NewsvendorModel.jl

This is a lightweight and simple Julia package for modeling and solving newsvendor problems.

Setup

NewsvendorModel.jl requires an installation of Julia (can be downloaded from the official website). You can install NewsvendorModel.jl like any other Julia package using the REPL as follows:

julia> import Pkg
julia> Pkg.add("NewsvendorModel")

After installation, it can be loaded with the usual command.

julia> using NewsvendorModel

Moreover, you need to load the Distributions.jl package.

julia> using Distributions

Usage

1. Define a model with the function nvm = NVModel(cost, price, demand) using the following required arguments:
   • unit production cost
   • unit selling price
   • demand distribution, which can be any choosen from the Distributions.jl package
2. Solve for optimal quanitity and obtain key metrics with the solve(nvm) function.

Note that additional keyword arguments can be passed in Step 1: salvage value and holding cost of left-over inventory, substitute profit obtained from serving a lost customer with an alternative, backorder penalty from an unserved customer, fixcost of the operations, a lower quantity bound q_min, and an upper quantity bound q_max.

Moreover, it is possible to obtain the unrounded optimal quantity by passing rounded=false in Step 2. For more details go to the documentation.

Example

Consider an example with

• unit cost = 5
• unit price = 7
• demand that draws from a normal distribution with
  • mean = 50
  • standard deviation = 20

Define the model and store it in the variable nvm as follows:

julia> nvm = NVModel(demand = Normal(50, 20), cost = 5, price = 7)

Julia shows the model data:

Data of the Newsvendor Model
 * Demand distribution: Normal{Float64}(μ=50.0, σ=20.0)
 * Unit cost: 5.00
 * Unit selling price: 7.00

Next, you can solve the model and store the result in the variable res like so:

julia> res = solve(nvm)

This gives the following output:

=====================================
Results of maximizing expected profit
 * Optimal quantity: 39 units
 * Expected profit: 52.41
=====================================
This is a consequence of
 * Cost of underage:  2.00
   ╚ + Price:               7.00
   ╚ - Cost:                5.00
 * Cost of overage:   5.00
   ╚ + Cost:                5.00
 * Critical fractile: 0.29
 * Rounded to nearest integer: true
-------------------------------------
Ordering the optimal quantity yields
 * Expected sales: 35.34 units
 * Expected lost sales: 14.66 units
 * Expected leftover: 3.66 units
-------------------------------------

Moreover, you have stored the result in the varial res. Reading the data from the stored result is straight-forward:

julia> q_opt(res)
39

julia> profit(res)
52.687735385066865

Analogously, underage_cost(res), overage_cost(res), critical_fractile(res), rounded(res), sales(res), lost_sales(res), leftover(res), read the other information the stored in res. The model that was solved can be retrieved with nvmodel(res).