num:[12,32],x_rang:19,x_star:16,xf:15,y:[7,12,15,19,20,21,23,24,34],yet:[6,27,34],yield:[14,24,29,31],yield_distribut:[24,35],yield_hi:14,yield_lo:14,yield_mean:[14,24,35],yield_sd:[14,24,35],you:[5,6,32,33,34,35],your:34,z:[15,19,23,24,34],z_:[20,21,26,34],zero:[6,20,27,33,34],zheng:[12,21,23,29,32,33,34],zip:[20,33],zipkin:[6,15,19,20,34]},titles:["API Documentation","Data Types","<code class=\"docutils literal notranslate\"><span class=\"pre\">demand_source</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">disruption_process</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">policy</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">supply_chain_network</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">supply_chain_node</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">gsm_helpers</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">gsm_serial</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">gsm_tree</span></code> Module","Multi-Echelon Inventory Optimization","<code class=\"docutils literal notranslate\"><span class=\"pre\">meio_general</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">ssm_serial</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">helpers</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">instances</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">loss_functions</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">optimization</span></code> Module","Other Modules","<code class=\"docutils literal notranslate\"><span class=\"pre\">eoq</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">finite_horizon</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">newsvendor</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">rq</span></code> Module","Single-Echelon Inventory Optimization","<code class=\"docutils literal notranslate\"><span class=\"pre\">ss</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">supply_uncertainty</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">wagner_whitin</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">sim</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">sim_io</span></code> Module","Simulation","Stockpyl","Installing Stockpyl","Tutorial","Multi-Echelon Inventory Optimization","Single-Echelon Inventory Optimization","Simulation","Supply Uncertainty"],titleterms:{"class":32,"function":34,The:[32,33,35],advanc:34,also:[7,8,9,10,11,12,18,19,20,21,22,23,24,25,26,27,28,34],api:[0,2,3,4,5,6,7,8,9,11,12,13,14,15,16,18,19,20,21,23,24,25,26,27],basic:34,content:[0,1,10,17,22,28,29,32,33,34,35],continu:34,convert:34,cost:34,custom:34,data:[1,34],demand:34,demand_sourc:2,displai:34,disrupt:[34,35],disruption_process:3,document:[0,29],echelon:[10,22,32,33],eoq:[18,33,35],event:34,exampl:[29,34],extern:34,featur:34,finit:33,finite_horizon:19,from:34,gener:32,gsm:32,gsm_helper:7,gsm_serial:8,gsm_tree:9,helper:13,hold:34,horizon:33,indic:29,instal:30,instanc:14,inventori:[10,22,32,33,34],lead:34,loss_funct:15,meio:32,meio_gener:11,modul:[2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18,19,20,21,23,24,25,26,27],multi:[10,32],multipl:34,newsvendor:[20,33,35],optim:[10,16,22,32,33],other:17,overview:[2,3,4,5,6,7,8,9,11,12,13,14,15,16,18,19,20,21,23,24,25,26,27],polici:[4,34],problem:[33,35],q:33,r:33,refer:[2,3,4,5,6,7,8,9,11,12,13,14,15,16,18,19,20,21,23,24,25,26,27,34],result:34,review:34,rq:21,run:34,s:33,see:[7,8,9,10,11,12,18,19,20,21,22,23,24,25,26,27,28,34],sequenc:34,serial:32,sim:26,sim_io:27,simul:[28,34],singl:[22,33],some:29,ss:23,ssm:32,ssm_serial:12,stochast:33,stockout:34,stockpyl:[29,30,31],structur:34,suppli:[34,35],supplier:34,supply_chain_network:5,supply_chain_nod:6,supply_uncertainti:24,supplychainnetwork:32,system:32,tabl:29,time:34,tree:32,trial:34,tutori:31,type:1,uncertainti:35,wagner:33,wagner_whitin:25,whitin:33,yield:35}})
\ No newline at end of file
+Search.setIndex({docnames:["api/api","api/datatypes/datatypes","api/datatypes/demand_source","api/datatypes/disruption_process","api/datatypes/policy","api/datatypes/supply_chain_network","api/datatypes/supply_chain_node","api/meio/gsm_helpers","api/meio/gsm_serial","api/meio/gsm_tree","api/meio/meio","api/meio/meio_general","api/meio/ssm_serial","api/other/helpers","api/other/instances","api/other/loss_functions","api/other/optimization","api/other/other","api/seio/eoq","api/seio/finite_horizon","api/seio/newsvendor","api/seio/rq","api/seio/seio","api/seio/ss","api/seio/supply_uncertainty","api/seio/wagner_whitin","api/simulation/sim","api/simulation/sim_io","api/simulation/simulation","index","install","tutorial/tutorial","tutorial/tutorial_meio","tutorial/tutorial_seio","tutorial/tutorial_sim","tutorial/tutorial_su"],envversion:{"sphinx.domains.c":2,"sphinx.domains.changeset":1,"sphinx.domains.citation":1,"sphinx.domains.cpp":5,"sphinx.domains.index":1,"sphinx.domains.javascript":2,"sphinx.domains.math":2,"sphinx.domains.python":3,"sphinx.domains.rst":2,"sphinx.domains.std":2,"sphinx.ext.viewcode":1,sphinx:56},filenames:["api/api.rst","api/datatypes/datatypes.rst","api/datatypes/demand_source.rst","api/datatypes/disruption_process.rst","api/datatypes/policy.rst","api/datatypes/supply_chain_network.rst","api/datatypes/supply_chain_node.rst","api/meio/gsm_helpers.rst","api/meio/gsm_serial.rst","api/meio/gsm_tree.rst","api/meio/meio.rst","api/meio/meio_general.rst","api/meio/ssm_serial.rst","api/other/helpers.rst","api/other/instances.rst","api/other/loss_functions.rst","api/other/optimization.rst","api/other/other.rst","api/seio/eoq.rst","api/seio/finite_horizon.rst","api/seio/newsvendor.rst","api/seio/rq.rst","api/seio/seio.rst","api/seio/ss.rst","api/seio/supply_uncertainty.rst","api/seio/wagner_whitin.rst","api/simulation/sim.rst","api/simulation/sim_io.rst","api/simulation/simulation.rst","index.rst","install.rst","tutorial/tutorial.rst","tutorial/tutorial_meio.rst","tutorial/tutorial_seio.rst","tutorial/tutorial_sim.rst","tutorial/tutorial_su.rst"],objects:{"stockpyl.demand_source":[[2,1,1,"","DemandSource"]],"stockpyl.demand_source.DemandSource":[[2,2,1,"","cdf"],[2,3,1,"","demand_distribution"],[2,4,1,"","demand_list"],[2,2,1,"","from_dict"],[2,2,1,"","generate_demand"],[2,4,1,"","hi"],[2,2,1,"","initialize"],[2,2,1,"","lead_time_demand_distribution"],[2,4,1,"","lo"],[2,4,1,"","mean"],[2,4,1,"","probabilities"],[2,4,1,"","round_to_int"],[2,4,1,"","standard_deviation"],[2,2,1,"","to_dict"],[2,4,1,"","type"],[2,2,1,"","validate_parameters"]],"stockpyl.disruption_process":[[3,1,1,"","DisruptionProcess"]],"stockpyl.disruption_process.DisruptionProcess":[[3,4,1,"","disrupted"],[3,4,1,"","disruption_probability"],[3,4,1,"","disruption_state_list"],[3,4,1,"","disruption_type"],[3,2,1,"","from_dict"],[3,2,1,"","initialize"],[3,4,1,"","random_process_type"],[3,4,1,"","recovery_probability"],[3,2,1,"","steady_state_probabilities"],[3,2,1,"","to_dict"],[3,2,1,"","update_disruption_state"],[3,2,1,"","validate_parameters"]],"stockpyl.eoq":[[18,5,1,"","economic_order_quantity"],[18,5,1,"","economic_order_quantity_with_backorders"],[18,5,1,"","economic_production_quantity"],[18,5,1,"","joint_replenishment_problem_silver_heuristic"]],"stockpyl.finite_horizon":[[19,5,1,"","finite_horizon_dp"],[19,5,1,"","myopic_bounds"]],"stockpyl.gsm_helpers":[[7,5,1,"","cst_to_base_stock_levels"],[7,5,1,"","inbound_cst"],[7,5,1,"","net_lead_time"],[7,5,1,"","safety_stock_levels"],[7,5,1,"","solution_cost_from_base_stock_levels"],[7,5,1,"","solution_cost_from_cst"]],"stockpyl.gsm_serial":[[8,5,1,"","optimize_committed_service_times"]],"stockpyl.gsm_tree":[[9,5,1,"","gsm_to_ssm"],[9,5,1,"","is_correctly_labeled"],[9,5,1,"","optimize_committed_service_times"],[9,5,1,"","preprocess_tree"],[9,5,1,"","relabel_nodes"]],"stockpyl.helpers":[[13,5,1,"","build_node_data_dict"],[13,5,1,"","change_dict_key"],[13,5,1,"","check_iterable_sizes"],[13,5,1,"","convolve_many"],[13,5,1,"","dict_match"],[13,5,1,"","ensure_dict_for_nodes"],[13,5,1,"","ensure_list_for_nodes"],[13,5,1,"","ensure_list_for_time_periods"],[13,5,1,"","find_nearest"],[13,5,1,"","irwin_hall_cdf"],[13,5,1,"","is_continuous_distribution"],[13,5,1,"","is_discrete_distribution"],[13,5,1,"","is_integer"],[13,5,1,"","is_iterable"],[13,5,1,"","is_list"],[13,5,1,"","min_of_dict"],[13,5,1,"","round_dict_values"],[13,5,1,"","sort_dict_by_keys"],[13,5,1,"","sum_of_continuous_uniforms_distribution"],[13,5,1,"","sum_of_discrete_uniforms_distribution"],[13,5,1,"","sum_of_discrete_uniforms_pmf"],[13,5,1,"","sum_of_discretes_distribution"]],"stockpyl.instances":[[14,5,1,"","load_instance"],[14,5,1,"","save_instance"]],"stockpyl.loss_functions":[[15,5,1,"","continuous_loss"],[15,5,1,"","continuous_second_loss"],[15,5,1,"","discrete_loss"],[15,5,1,"","discrete_second_loss"],[15,5,1,"","exponential_loss"],[15,5,1,"","exponential_second_loss"],[15,5,1,"","gamma_loss"],[15,5,1,"","gamma_second_loss"],[15,5,1,"","geometric_loss"],[15,5,1,"","geometric_second_loss"],[15,5,1,"","lognormal_loss"],[15,5,1,"","negative_binomial_loss"],[15,5,1,"","negative_binomial_second_loss"],[15,5,1,"","normal_loss"],[15,5,1,"","normal_second_loss"],[15,5,1,"","poisson_loss"],[15,5,1,"","poisson_second_loss"],[15,5,1,"","standard_normal_loss"],[15,5,1,"","standard_normal_second_loss"],[15,5,1,"","uniform_loss"],[15,5,1,"","uniform_second_loss"]],"stockpyl.meio_general":[[11,5,1,"","meio_by_coordinate_descent"],[11,5,1,"","meio_by_enumeration"],[11,5,1,"","truncate_and_discretize"]],"stockpyl.newsvendor":[[20,5,1,"","myopic"],[20,5,1,"","myopic_cost"],[20,5,1,"","newsvendor_continuous"],[20,5,1,"","newsvendor_discrete"],[20,5,1,"","newsvendor_normal"],[20,5,1,"","newsvendor_normal_cost"],[20,5,1,"","newsvendor_normal_explicit"],[20,5,1,"","newsvendor_poisson"],[20,5,1,"","newsvendor_poisson_cost"],[20,5,1,"","newsvendor_poisson_explicit"],[20,5,1,"","set_myopic_cost_to"]],"stockpyl.optimization":[[16,5,1,"","golden_section_search"]],"stockpyl.policy":[[4,1,1,"","Policy"]],"stockpyl.policy.Policy":[[4,4,1,"","base_stock_level"],[4,2,1,"","from_dict"],[4,2,1,"","get_order_quantity"],[4,2,1,"","initialize"],[4,4,1,"","node"],[4,4,1,"","order_quantity"],[4,4,1,"","order_up_to_level"],[4,4,1,"","reorder_point"],[4,2,1,"","to_dict"],[4,4,1,"","type"],[4,2,1,"","validate_parameters"]],"stockpyl.rq":[[21,5,1,"","r_q_cost"],[21,5,1,"","r_q_cost_poisson"],[21,5,1,"","r_q_eil_approximation"],[21,5,1,"","r_q_eoqb_approximation"],[21,5,1,"","r_q_eoqss_approximation"],[21,5,1,"","r_q_loss_function_approximation"],[21,5,1,"","r_q_optimal_r_for_q"],[21,5,1,"","r_q_poisson_exact"]],"stockpyl.sim":[[26,5,1,"","close"],[26,5,1,"","initialize"],[26,5,1,"","run_multiple_trials"],[26,5,1,"","simulation"],[26,5,1,"","step"]],"stockpyl.sim_io":[[27,5,1,"","write_instance_and_states"],[27,5,1,"","write_results"]],"stockpyl.ss":[[23,5,1,"","s_s_cost_discrete"],[23,5,1,"","s_s_discrete_exact"],[23,5,1,"","s_s_power_approximation"]],"stockpyl.ssm_serial":[[12,5,1,"","expected_cost"],[12,5,1,"","expected_holding_cost"],[12,5,1,"","newsvendor_heuristic"],[12,5,1,"","optimize_base_stock_levels"]],"stockpyl.supply_chain_network":[[5,1,1,"","SupplyChainNetwork"],[5,5,1,"","echelon_to_local_base_stock_levels"],[5,5,1,"","local_to_echelon_base_stock_levels"],[5,5,1,"","mwor_system"],[5,5,1,"","network_from_edges"],[5,5,1,"","owmr_system"],[5,5,1,"","serial_system"],[5,5,1,"","single_stage_system"]],"stockpyl.supply_chain_network.SupplyChainNetwork":[[5,2,1,"","add_edge"],[5,2,1,"","add_edges_from_list"],[5,2,1,"","add_node"],[5,2,1,"","add_predecessor"],[5,2,1,"","add_successor"],[5,2,1,"","deep_equal_to"],[5,3,1,"","edges"],[5,2,1,"","from_dict"],[5,2,1,"","get_node_from_index"],[5,2,1,"","has_directed_cycle"],[5,2,1,"","initialize"],[5,4,1,"","max_max_replenishment_time"],[5,2,1,"","networkx_digraph"],[5,3,1,"","node_indices"],[5,3,1,"","nodes"],[5,4,1,"","period"],[5,4,1,"","problem_specific_data"],[5,2,1,"","reindex_nodes"],[5,2,1,"","remove_node"],[5,3,1,"","sink_nodes"],[5,3,1,"","source_nodes"],[5,2,1,"","to_dict"]],"stockpyl.supply_chain_node":[[6,1,1,"","NodeStateVars"],[6,1,1,"","SupplyChainNode"]],"stockpyl.supply_chain_node.NodeStateVars":[[6,3,1,"","backorders"],[6,4,1,"","backorders_by_successor"],[6,2,1,"","deep_equal_to"],[6,4,1,"","demand_cumul"],[6,4,1,"","demand_met_from_stock"],[6,4,1,"","demand_met_from_stock_cumul"],[6,4,1,"","disrupted"],[6,3,1,"","echelon_inventory_level"],[6,2,1,"","echelon_inventory_position"],[6,3,1,"","echelon_on_hand_inventory"],[6,4,1,"","fill_rate"],[6,2,1,"","from_dict"],[6,4,1,"","holding_cost_incurred"],[6,3,1,"","in_transit"],[6,2,1,"","in_transit_from"],[6,4,1,"","in_transit_holding_cost_incurred"],[6,2,1,"","in_transit_to"],[6,4,1,"","inbound_disrupted_items"],[6,3,1,"","inbound_disrupted_items_aggregate"],[6,4,1,"","inbound_order"],[6,4,1,"","inbound_order_pipeline"],[6,4,1,"","inbound_shipment"],[6,4,1,"","inbound_shipment_pipeline"],[6,4,1,"","inventory_level"],[6,2,1,"","inventory_position"],[6,4,1,"","node"],[6,3,1,"","on_hand"],[6,3,1,"","on_order"],[6,4,1,"","on_order_by_predecessor"],[6,4,1,"","order_quantity"],[6,4,1,"","outbound_disrupted_items"],[6,4,1,"","outbound_shipment"],[6,4,1,"","period"],[6,3,1,"","raw_material_aggregate"],[6,4,1,"","raw_material_inventory"],[6,2,1,"","reindex_state_variables"],[6,4,1,"","revenue_earned"],[6,4,1,"","stockout_cost_incurred"],[6,2,1,"","to_dict"],[6,4,1,"","total_cost_incurred"]],"stockpyl.supply_chain_node.SupplyChainNode":[[6,2,1,"","add_predecessor"],[6,2,1,"","add_successor"],[6,3,1,"","ancestors"],[6,2,1,"","deep_equal_to"],[6,4,1,"","demand_source"],[6,3,1,"","derived_demand_mean"],[6,3,1,"","derived_demand_standard_deviation"],[6,3,1,"","descendants"],[6,3,1,"","disrupted"],[6,4,1,"","disruption_process"],[6,4,1,"","echelon_holding_cost"],[6,3,1,"","equivalent_lead_time"],[6,3,1,"","forward_echelon_lead_time"],[6,2,1,"","from_dict"],[6,2,1,"","get_one_predecessor"],[6,2,1,"","get_one_successor"],[6,3,1,"","holding_cost"],[6,4,1,"","in_transit_holding_cost"],[6,4,1,"","initial_inventory_level"],[6,4,1,"","initial_orders"],[6,2,1,"","initialize"],[6,4,1,"","inventory_policy"],[6,4,1,"","lead_time"],[6,4,1,"","local_holding_cost"],[6,4,1,"","local_holding_cost_function"],[6,3,1,"","neighbor_indices"],[6,3,1,"","neighbors"],[6,4,1,"","network"],[6,4,1,"","order_lead_time"],[6,2,1,"","predecessor_indices"],[6,2,1,"","predecessors"],[6,4,1,"","problem_specific_data"],[6,4,1,"","purchase_cost"],[6,2,1,"","reindex_all_state_variables"],[6,2,1,"","remove_predecessor"],[6,2,1,"","remove_successor"],[6,4,1,"","revenue"],[6,4,1,"","shipment_lead_time"],[6,4,1,"","state_vars"],[6,3,1,"","state_vars_current"],[6,4,1,"","stockout_cost"],[6,4,1,"","stockout_cost_function"],[6,2,1,"","successor_indices"],[6,2,1,"","successors"],[6,4,1,"","supply_type"],[6,2,1,"","to_dict"]],"stockpyl.supply_uncertainty":[[24,5,1,"","eoq_with_additive_yield_uncertainty"],[24,5,1,"","eoq_with_disruptions"],[24,5,1,"","eoq_with_disruptions_cost"],[24,5,1,"","eoq_with_multiplicative_yield_uncertainty"],[24,5,1,"","newsvendor_with_additive_yield_uncertainty"],[24,5,1,"","newsvendor_with_disruptions"]],"stockpyl.wagner_whitin":[[25,5,1,"","wagner_whitin"]],stockpyl:[[2,0,0,"-","demand_source"],[3,0,0,"-","disruption_process"],[18,0,0,"-","eoq"],[19,0,0,"-","finite_horizon"],[7,0,0,"-","gsm_helpers"],[8,0,0,"-","gsm_serial"],[9,0,0,"-","gsm_tree"],[13,0,0,"-","helpers"],[14,0,0,"-","instances"],[15,0,0,"-","loss_functions"],[11,0,0,"-","meio_general"],[20,0,0,"-","newsvendor"],[16,0,0,"-","optimization"],[4,0,0,"-","policy"],[21,0,0,"-","rq"],[26,0,0,"-","sim"],[27,0,0,"-","sim_io"],[23,0,0,"-","ss"],[12,0,0,"-","ssm_serial"],[5,0,0,"-","supply_chain_network"],[6,0,0,"-","supply_chain_node"],[24,0,0,"-","supply_uncertainty"],[25,0,0,"-","wagner_whitin"]]},objnames:{"0":["py","module","Python module"],"1":["py","class","Python class"],"2":["py","method","Python method"],"3":["py","property","Python property"],"4":["py","attribute","Python attribute"],"5":["py","function","Python function"]},objtypes:{"0":"py:module","1":"py:class","2":"py:method","3":"py:property","4":"py:attribute","5":"py:function"},terms:{"0":[3,5,6,7,8,9,11,12,13,14,15,18,19,20,21,23,24,25,26,29,32,33,34,35],"00":[7,33],"0000":34,"000000001":24,"0000005374905":16,"0001":11,"001353352589297054":15,"0013533528323661267":15,"002394806823354":[20,33],"007":13,"007824431159359786":15,"008646647165633875":15,"01":[11,14],"010958904109589041":14,"012332294949644":[12,32],"013533528103402742":15,"013533528323661264":15,"01880706693657111":15,"0198":[24,35],"02":[14,19,34],"027434723327854":[12,32],"03":14,"031731173050459915":15,"034111561471642":[23,33],"04":[14,24,34,35],"0430622009569378":18,"04552796208651397":15,"0467800264368":[18,21,29,33],"0479999999999743":15,"048":15,"04837003438256":33,"0485760000000004":15,"0485760000000006":15,"05":[12,14,16],"052":13,"05773502691896258":14,"06":[14,21,24,35],"063":23,"0631099655841":32,"0689302470355":24,"07114627035178":33,"07116250928294":21,"08":[5,6,14],"08333333333333333":14,"09":13,"0936537653899085":15,"09365376538990855":15,"09891883213067":20,"0s":13,"0th":[13,19,25],"1":[3,4,5,6,7,8,9,11,12,13,14,15,16,18,19,20,21,23,24,25,26,27,29,32,33,34,35],"10":[2,7,11,13,14,15,23,29,32,33,34],"100":[11,12,14,19,21,29,32,33,34],"1000":[11,12,14,29,34],"10000":34,"1000000":[14,24,35],"10108087745232":15,"102":15,"1020":33,"103":[8,21],"103164454170876":[18,33],"104":34,"10522318598177341":15,"1067":[19,20],"107":[21,24,33,34],"108":24,"1083":[19,20],"11":[12,14,32,34],"110":[14,19,29,33],"1100":14,"111":[19,29,33],"113":8,"11353352830366131":15,"115":14,"116":23,"12":[12,14,15,20,21,32,33,34],"120":[14,18,25,29,33],"1200":[14,24],"121":24,"122195054841043":15,"125":14,"12500":14,"126":[19,21,29,33],"128":[21,33],"129":[21,24],"12914":[24,35],"13":[12,14,15,16,34],"1300":[14,18,21,24,29,33,35],"13086":[24,35],"132":24,"13263":24,"133":[19,29,33],"13426":24,"135":14,"1380":[25,29,33],"14":[14,15,19,20,24,34,35],"140":14,"1400":14,"14085904245475275":14,"142":14,"1421":34,"1426":[12,34],"1432417118889":[24,35],"1443":[12,34],"1443484":35,"15":[11,14,15,24,34,35],"150":[14,21,25,29,33],"1500":14,"15000":[14,24,35],"1500000":35,"15000000":14,"15328525645054":29,"155":24,"1558":19,"156131552870387":20,"15945901616041":12,"16":[12,14,20,21,34],"160":[14,18,33],"16169098594":[24,35],"167124183311998e":12,"16794575837224":29,"1683073521514889":15,"1689463285519":29,"17":[14,15,20,21,34],"170":14,"1700":18,"171":14,"173":[24,35],"1736":14,"174":24,"175":14,"176":[7,9],"1765":[14,20],"177":[7,9],"1780":14,"18":[14,15,20,21,23,24,29,33,34],"180":14,"1800":14,"182":13,"182500":14,"183":23,"1833333":[24,35],"183979125298336":18,"18500":[14,24,35],"19":[14,15,34],"190":[14,21,33],"191":19,"19102133030678":33,"1912":14,"192":14,"192z":23,"194304":33,"194304000000002":15,"19461695647407":[23,33],"1953":[21,33],"1960":[12,29,32],"1963":[21,33],"1966":[19,20],"1976":[14,18,33],"198":33,"1984":[23,33],"1989":[6,14],"1991":[8,23,24,32,33,35],"1992":[21,33],"1994":[12,24,29,32,34,35],"1996":[12,32],"1998":14,"1e":[5,6,13,16,21],"2":[3,5,7,8,9,11,12,13,14,15,16,18,19,20,21,23,24,25,26,29,32,33,34,35],"20":[14,15,18,19,21,29,32,33,34],"200":14,"2000":[6,7,9,14,15,19,20,24,29,32,34,35],"20000":14,"200000":35,"2003":[7,9,12,14,34],"2014":[24,35],"2017":14,"2019":[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],"20243187688158":33,"2080":14,"20800":14,"21":[14,21,34],"210":[25,29,33],"213":[21,33],"21428571428571427":14,"21449789525488":32,"21486028212500707":15,"22":[12,14,15,24,32,34],"220":14,"2222222222222222":15,"223748044859164":33,"225":[14,18,21,24,29,33,35],"2250":14,"226":29,"227":29,"23":[15,24,34],"230246":[24,35],"24":[8,14,20,24,34],"25":[3,14,24,29,34,35],"250000":35,"25317":35,"254477":[24,35],"2591674214654":34,"259837154163556":34,"26":34,"26036848597217":19,"26119040852187103":34,"264":34,"27":[7,14,15,18,20,21,24,34],"270":[14,33],"27039814681794644":34,"27335621540425":34,"2737":24,"275":14,"277916867529369":[7,9,29,32],"28":[14,15,21,24,34],"280288386513346":15,"2831":34,"28364973888106326":15,"28687665608078":33,"29":[14,18,20,21],"29017010980579":[23,33],"29236193":13,"295":20,"29720380302459":34,"2_l":23,"2d":24,"2e":24,"2h":24,"2k":[18,21],"2kd":24,"2l":23,"2nd":[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],"2p":24,"2r":15,"3":[3,7,8,9,12,13,14,15,18,19,20,21,24,25,29,32,33,34,35],"30":[14,15,20,23,33,34],"300":[14,18,21,33],"3000":14,"300000":24,"3023987673176":33,"304":[18,21,29,33],"308":[21,33],"309493362512628":[18,33],"31":[7,14,15,18,34],"310":18,"3132203403":35,"318":[21,33],"31910867996449":34,"32":[12,14,15,18,34],"326192933063429":15,"326459980156931":15,"32645998015693145":15,"327":13,"328":[21,33],"33":[14,15,18,20,33,34],"3333333333333333":15,"3333333335":[24,35],"33491040676202":32,"3369965715624":[21,33],"34":[15,29,34],"34000":14,"342":13,"344790717086":24,"3453768":13,"345527962086514":15,"35":[7,14,20],"35613154776623":20,"36":[14,15,34],"36000":14,"3600000000000003":14,"365":14,"36782387894158":19,"37":[12,14,15,20,32,34],"37046881882":[24,35],"38":[15,21,24,34],"38000":14,"39":[23,25],"394684658734164":20,"4":[7,9,11,12,13,14,15,18,19,20,21,23,24,25,29,32,33,34],"40":[12,14,15,20,21,23,29,32,33,34],"400":14,"4000":14,"41":[7,15,20,24,34],"41052550594829":[18,29,33],"4142135623730951":7,"42":[15,29,32,34],"42277610622506":33,"4272799263067":21,"428":14,"43":[12,14,34],"44":29,"4400":14,"44254351324322":20,"445":14,"447304632028364":15,"4491421980451":[21,33],"4494897427831783":7,"4497316":35,"45":[7,14,34],"45114022285196":21,"457":15,"46":[2,32,34],"46000":14,"46130342316":[24,35],"46826882694954":15,"47":[12,14,32,34],"475":12,"475292852532866":34,"48":[14,21,32,34],"49":[12,14,20,34],"490":12,"490880975286938":[12,32],"494":23,"5":[4,7,9,11,12,13,14,15,16,18,19,20,21,23,24,25,29,32,33,34,35],"50":[2,13,14,18,19,20,23,29,33,34],"500":[14,25,29,33],"500000":[14,24,35],"506":23,"51":34,"5135882931757045":32,"5144388073261155":[12,32],"5176095282584723":15,"5176095282584724":15,"519":33,"52":4,"53":[14,33],"55":34,"5544912009711833":15,"558":14,"56":[14,20,29,33],"57":[14,34],"570106945770941":20,"5701069457709416":20,"5710":24,"5737801203754":[21,33],"58":20,"580":14,"59":14,"5901810768729":[21,33],"590296024616343":20,"5e6":24,"6":[7,8,9,11,12,13,14,15,19,20,21,23,24,29,32,33,34],"60":[4,14,20],"600":[14,18,33],"60395592743389":[20,29,33],"61530461":13,"618":[12,23,34],"62":[14,20,32,34],"6200":14,"622":23,"6249999":[24,35],"625":12,"6250000":24,"626":18,"6266448071368":20,"63":2,"634032391786285":[12,32],"635971381157268":15,"63781442427097":[21,33],"638":[12,34],"64":14,"640":[25,29,33],"65":34,"650":14,"651659697082211":15,"654":23,"656":14,"66":[18,19],"66022942788436":19,"661338147750939e":12,"665":23,"668653127136345":[12,32],"67":[15,34],"68":[7,9,18,29,33],"680099140842174":[12,32],"682411764618777":20,"69":14,"6946467384012":19,"69602421013684":29,"69842911":13,"7":[4,13,14,15,19,20,21,23,29,32,33,34],"70":[14,20,23,25,29,33,34],"700":24,"700237234889784":[12,32],"71":[20,23,34],"7197116134866537":15,"7257":14,"726131552870388":20,"73":14,"730":14,"74":[23,33,34],"74000":35,"7499999999999999":3,"75":[23,24,35],"75000":[14,24,35],"75000000":14,"75370030596123":2,"758375187638261":32,"76":14,"760000000000001":14,"762":32,"765139717874998":15,"7683073521514903":15,"7692307692307693":34,"77":23,"770562822512":24,"772":[24,35],"773":[24,35],"7777777777777777":15,"78":[21,33],"78222812913":[24,35],"78528000921442":34,"78711738886236":24,"789138050714946":34,"79":[14,34],"797235211809178":[20,33],"8":[7,9,13,14,15,18,19,20,21,23,24,29,30,32,33,34,35],"80":[13,14,23,25,29,33,34],"800":14,"8000":[24,34],"8050847457627118":34,"805695999999998":15,"80614234644133":24,"808":21,"8084945889684":18,"8110739983106":[24,35],"81255515896464":18,"813":21,"82":34,"8284271247461903":[8,32],"83":[7,9],"83200":14,"8333":[24,35],"8333333333333334":[14,34],"837":[18,33],"84":14,"840":[14,18,33],"848340302917789":15,"84861989932769":20,"85":[14,34],"850319828088736":20,"8544026261366":[18,33],"86000":14,"8670634479628":[21,33],"8695652173913043":34,"87":[14,19,21,33,34],"877804945158942":15,"880":14,"8823529411764706":34,"887604785075":35,"888960377059731e":16,"892036436905893":32,"8989191225476816":15,"9":[7,14,15,18,21,24,25,33,34],"90":[14,25,29,33],"900":14,"9000":[14,24,35],"90365729191992":32,"90625":34,"91":24,"9100":14,"9152542372881356":34,"9166666666666666":34,"9183673469387755":34,"92":[14,33],"920":14,"9200000000000004":14,"9210526315789473":34,"92136355097325":18,"92358063314975":[21,33],"9264705882352942":34,"9285714285714286":34,"93":14,"9310527835":35,"93248526934437":29,"9342105263157895":34,"93hall_distribut":13,"94":14,"940":[25,29,33],"9411764705882353":34,"947368421053":24,"9484536082474226":34,"95":[14,21,34],"95000257319708":[24,35],"9519230769230769":34,"9555555555555556":34,"957229385175":[24,35],"97044213580244":[21,33],"973":23,"98":[14,20],"9803921568627451":34,"99":[13,14,34],"9906261152138731":34,"994095842987605":32,"995771265226075":32,"997499999":[24,35],"997605188935892":20,"9976051931766445":[20,29,33],"99995914365099":32,"999999999999996":20,"boolean":13,"case":[2,4,5,6,8,9,12,13,14,19,25,27,34],"class":[2,3,4,5,6,15,29,31,34],"default":[2,3,4,5,6,12,13,19,20,26,27,34],"do":[2,3,5,6,9,11,12,13,14,26,34],"final":[19,34],"float":[2,3,4,5,6,7,8,9,11,12,13,15,16,18,19,20,21,23,24,25,26],"function":[2,4,5,6,9,11,12,13,14,15,16,19,20,21,23,24,26,27,29,32,33,35],"import":[7,8,9,14,15,20,24,29,32,33,34,35],"int":[2,3,4,5,6,7,8,9,11,12,13,15,18,19,20,23,25,26,27],"new":[2,3,4,5,6,9,13,14,19,20],"return":[2,3,4,5,6,7,8,9,11,12,13,14,15,16,18,19,20,21,23,24,25,26,33,34,35],"true":[2,3,5,6,9,11,12,13,14,16,20,23,24,26,27,33,34,35],"try":19,"var":[15,24],"while":[6,32],A:[2,3,4,5,6,7,8,11,12,13,14,19,20,21,23,24,27,32,34],And:[29,32,34],As:34,At:34,By:[5,12],For:[2,5,6,7,8,9,10,11,12,13,15,18,19,20,21,22,23,24,25,26,27,28,32,33,34],IS:[27,34],If:[2,3,4,5,6,8,9,11,12,13,14,15,18,19,20,21,23,24,25,26,27,33,34,35],In:[2,5,6,13,19,25,27,32,34,35],Is:6,It:[6,20,29,34],Its:34,No:26,Not:13,Of:34,On:[6,19,20,21],Or:[15,29,32,33],That:[5,6,12,13],The:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,31,34],Then:34,There:32,These:[11,12,14,32,33,34],To:[6,26,30,32,34],_0:12,_1:12,_5:19,_:[12,19,29,33,34],_d:19,_j:[6,12],_pdf:15,_pmf:15,_predecessor:[5,6],_successor:[5,6],_t:[19,20],abbrevi:[14,27],about:[5,23,34],abov:[5,20,27,29,34,35],abs_tol:13,absolut:[13,21],access:32,accord:[3,34],accordingli:3,account:[12,15,19,34],accumul:[3,34],accur:[11,24,32],accuraci:32,across:[19,26],act:19,action:[19,26],acycl:29,ad:[5,19,34],adapt:[13,16],add:[5,6,32],add_edg:5,add_edges_from_list:[5,14],add_nod:[5,14,32],add_predecessor:[5,6,14],add_successor:[5,6,32],addit:[14,24,35],adjac:[6,9],adjust:[4,14,15,19,34],advanc:[29,31],after:[4,19,26,34],again:[19,34],against:19,aggreg:6,ago:34,algorithm:[6,7,8,9,11,12,16,19,21,23,25,29,32,33,34],alia:6,all:[5,6,7,8,9,11,12,13,14,19,26,27,32,34],allow:[2,4,5,32,34],alpha:[3,20,21,24,26,34,35],alreadi:[5,9,14,34],also:[2,5,6,15,29,32,33],altern:[27,32,34,35],although:32,alwai:[6,12,34,35],ambigu:5,among:[5,34],an:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,18,19,20,21,22,23,24,25,26,27,28,29,32,33,34,35],analog:[19,26],analysi:21,ancestor:6,ani:[2,3,4,5,6,7,8,11,12,13,14,19,20,25,26,32,34],anyth:[5,9,14],api:[29,34],appear:[5,12,13,34],appl:[19,20],appli:5,applic:4,approach:[11,32],appropri:[2,3,4],approxim:[11,12,21,23,24,32,33,34,35],ar:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],arbitrari:[11,15,32,33,34,35],argmin:[12,13],argument:[2,3,4,5,6,11,13,15,24,32],aris:34,around:[2,19],arrai:[12,13,14,19,20,25,29,33],arreola:[24,35],arriv:[6,27,34],articl:29,ascend:13,asid:26,assembl:[5,6,14],assembly_3_stag:14,assign:[5,12,29],assum:[3,5,6,8,11,12,13,15,19,20,21,23,25,34,35],assumpt:29,atan:14,attain:[13,18,20,24],attribut:[2,3,4,5,6,9,12,13,32,34],attribute_dict:13,attributeerror:5,atyp:34,automat:[11,12],avail:[11,30,32],averag:[26,29,34],avoid:[5,19],awar:34,b:[5,13,14,15,16,20],back:21,backord:[6,18,21,26,27,33,34],backorders_by_successor:6,balanc:[4,14],bar:[11,15,19,20,24,26],base:[4,5,7,11,12,14,20,24,26,29,32,33,34,35],base_cycle_tim:18,base_stock_level:[4,5,7,11,14,20,24,29,32,33,34],basic:[12,27,29,31,33],beb:[4,14],becaus:[6,19,34],been:[2,3,4,5,6,7,9,15,27,34],befor:[3,4,6,9,13,34],began:34,begin:[2,3,12,19,34],being:[3,6,16,34],below:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],berk:[24,35],berkin:[24,35],bernoulli:15,best:[11,32],best_:[11,32],best_cost:[11,32],beta:[3,15,24,35],between:[6,18,34],beyond:[2,3],binomi:15,bisect:21,bo:[27,34],bool:[2,3,5,6,9,11,12,13,14,16,20,23,24,26,27],both:[13,15,20,21,29,32,33,34,35],bound:[8,12,13,15,16,19,32,34],bring:19,broader:32,brute:[11,32],bs:[4,5,14,29,32,34],buffer:19,bui:20,build:[5,13,14,26,29,32,34],build_node_data_dict:13,build_test_pack:14,built:[14,15,32,34],bullwhip:34,bump:19,c:[7,9,12,13,14,15,19,20,23,25,29,33],c_:20,c_star:[12,29,32],c_t:[20,25],c_ty:20,calcul:[2,3,4,6,7,12,13,15,18,19,20,21,23,24,26,33,34],call:[4,5,6,9,12,13,26,33],camera:14,can:[2,3,5,6,11,12,14,29,32,33,34,35],candid:32,cannot:[3,6,14,15,27,34],categori:34,caveat:6,cd:2,cdf:[2,13,15,20],cdot:[12,13,15,19,20,21,23,24],certain:[32,34],chain:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],chang:[2,3,5,6,12,13],change_dict_kei:13,check:[2,3,4,5,6,13,26],check_iterable_s:13,chen:[12,29,32,34],choos:15,ci:34,circuit_board:14,clark:[12,29,32],classic:29,classmethod:[2,3,4,5,6],clear:34,cliff:21,close:[26,34],closest:13,coars:32,code:[7,8,12,13,14,15,16,18,19,20,21,23,24,25,26,32,33,34,35],coeffici:[6,34],column:[19,27,34],columns_to_print:[27,34],com:13,combin:[11,34],come:13,commit:[7,8,9,29,32],common:34,commonli:34,compar:[5,6,34],comparison:13,complementari:[15,20,24],complet:[6,34],complex:[11,32],compon:11,comput:[21,23],computation:19,condit:[19,20,25],confid:[26,34],connect:5,consecut:[6,9,18],conserv:19,consid:[6,12,16,19,32,34],consist:[5,13,14,24,26,32,34],consistency_check:26,consol:[27,34],constant:8,construct:[5,34],contain:[2,3,4,5,6,7,8,9,11,12,13,14,15,16,18,19,20,21,23,24,25,26,27,29,32,33,34,35],continu:[2,13,15,20,21,33],continuous_loss:[15,24],continuous_second_loss:15,continuousreview:24,control:[32,34],converg:21,convert:[2,3,4,5,6,9,29,32],convex:32,convolut:13,convolv:13,convolve_mani:13,coordin:[11,32],copi:[2,3,4,5,6,9,13],correctli:9,correpond:12,correspond:[5,8,12,13,27,33,34],cost:[6,7,8,9,11,12,14,18,19,20,21,23,24,25,26,27,29,32,33,35],cost_matrix:19,costs_to_go:25,could:19,count:[6,13],cours:34,creat:[2,3,4,5,6,13,14,32],create_if_non:14,creation:34,cst:[7,8,9,29,32],cst_to_base_stock_level:7,csv:[27,34],csv_filenam:27,cumul:[2,6,27,34],current:[2,3,4,5,6,9,20,26,27,34,35],custom:[2,6,8,13,15,23,27],cycl:[5,26,33],d1:13,d2:13,d:[2,12,13,19,20,23,24,25,29,33,34,35],d_i:25,d_j:12,d_k:12,d_num:[12,32],d_rang:19,d_spread:19,d_t:20,d_val:[20,33],data:[0,5,6,8,9,12,13,14,26,27,29,31,32],data_dict:13,dataset:14,date:21,debug:27,decis:[6,26],deck:32,declar:[6,15],decreas:6,deep:[2,3,6],deep_equal_to:[5,6],deepli:[5,6],def:[15,34],default_valu:13,defin:[15,19,20,32],deliv:[6,35],delta:19,demand:[2,4,5,6,7,8,9,12,14,15,18,19,20,21,23,24,25,26,27,29,31,32,33,35],demand_bound_const:[8,9,14,32],demand_cumul:6,demand_distrib:[20,33],demand_distribut:2,demand_hi:23,demand_list:[2,34],demand_mean:[8,12,13,14,19,20,21,23,29,32,33],demand_met_from_stock:6,demand_met_from_stock_cumul:6,demand_pdf:[20,23],demand_pmf:[14,20,23,33],demand_r:[14,18,24,29,33,35],demand_sd:[14,19,20,21,23,29,33],demand_sourc:[0,1,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],demand_standard_devi:[8,12,32],demand_typ:[5,14,29,32,34],demandsourc:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],denot:[19,20,34],depend:[13,19,24],deriv:6,derived_demand_mean:6,derived_demand_standard_devi:6,descend:6,descent:[11,32],describ:[6,8,9,12,23],descript:[12,14,29],descrtipt:14,desir:[13,15,19],detail:[19,34],determin:[5,6,7,9,11,12,13,14,21,23,34],determinist:[2,14,24,34,35],deviat:[2,6,8,12,15,19,20,21,23,24,29,35],df:24,dh:24,dict:[2,3,4,5,6,7,8,9,11,12,13,14,15,20,26,32,33],dict_match:13,dict_to_chang:13,dictionari:[7,11,13,14,26,33],differ:[6,15,34,35],digraph:5,dimension:13,direct:[5,6,26,32],directli:[6,26,32,34],discount:[19,20],discount_factor:[14,19,20],discret:[2,11,12,13,14,15,19,20,23,32,33],discrete_loss:[15,24],discrete_second_loss:15,discretization_num:11,discretization_step:11,discuss:[12,19,34],displai:[11,26,29,31],disr:[27,34],disrupt:[3,6,14,24,26,27,29,31],disruption_prob:[3,14,24,34],disruption_process:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],disruption_r:[14,24,35],disruption_state_list:3,disruption_typ:[3,34],disruptionprocess:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],distrbut:20,distrib:15,distribut:[2,5,8,12,13,14,15,19,20,21,23,24,29,32,33,34,35],divid:6,dmf:[27,34],doc:15,docstr:[12,26,34],document:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,30,32,33,34,35],doe:[5,6,9,13,14,19,32,34],don:19,done:19,doubl:19,down:[3,12,13,24,26],download:34,downstream:[5,6,12,34],dp:[3,7,8,9,19,25,32,33],ds:2,due:[6,15,21,27,34],dump:26,dure:[3,6,34],dy:[15,21],dynam:[7,8,9,19,25,29,32,33],e2:13,e:[2,3,4,5,6,12,13,14,15,19,20,24,26,32,33,34],each:[2,3,5,6,7,8,9,11,12,13,14,16,19,21,25,26,27,32,33,34],earlier:34,earn:6,eb:[4,34],echelon:[0,4,5,6,7,8,9,11,12,14,18,19,20,21,23,24,25,26,27,29,31,34,35],echelon_:12,echelon_holding_cost:[6,12,14,29,32],echelon_inventory_level:6,echelon_inventory_posit:6,echelon_inventory_position_adjust:4,echelon_on_hand_inventori:6,echelon_to_local_base_stock_level:[5,29,34],econom:[8,18,24,29,33,35],economic_order_quant:[18,29,33],economic_order_quantity_with_backord:18,economic_production_quant:18,edg:[5,14,32,34],edge_list:5,edit:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],ef:26,effect:[3,34],effici:21,ehrhardt:[23,33],eil:[21,33],eipa:4,either:[5,8,11,12,15,19,20,24,32,33,35],element:[5,13,19,25],els:[14,15],empti:5,en:[6,13,16],encapsul:4,end:[3,6,11,12,13,16,19,27,34],englewood:21,ensur:13,ensure_dict_for_nod:13,ensure_list_for_nod:13,ensure_list_for_time_period:13,entir:[6,19,25],entri:[8,13],enumer:[11,32],environ:26,eoq:[0,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,19,20,21,22,23,24,25,26,27,28,29,30,31,32,34],eoq_with_additive_yield_uncertainti:[24,35],eoq_with_disrupt:[24,35],eoq_with_disruptions_cost:24,eoq_with_multiplicative_yield_uncertainti:[24,35],eoqb:[14,18,19,21,33],eoqd:[14,24,35],epq:[14,18,33],epsilon:21,eq:23,equal:[5,6,8,11,13,14,16,19,20,33,34],equat:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],equiv:34,equival:[6,26,27,34],equivalent_lead_tim:6,equivalentlli:34,erratum:[7,9],error:[13,26,34],estim:19,etc:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],evalu:[11,12,16,18,20,23,24,32,33],even:[4,5,6,9,14,27,32],event:[29,31],ever:6,everi:[2,9,11,13,18,19,25,34],evid:34,exact:[21,23,32,33,34],exactli:[6,9,12,32,35],exampl:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,30,31,32,33,35],example_3_1:14,example_3_8:14,example_3_9:14,example_4_1:14,example_4_1_network:14,example_4_2:14,example_4_3:14,example_4_4:14,example_4_7:14,example_4_8:14,example_5_1:14,example_5_8:14,example_6_1:[14,32,34],example_6_1_network:32,example_6_3:[8,14,32],example_6_3_network:32,example_6_5:[7,9,14,29,32],example_6_5_network:32,example_9_1:14,example_9_3:14,example_9_4:14,example_9_5:14,example_9_6:14,except:[2,3,4,5,6,12,15,26],exclud:6,execut:[13,19,26,32],exist:[13,14],exogen:34,exp:[15,20,33],expect:[7,8,9,11,12,19,20,21,23,24,29,32,33,34,35],expected_cost:[12,32],expected_holding_cost:12,expens:19,experi:32,explicit:[3,14,20,33],explicitli:[3,34],explor:21,expon:15,exponenti:[15,24],exponential_loss:15,exponential_second_loss:15,express:9,ext:[27,34],extens:29,extern:[2,4,6,7,8,27],external_inbound_cst:[8,9,14,32],external_outbound_cst:[8,9,14,32],f:[2,12,13,15,16,19,20,21,24,29,33,34],f_star:16,f_y:24,face:34,factor:[19,20],fail:[11,26],failur:15,fairer:32,fall:19,fals:[3,5,6,9,11,12,13,14,16,20,23,24,27,34],fast:13,faster:[13,19,32],featur:[29,31],federgruen:[21,23,33],fft:13,field:9,figur:14,figure_6_12:14,figure_6_14:14,file:[14,26,27,34],filenam:27,filepath:[14,27],fill:[5,6,9,13,26,27,34],fill_rat:6,find:[5,20,21,23,32],find_nearest:13,finish:34,finit:[14,19,29,31],finite_horizon:[0,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],finite_horizon_dp:[19,29,33],fire:14,first:[2,3,5,6,12,13,21,26,32,34],fix:[4,18,19,21,23,24,25,29,33,34],fixed_cost:[14,18,19,21,23,24,25,29,33],flexibl:34,follow:[3,5,6,8,12,19,24,27,32,33,34,35],forc:[11,32],force_relabel:9,form:[13,14,32,33],format:[27,34],former:[19,25],forthcom:14,forward:6,forward_echelon_lead_tim:6,fosct:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],found:[5,11,14],foundat:[15,19,20,34],four:34,fourier:13,fourth:19,fq:4,fr:[27,34],frac12:15,frac:[12,15,18,20,21,23,24],fraction:18,from:[2,3,4,5,6,7,8,9,13,14,15,16,19,20,24,25,26,27,29,32,33,35],from_dict:[2,3,4,5,6],from_index:5,frozen:[15,24],fundament:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],further:19,futur:24,fx:16,g:[2,3,4,7,12,14,18,19,20,21,23,24,25,26,34],g_:12,g_i:[19,20],g_j:12,g_t:[19,20],gamma:[15,19,20],gamma_loss:15,gamma_second_loss:15,gamma_tc_:20,gamma_tk_:19,gather:12,ge:[19,20,24],gener:[2,3,5,12,13,15,19,20,24,26,29,31,34],generate_demand:2,geom:[15,33],geometr:15,geometric_loss:15,geometric_second_loss:15,get:[2,3,6],get_node_from_index:[5,14,32,34],get_one_predecessor:6,get_one_successor:6,get_order_quant:4,give:[15,19,32,33],given:[2,3,4,5,6,7,11,12,13,15,16,18,19,20,21,23,24,25,26,27,33,34],glaze:14,global:32,go:[25,29,33],golden:[11,16,24],golden_section_search:16,good:[32,34],govern:[3,24],graph:7,grave:[7,9,29,32],greater:[9,19],group:[11,27,34],gsm:[7,8,9,14,29,31],gsm_helper:[0,2,3,4,5,6,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],gsm_serial:[0,2,3,4,5,6,7,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],gsm_to_ssm:9,gsm_tree:[0,2,3,4,5,6,7,8,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],guarante:[7,8,29,32],h:[6,8,12,18,19,20,21,23,24,25,29,33,34,35],h_:18,h_i:12,h_jx:12,h_n:18,h_nm_n:18,h_t:[19,20],h_termin:[29,33],ha:[2,4,5,6,9,12,13,14,15,16,27,29,34],hadlei:[21,33],hall:[13,21],hand:[6,34],handl:13,has_directed_cycl:5,hat:[12,18],have:[2,3,4,5,6,7,8,9,11,13,14,19,27,34,35],hc:[27,34],header:34,held:[6,27,34],helper:[0,2,3,4,5,6,7,8,9,10,11,12,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],here:[12,14,15,32],heurist:[11,12,18,23,32,33,34,35],hi:[2,13,14,23],hi_heur:34,hi_opt:34,high:[2,11,19],highest:9,hill:[15,19,20,34],histori:27,hn:24,hold:[6,8,9,12,18,19,20,21,23,24,25,27,29,33],holding_cost:[6,12,14,18,19,20,21,23,24,25,29,33,34],holding_cost_incur:6,horizon:[14,19,25,29,31],how:[5,32,34],howev:34,hp:[18,21],hq:[18,21,24],html:15,http:[13,15,16],hyperlink:34,i:[3,4,5,6,12,13,14,15,19,25,27,32,33,34],idea:12,ident:13,idi:[27,34],ifi:13,ignor:[5,6,8,9,11,12,13,14,15,19,20,23,24,25,27],ignore_state_var:14,il:[6,19,27,34],il_t:19,imager_assembl:14,imager_bas:14,immedi:[4,34],implement:[7,8,9,12,16,19,29,32,33],implic:34,improv:11,in_transit:6,in_transit_from:6,in_transit_holding_cost:6,in_transit_holding_cost_incur:6,in_transit_to:6,inaccur:32,inbound:[6,7,8,27,34],inbound_cst:7,inbound_disrupted_item:6,inbound_disrupted_items_aggreg:6,inbound_ord:6,inbound_order_pipelin:6,inbound_ship:6,inbound_shipment_pipelin:6,includ:[4,5,6,9,13,18,21,27,29,33,34],include_extern:6,increas:34,increment:26,incur:[6,27,34],ind:13,independ:[2,9],inderfurth:[8,32],index:[4,5,6,7,8,9,11,12,13,14,19,25,27,29,32,34],indic:[4,5,6,7,8,9,11,12,13,19,26,27,33],individu:[5,8,11,12,18,26,32],individual_fixed_cost:[14,18,33],inform:[32,34],infti:[12,15,24],initi:[2,3,4,5,6,11,19,25,26],initial_inventory_level:[6,14,19,26],initial_ord:[6,14],initial_ship:14,initial_solut:11,input:[9,32,34],instal:29,instanc:[0,2,3,4,5,6,7,8,9,10,11,12,13,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],instance_data:14,instance_descript:14,instance_nam:[14,27],instead:[4,6,12,14,15,32,34],insuffici:34,int_0:15,int_:15,int_r:21,int_x:15,integ:[2,9,12,13,15,19,20,21,23],integr:[13,15],interchang:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],intermedi:6,intern:[6,8,9,24],interpret:34,interv:[11,12,16,18,24,26,34],introduc:23,invalid:19,inventori:[0,4,5,6,7,8,9,11,12,14,15,18,19,20,21,23,24,25,26,27,29,31,35],inventory_level:6,inventory_polici:[5,6,14,29,34],inventory_posit:[4,6],io:[27,34],iopl:[27,34],ip:4,irwin:[13,15,19,20,34],irwin_hall_cdf:13,is_continuous_distribut:13,is_correctly_label:9,is_discrete_distribut:13,is_integ:13,is_iter:13,is_list:13,ispl:[27,34],issu:[14,19,26,32],item:[3,6,12,13,18,19,20,21,23,24,25,27,34],iter:[7,11,13,16,21],iterable_list:13,ithc:[27,34],its:[2,3,5,6,8,11,13,18,20,26,32,33,34],itself:[3,5,6,24],j:[12,19,20,34],joint:[18,33],joint_replenishment_problem_silver_heurist:[18,33],jointli:32,journal:[8,24],jr:[19,20],jrp:[14,18,33],json:[14,27],jsonpickl:14,just:[2,3,12,32,34],k:[5,8,12,13,18,19,21,23,24,25,29,33,35],k_:18,k_n:18,k_t:19,kd:24,keep:3,kei:[5,6,7,8,9,11,12,13,14,15,20],kept:34,keyerror:13,keyword:[2,3,4,5],know:[13,34],known:21,kwarg:[2,3,4,5,6],l2:15,l2_bar:15,l:[2,6,8,12,14,15,20,21,23,33,34],l_bar:15,l_i:6,label:[5,7,9,23,27,34],lambda:[16,18,21,24,32,34],lambda_:18,lambda_n:18,larg:34,larger:[12,13,19],larger_adjacent_nod:9,larger_adjacent_node_is_downstream:9,largest:[5,13,19],last:[5,13],later:[14,30,34],latter:[5,19,25,27],ldot:[8,12,13,19],le:[19,20,25],lead:[2,6,7,9,12,14,19,20,21,23,29,31],lead_tim:[2,6,12,13,14,20,21,32,33,34],lead_time_demand_distribut:2,learn:26,least:13,left:[12,15,20,21,23,24,25],left_half:20,lemma:24,len:13,length:[2,3,8,13,14,19,23,24,25],less:[6,15,16,19,20],let:13,level:[4,5,6,7,9,11,12,19,20,21,23,24,26,27,29,32,33,34,35],like:[4,6,19,29,32],lim_:12,limit:[12,23],line:11,line_search_tol:11,linear:[12,34],list:[2,3,5,6,7,8,11,12,13,14,18,19,23,25,26,27,32,34],literatur:[11,32,34],ln:15,lo:[2,13,14],lo_heur:34,lo_opt:34,load:[14,29,32,34],load_inst:[7,8,9,14,29,32,34],local:[5,6,7,8,9,16,29,32],local_bsl:7,local_holding_cost:[6,8,13,14,29,32,34],local_holding_cost_funct:[6,34],local_to_echelon_base_stock_level:[5,32],logist:24,lognorm:[14,15,20,33],lognormal_loss:15,longer:[14,29],loss:[15,20,21,24,33],loss_funct:[0,2,3,4,5,6,7,8,9,10,11,12,13,14,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],low:[2,11,19],lower:[12,13,15,16,19,23,32,34],ltd_lower_tail_prob:12,ltd_upper_tail_prob:12,m:[3,21,23,33,34],m_:18,m_i:6,m_n:18,made:[14,34],mai:[5,8,9,11,12,13,19,25,32,33,34],main:27,make:[4,6,13,32,34],manag:[7,9,12,15,19,20,21,23,34],mani:[6,34],manual:[14,34],manufactur:[7,9],markov:[3,34,35],markovian:3,match:[5,13,34],materi:[6,27,34],math:[14,15,19,20,24,33,34,35],mathbb:19,mathrm:12,mathscr:15,matric:19,matrix:19,matter:5,max:[6,13,15,19,34],max_max_replenishment_tim:[5,9],max_replenishment_tim:[5,9],maxim:[20,33],maximum:7,mcgraw:[15,19,20,34],mean:[2,5,6,7,8,12,13,14,15,19,20,21,23,24,25,26,29,32,34,35],mean_cost:[26,34],mean_heur:34,mean_opt:34,measur:[6,26],meio:[5,6,10,11,29,31,34],meio_by_coordinate_desc:[11,32],meio_by_enumer:[11,32],meio_gener:[0,2,3,4,5,6,7,8,9,10,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],member:32,messag:[11,13,16],met:[6,27,34],method:[2,4,5,6,11,15,23,32],middl:27,might:[5,6,13],min:[12,13,15,19],min_:[19,25],min_kei:13,min_of_dict:13,min_valu:13,minim:[16,18,19,20],minimum:[13,16,19],minu:[6,7],miss:[2,3,9,13],mix:[19,25],model:[7,8,12,14,24,29,32,33,34,35],modif:11,modifi:[9,20,25],modul:[0,1,10,22,28,29,32,33,34,35],more:[2,3,4,5,6,7,11,13,24,29,32,34],mosier:[23,33],most:[5,6,12,13,14,19,21,25,26,29],mostli:[26,27,34],move:34,mu:[2,8,12,14,15,18,19,20,21,23,24,29,33],mu_l:23,much:32,multi:[0,5,6,7,8,9,11,12,14,26,27,29,31,34],multiechelon:[12,34],multipl:[5,13,14,24,33,35],multistag:8,must:[5,6,8,9,11,12,13,15,19,20,23,25,32,34],mwor:5,mwor_system:[5,14],my_dist:15,my_exp:15,my_geom:15,my_nod:32,my_other_nod:32,myopic:[19,20],myopic_bound:19,myopic_cost:20,n1:32,n2:[15,32],n2_bar:15,n:[2,8,12,13,14,15,18,20,21,24,26,29,32,34],n_bar:15,name:[5,6,13,14,27,29,32,34],narrow:32,naval:24,nb:15,nbinom:15,ndarrai:[12,13,19],nearest:[2,12,13,19],necessari:[4,8,12],necessarili:[6,11,32],need:[6,7,9,12,13,34],neg:[6,15,23,27,34],negative_binomial_loss:15,negative_binomial_second_loss:15,neighbor:6,neighbor_indic:6,neither:13,ness:13,net:7,net_demand_mean:9,net_demand_standard_devi:9,net_lead_tim:7,network:[4,5,6,7,8,9,11,12,14,26,27,29,32,34],network_from_edg:[5,14,32,34],networkx:5,networkx_digraph:5,never:34,new_kei:13,new_nam:5,new_tre:9,newsvendor:[0,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,21,22,23,24,25,26,27,28,29,30,31,32,34],newsvendor_continu:[20,33],newsvendor_discret:[20,33],newsvendor_heurist:[12,32,34],newsvendor_norm:[20,29,33],newsvendor_normal_cost:[20,33],newsvendor_normal_explicit:[20,33],newsvendor_poisson:[20,33],newsvendor_poisson_cost:20,newsvendor_poisson_explicit:20,newsvendor_with_additive_yield_uncertainti:[24,35],newsvendor_with_disrupt:[24,35],next:[12,13,20,25,29,33,34],next_order_period:25,nj:21,nlt:7,node:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],node_index:7,node_indic:[5,7,11,13],node_order_in_list:[5,12,13,14,32,34],node_order_in_system:[5,12,14,29,32,34],nodestatevar:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],non:[3,6,13,19,20,23,32,33],none:[2,3,4,5,6,8,9,11,12,13,14,15,18,19,20,23,24,26,27,32,34],nonstationari:14,norm:[14,20,34],normal:[2,8,12,14,15,19,20,21,23,24,29,32,33,35],normal_loss:15,normal_second_loss:15,notat:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],note:[5,6,14,15,24,26,27,29,34],noth:[5,14],now:[32,34],np:[14,15,20],num_nod:[5,8,12,13,14,29,32,34],num_period:[13,14,19,25,26,27,29,34],num_retail:5,num_trial:[26,34],num_warehous:[5,14],number:[5,6,8,11,12,13,14,15,19,21,25,26,27,33,34],numer:[13,14,15,24,32,35],numpi:[14,26],o_i:34,obj_fcn:32,object:[2,3,4,5,6,8,9,11,12,13,14,15,20,24,26,32,33,34,35],objective_funct:[11,32],observ:[2,34],obtain:[4,29],obvious:32,occur:34,odi:[27,34],offload:13,often:34,old:[5,6],old_kei:13,old_to_new_dict:[5,6],oldest:21,omit:[2,3,4,5,11,12,14,27,32],omit_state_var:14,on_hand:6,on_ord:6,on_order_by_predecessor:6,onc:26,one:[2,3,4,5,6,7,9,13,15,21,26,32,34],onli:[2,3,4,5,6,14,24,32,33,34,35],oo:[27,34],op:[3,34],oper:[7,9,21,23],opt_cost:[8,9,29,32],opt_cst:[8,9,29,32],optim:[0,2,3,4,5,6,7,8,9,11,12,13,14,15,17,18,19,20,21,23,24,25,26,27,28,29,30,31,34,35],optimize_base_stock_level:[6,12,29,32,34],optimize_committed_service_tim:[6,8,9,29,32],option:[2,3,4,5,6,8,9,11,12,13,14,15,16,18,20,23,24,25,26,27,33],oq:[27,34],order:[3,4,5,6,12,13,15,18,19,21,23,24,25,26,27,29,33,34,35],order_lead_tim:[6,27,34],order_multipl:18,order_quant:[4,6,18,21,24,25,34],order_quantity_overrid:26,order_up_to_level:[4,19,23],org:[13,15,16],origin:[2,3,6,9,14],original_label:9,os:[27,34],other:[0,4,5,6,9,12,13,14,16,21,26,29,32,33,34],other_nod:32,other_part:14,otherwis:[3,5,6,12,13,14,15,19,20,23,26,27,34],oul_matrix:19,out:34,outbound:[6,7,8,27,34],outbound_disrupted_item:6,outbound_ship:6,output:[9,11,13,19,25,34],outsid:[12,19,26],over:[6,16,19,20,26],overag:33,overlap:34,overrid:[4,26],overview:[10,22,28],ow:[27,34],owmr:5,owmr_system:5,own:34,p:[2,6,7,9,12,13,14,15,18,19,20,21,23,24,27,29,33,34,35],p_t:[19,20],p_termin:[29,33],packag:[13,26,29],package_test_waf:14,page:[7,8,9,10,11,12,18,19,20,21,22,23,24,25,26,27,28,34],pair:13,paper:34,paramet:[2,3,4,5,6,7,8,9,11,12,13,14,15,16,18,19,20,21,23,24,25,26,27,29,32,33,34],parlar:[24,35],part:14,particularli:[11,32],pass:[5,13,32,33,34],path:[6,14,27],paus:[3,34],pd:24,pdf:[15,20],per:[2,3,6,7,8,11,12,16,18,19,20,21,23,24,25,26,29,32,34],perform:[6,9,12,18,19,20,24,26,32],period:[2,3,5,6,7,11,13,14,19,20,23,24,25,26,27,29,32,33,34],periods_to_print:[27,34],peterson:14,phi:[15,20],pi:20,pi_0:24,pi_down:3,pi_n:24,pi_up:3,pip:30,pipelin:[26,27,34],place:[3,4,6,13,27,34],placehold:[5,6],placement:[7,9],plot:12,plu:[6,13,21,33],pm:[19,26,34],pmf:[13,15,20,23,33],pn:[20,21],poi:15,point:[4,16,19,21,23,29,33,34],poisson:[2,14,15,20,21,23,33,34],poisson_loss:15,poisson_second_loss:15,pol:4,polici:[0,1,2,3,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,35],policy_typ:[5,14,32,34],posit:[4,6,19,27,34],possibl:[2,13,19,20,34],power:[23,33],ppf:[14,34],pqx:18,pre:9,precis:29,predecessor:[4,5,6,7,27,34],predecessor_index:[4,6],predecessor_indic:6,predecessor_nod:5,predict:[29,34],prentic:21,preprocess:9,preprocess_tre:[7,9],present:[12,13,14,24],press:21,pretti:[32,34],prevent:34,previou:21,primari:[9,26],primarili:[5,6],princeton:21,principl:32,print:[11,16,27,29,34],print_solut:11,prng:26,probabl:[2,3,12,13,15,19,20,24,33,34],problem:[5,6,7,8,12,14,18,19,20,21,23,24,25,29,31,32],problem_3_1:14,problem_3_22:14,problem_3_27:14,problem_3_29:14,problem_3_2b:14,problem_4_1:14,problem_4_29:14,problem_4_30:14,problem_4_31:14,problem_4_32:14,problem_4_3b:14,problem_4_7b:14,problem_4_8a:14,problem_4_8b:14,problem_5_1:14,problem_5_2:14,problem_5_3:14,problem_6_16:14,problem_6_1:14,problem_6_2a:14,problem_6_2a_adj:14,problem_6_2b:14,problem_6_2b_adj:14,problem_6_7:14,problem_6_8:14,problem_6_9:[7,14],problem_9_4a:14,problem_9_4b:14,problem_9_5:14,problem_9_8:14,problem_specific_data:[5,6],process:[3,6,8,9,34,35],process_waf:14,processing_tim:[6,8,13,14,32],produc:[32,34],product:[6,8,18,24,33,34],production_r:[14,18],profit:[20,33],program:[7,8,9,19,25,29,32,33],progress:[11,26],progress_bar:[11,26,34],proof:[19,20],propag:[2,3,6],properti:[2,5,6,21],provi:23,provid:[2,3,4,5,6,8,9,11,12,13,14,15,19,20,23,24,26,32,34,35],psi:24,purchas:[14,19,20,25,33],purchase_cost:[6,14,19,20,25,33],purchase_cost_next_p:20,pyke:14,pypi:30,python:[29,30,32],q:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,34,35],q_:19,q_eil:33,q_eoqb:33,q_eoqss:33,q_lf:33,q_n:18,qe:24,qh:21,quad:24,quantiti:[4,6,18,19,21,24,25,26,27,29,33,34,35],queri:4,quickli:32,quit:[11,32],r:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,34,35],r_eil:33,r_eoqb:33,r_eoqss:33,r_lf:33,r_q_cost:[21,33],r_q_cost_poisson:21,r_q_eil_approxim:[21,33],r_q_eoqb_approxim:[21,33],r_q_eoqss_approxim:[21,33],r_q_loss_function_approxim:[21,33],r_q_optimal_r_for_q:21,r_q_poisson_exact:[21,33],rais:[2,3,4,5,12,13,14,15,19,20,21,23,24,25,26],rand:11,rand_se:[26,29,34],random:[2,3,13,15,26],random_process_typ:[3,34],randomli:35,rang:[2,5,11,12,13,14,19,20,32,33,34],rare:6,rate:[6,15,27,29,34],rather:[4,5,6,13,15,29],raw:[6,27,34],raw_materi:14,raw_material_aggreg:6,raw_material_inventori:6,reach:6,read:[2,5,6],reason:19,recalcul:19,receipt:[3,6,34],receiv:[3,6,27,34],recent:[6,13,26],recoveri:[3,34],recovery_prob:[3,14,24,34],recovery_r:[14,24,35],recurs:[4,5,6],ref:34,refer:[10,22,28,29,30,31,32,33,35],reflect:34,reindex_all_state_vari:6,reindex_nod:5,reindex_state_vari:6,reinforc:26,rel:[5,6,11,13,32],rel_tol:[5,6,13],relabel:[7,9],relabel_nod:9,relabeled_tre:9,relat:16,relev:34,reliabl:13,remain:34,remov:[5,6],remove_nod:[5,6],remove_predecessor:6,remove_successor:6,reorder:[4,19,21,23,29,33],reorder_point:[4,19,21,23,34],replac:[6,14],replenish:[18,33],report:34,repres:[2,3,4,5,13,15,25,27,34],represent:[2,3,4,5,6,9],request:27,requir:[2,3,4,5,8,12,13,15,19,20,23,24,27,30,32],require_pres:13,research:[21,23,24],respect:[15,19,20,24,34],restart:[2,3,19],result:[6,15,19,27,29,31,33],retail:[5,14],retrev:14,return_list:13,return_valu:13,reus:16,rev:[27,34],revenu:[6,14,20,27,33,34],revenue_earn:6,revers:34,review:[14,21,23],revis:23,rework:29,rho:18,right:[12,13,15,20,21,23,24,25],rightarrow:12,risa:[24,35],rm:[27,34],rong:14,rong_atan_snyder_figure_1a:14,rong_atan_snyder_figure_1b:14,rong_atan_snyder_figure_1c:14,rosl:[6,14],rosling_figure_1:14,round:[2,12,13,18,19],round_dict_valu:13,round_to_int:[2,5,14],round_typ:[12,13],rout:6,row:[14,27,34],rp:[3,6,27,34],rq:[0,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,22,23,24,25,26,27,28,29,30,32,33,34,35],rule:5,run:[11,26,32],run_multiple_tri:[26,34],rv_continu:[2,13,15,20,24,33,35],rv_discret:[2,13,15,20,24,33,35],rv_frozen:13,s:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,34,35],s_5:19,s_echelon:5,s_heur:[12,32,34],s_heur_loc:34,s_i:34,s_j:12,s_local:5,s_opt:34,s_opt_loc:34,s_overbar:19,s_s_cost_discret:23,s_s_discrete_exact:[23,33],s_s_power_approxim:[23,33],s_spread:19,s_star:[12,29,32],s_star_loc:29,s_t:19,s_underbar:19,safeti:[7,8,9,21,33],safety_stock_level:7,sai:34,salvag:[20,33],salvage_valu:[14,20,33],same:[5,7,11,12,13,14,15,19,25,29,32,34],save:[14,16,27],save_inst:14,sc:[27,34],scalar:[19,25],scale:15,scarf:[12,29,32],scienc:[12,21,23,34],scipi:[2,14,15,20,24,33,34,35],scmo:14,scmo_jrp_ex:14,scmo_jrp_hw_1:14,scmo_jrp_hw_2:14,scmo_jrp_hw_3:14,scmo_ww_hw_c:14,sd:[15,24],search:[11,13,16,21,24,32],search_hi:[11,32],search_lo:[11,32],second:[13,15,21],section:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],section_search:16,see:[5,13,15,32,33],seed:[11,26],self:[4,6,15],sell:[20,33],sem:[26,34],sem_cost:[26,34],sem_heur:34,sem_opt:34,send:34,sens:34,sent:34,sequenc:[29,31],serial:[5,8,11,12,14,29,31,34],serial_3:32,serial_system:[5,12,14,29,32,34],serv:34,servic:[7,8,9,12,29,32],set:[2,3,4,5,6,7,8,11,12,13,16,19,20,23,24,26,27,29,32,34],set_myopic_cost_to:20,sever:[13,32],shang:[12,14,32,34],shang_song_17:14,shang_song_1:14,shang_song_25:14,shang_song_9:14,shape:15,share:18,shared_fixed_cost:[14,18,33],shen:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],shift:13,ship:[3,34],ship_to_final_assembl:14,shipment:[3,6,12,26,27,34],shipment_lead_tim:[6,14,27,29,32,34],shortcut:[27,34],shorter:29,should:[4,5,6,11,13,34],show:34,shown:34,si:7,siam:[19,20],sigma:[2,14,15,19,20,21,23,29,33],sigma_l:23,silver:[14,18,33],silver_jrp:14,sim:[0,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,27,28,29,30,32,33,34,35],sim_io:[0,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,28,29,30,32,33,34,35],sim_num_period:[11,32],sim_num_tri:[11,32],sim_rand_se:[11,32],similar:[13,26,29],similarli:[5,6],simpl:23,simpli:6,simul:[0,5,6,11,26,27,29,31,32],simultan:13,sinc:[6,11,12,14,32,34],singl:[0,5,7,11,14,16,18,19,20,21,23,24,25,29,31,34,35],single_stage_system:[5,14,34],singleton:[2,5,8,11,12,13,19,20,25,32],sink:[5,34],sink_nod:5,size:[13,34],skip:27,slightli:15,slot:[5,12,13],slow:[11,32],slower:32,small:32,smallest:[6,9,13,19,20],smilowitz:14,snippet:32,snyder:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],so:[2,3,6,9,20,32,34],soe:34,sold:20,solut:[7,11,12,18,19,20,21,23,24,32,33,34],solution_cost_from_base_stock_level:7,solution_cost_from_cst:7,solv:[7,11,12,18,19,20,21,23,24,25,29,32,33,35],some:[2,6,18,19,20,25,27,32,33],someth:34,sometim:[4,11,12,32],somewhat:34,song:[12,14,32,34],soon:34,sort:[5,13],sort_dict_by_kei:13,sourc:[2,3,4,5,6,7,8,9,11,12,13,14,15,16,18,19,20,21,23,24,25,26,27,34],source_nod:5,sp:[3,6,27,34],space:[13,19,32],special:13,specif:[5,6,8,12],specifi:[2,3,4,5,7,8,12,13,14,19,26,32,33,34],speed:[11,32],spp_jrp:14,sqrt:[14,18,21,23,24,34,35],ss:[0,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,24,25,26,27,28,29,30,32,33,34,35],ss_power_approx3:23,ssm:[9,12,14,29,31],ssm_serial:[0,2,3,4,5,6,7,8,9,10,11,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],ssm_tree:9,stack:32,stackoverflow:13,stage:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],standalon:[6,34],standard:[2,6,8,12,15,19,20,21,23,24,26,29,34,35],standard_devi:[2,14,29,32,34],standard_normal_loss:15,standard_normal_second_loss:15,start:[9,11,19,27,34],start_index:9,stat:[2,14,15,20,24,33,34,35],state:[3,4,6,14,19,26,27,34,35],state_var:6,state_vars_curr:6,statist:34,stdout:27,steadi:3,steady_state_prob:3,step:[26,34],still:[32,34],stochast:[12,14,19,21,29,31,32,34],stock:[4,5,6,7,8,9,11,12,14,20,21,24,26,27,29,32,33,34,35],stockout:[6,9,12,18,19,20,21,23,24,27,29,33],stockout_cost:[5,6,9,12,13,14,18,19,20,21,23,24,29,32,33,34],stockout_cost_funct:[6,34],stockout_cost_incur:6,stockout_fract:18,stockpyl:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,32,33,34,35],stockpyl_inst:14,stop:15,store:6,str:[2,3,4,6,13,14,26,27],straightforward:19,strateg:[7,9],string:[2,3,4,6,12,13,26,27,34],structur:[5,7,8,9,14,29,31,32],subclass:13,subject:[3,34],suboptim:19,subtract:[4,19],succesor:[27,34],success:15,successor:[5,6,27,34],successor_indic:6,successor_nod:5,suffici:34,suggest:19,suitabl:13,sum:[2,6,12,13],sum_:[12,15,18,21,23,24,25],sum_i:13,sum_ltd_lower_tail_prob:12,sum_ltd_upper_tail_prob:12,sum_of_continuous_uniforms_distribut:13,sum_of_discrete_uniforms_distribut:13,sum_of_discrete_uniforms_pmf:13,sum_of_discretes_distribut:13,suppli:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33],supplier:[3,4,6,8,24,27,35],supply_chain_network:[0,1,2,3,4,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],supply_chain_nod:[0,1,2,3,4,5,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],supply_typ:[5,6,14,34],supply_uncertainti:[0,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,25,26,27,28,29,30,32,33,34,35],supplychainnetwork:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,31,33,34,35],supplychainnod:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],support:[2,3,4,6,12,13,15,23,26,27,33,34,35],swap:34,system:[5,6,7,8,9,11,12,14,21,26,29,31,34],sytem:34,t:[3,18,19,20,21,24,25,29,33,34],tabl:[14,27,34],tail:12,take:[6,11,13,15,24,34],taken:14,tau:21,tc:[27,34],tell:[2,34],tend:[11,32],term:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],termin:[6,11,16,19,21],terminal_holding_cost:[14,19],terminal_stockout_cost:[14,19],test:[11,13,32],text:[12,15,18,19,20,24],textbook:[14,29],texttt:12,th:[5,8,12,13],than:[4,5,6,9,11,13,15,16,19,20,29,32,33,34],the_dict:[2,3,4,5,6,13],thei:[3,4,5,6,11,12,13,14,19,32,34],them:[3,13,29,32,34],themselv:[5,6],theoret:29,theori:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],thereaft:19,therefor:[2,6,34],theta:[25,29,33],theta_1:19,theta_:[19,25],theta_t:[19,25],thi:[2,3,4,5,6,9,11,12,13,14,15,16,19,21,26,27,32,34],thorough:21,those:[5,12,34],though:5,through:6,throughout:13,tight:24,tild:12,time:[2,6,7,8,9,12,13,14,18,19,20,21,23,24,25,26,29,31,32,33],tm_n:18,to_dict:[2,3,4,5,6],to_index:5,togeth:[5,13],tol:[11,16,21],toler:[5,6,11,13,16,19,21],too:19,topolog:[11,32],total:[6,19,26,27,29,34],total_cost:[19,29,34],total_cost_incur:6,tp:[3,34],traceback:13,track:3,transform:13,transit:[3,6,27,34],treat:[13,14],tree:[7,9,11,14,29,31],trial:[11,15,26,32],trivial:32,trunc_tol:19,truncat:[11,12,19,32],truncate_and_discret:11,truncated_discretized_valu:11,truncation_hi:[11,32],truncation_lo:[11,32],tupl:[5,24],turn:[12,32],tutori:[7,8,9,10,11,12,18,19,20,21,22,23,24,25,26,27,28,29,34],tutorial_meio:32,two:[5,6,13,15,19,34],type:[0,2,3,4,5,6,7,9,11,12,13,14,20,21,23,24,26,27,29,32,33,34,35],typeerror:13,typic:[2,3,4,5,6,32,34],u:[5,6,13,14,15],uc:2,ud:[2,14],uncertainti:[14,24,29,31,33],undefin:13,under:[12,21,23,29,32,33,34],underag:33,underlin:[6,12,19,20],uniform:[2,13,15,24,35],uniform_loss:[15,24],uniform_second_loss:15,unit:[6,8,12,18,20,21,24,34],univers:21,unless:[5,9,13,24],unlimit:6,unrecogn:27,unreli:6,unsold:20,until:[6,15,34],up:[3,4,12,13,14,19,23,24,29,33],upcom:34,updat:[3,5,6,26,34],update_disruption_st:3,upper:[12,13,15,16,19,23,32],uppper:19,upstream:[5,6,12,34],us:[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,25,26,27,28,29,30,32,33,34,35],use_poisson:[23,33],user:19,usual:[25,26],v3:30,v:20,valid:[5,19,26,34],validate_paramet:[2,3,4],valu:[2,3,4,5,6,7,8,9,11,12,13,14,15,16,19,20,21,23,24,25,26,27,33,34],valueerror:[2,5,12,13,14,15,19,20,21,23,24,25,26],var_nam:13,vari:33,variabl:[2,4,6,13,14,15,26,27,34],variant:[18,20,33],variat:19,varieti:34,variou:34,vector:19,veinott:[19,20],verbos:[11,16],veri:[32,34],version:[15,20,33],via:6,vs:13,w:26,wa:[6,9,14,27,34],wagner:[14,25,29,31],wagner_whitin:[0,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,24,26,27,28,29,30,32,33,34,35],wai:[6,8,15,32],want:33,warehous:[5,14],warn:[14,19,26],we:[6,14,15,19,29,32,33,34],weight:12,well:[3,6,11,20,27,32],were:34,wf:26,what:[26,29],when:[3,5,6,11,12,13,16,19,21,26,27,32,34],where:[4,5,6,13,15,18,19,20,21,23,24,34],whether:[5,6,9,13,26,34],which:[2,4,5,6,7,8,9,11,12,13,14,15,19,20,24,25,26,27,32,33,34],whitin:[14,21,25,29,31],whose:[5,6,13,33,34],wide:21,width:[11,16],wiki:[13,16],wikipedia:[13,16],willem:[7,9,29,32],wish:[19,32],within:[5,16,21],without:[11,12,13,19,33],word:13,work:[6,13],wors:[32,34],worth:34,would:[26,32,34],wrapper:[2,12],write:[14,27],write_csv:27,write_instance_and_st:27,write_result:[27,34],x:[2,12,13,15,16,18,19,24,34],x_1:[13,19],x_2:13,x_3:13,x_4:13,x_:19,x_i:13,x_n:13,x_new:13,x_num:[12,32],x_rang:19,x_star:16,xf:15,y:[7,12,15,19,20,21,23,24,34],yet:[6,27,34],yield:[14,24,29,31],yield_distribut:[24,35],yield_hi:14,yield_lo:14,yield_mean:[14,24,35],yield_sd:[14,24,35],you:[5,6,32,33,34,35],your:34,z:[15,19,23,24,34],z_:[20,21,26,34],zero:[6,20,27,33,34],zheng:[12,21,23,29,32,33,34],zip:[20,33],zipkin:[6,15,19,20,34]},titles:["API Documentation","Data Types","<code class=\"docutils literal notranslate\"><span class=\"pre\">demand_source</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">disruption_process</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">policy</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">supply_chain_network</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">supply_chain_node</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">gsm_helpers</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">gsm_serial</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">gsm_tree</span></code> Module","Multi-Echelon Inventory Optimization","<code class=\"docutils literal notranslate\"><span class=\"pre\">meio_general</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">ssm_serial</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">helpers</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">instances</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">loss_functions</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">optimization</span></code> Module","Other Modules","<code class=\"docutils literal notranslate\"><span class=\"pre\">eoq</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">finite_horizon</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">newsvendor</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">rq</span></code> Module","Single-Echelon Inventory Optimization","<code class=\"docutils literal notranslate\"><span class=\"pre\">ss</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">supply_uncertainty</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">wagner_whitin</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">sim</span></code> Module","<code class=\"docutils literal notranslate\"><span class=\"pre\">sim_io</span></code> Module","Simulation","Stockpyl","Installing Stockpyl","Tutorial","Multi-Echelon Inventory Optimization","Single-Echelon Inventory Optimization","Simulation","Supply Uncertainty"],titleterms:{"class":32,"function":34,The:[32,33,35],advanc:34,also:[7,8,9,10,11,12,18,19,20,21,22,23,24,25,26,27,28,34],api:[0,2,3,4,5,6,7,8,9,11,12,13,14,15,16,18,19,20,21,23,24,25,26,27],basic:34,content:[0,1,10,17,22,28,29,32,33,34,35],continu:34,convert:34,cost:34,custom:34,data:[1,34],demand:34,demand_sourc:2,displai:34,disrupt:[34,35],disruption_process:3,document:[0,29],echelon:[10,22,32,33],eoq:[18,33,35],event:34,exampl:[29,34],extern:34,featur:34,finit:33,finite_horizon:19,from:34,gener:32,gsm:32,gsm_helper:7,gsm_serial:8,gsm_tree:9,helper:13,hold:34,horizon:33,indic:29,instal:30,instanc:14,inventori:[10,22,32,33,34],lead:34,loss_funct:15,meio:32,meio_gener:11,modul:[2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18,19,20,21,23,24,25,26,27],multi:[10,32],multipl:34,newsvendor:[20,33,35],optim:[10,16,22,32,33],other:17,overview:[2,3,4,5,6,7,8,9,11,12,13,14,15,16,18,19,20,21,23,24,25,26,27],polici:[4,34],problem:[33,35],q:33,r:33,refer:[2,3,4,5,6,7,8,9,11,12,13,14,15,16,18,19,20,21,23,24,25,26,27,34],result:34,review:34,rq:21,run:34,s:33,see:[7,8,9,10,11,12,18,19,20,21,22,23,24,25,26,27,28,34],sequenc:34,serial:32,sim:26,sim_io:27,simul:[28,34],singl:[22,33],some:29,ss:23,ssm:32,ssm_serial:12,stochast:33,stockout:34,stockpyl:[29,30,31],structur:34,suppli:[34,35],supplier:34,supply_chain_network:5,supply_chain_nod:6,supply_uncertainti:24,supplychainnetwork:32,system:32,tabl:29,time:34,tree:32,trial:34,tutori:31,type:1,uncertainti:35,wagner:33,wagner_whitin:25,whitin:33,yield:35}})
\ No newline at end of file
diff --git a/src/stockpyl/sim.py b/src/stockpyl/sim.py
index aa642cc..1216153 100644
--- a/src/stockpyl/sim.py
+++ b/src/stockpyl/sim.py
@@ -130,7 +130,6 @@ def initialize(network, num_periods, rand_seed=None):
 	"""Initialize the simulation:
 
 		* Check validity of the network
-		* Initialize ``network.period`` to 0
 		* Initialize state and decision variables at each node
 		* Set the numpy PRNG seed
 		* Set network.period to None (will be set to 0 in first call to :func:`stockpyl.sim.step`)
@@ -163,9 +162,6 @@ def initialize(network, num_periods, rand_seed=None):
 
 	# INITIALIZATION
 
-	# Initialize time period.
-	network.period = 0
-
 	# Check that the network doesn't contain a directed cycle.
 	if network.has_directed_cycle():
 		raise ValueError("network may not contain a directed cycle")