Problem statement

Describes a model using piecewise linear functions.

Assume that a company must ship cars from factories to showrooms. Each factory can supply a fixed number of cars, and each showroom needs a fixed number of cars. There is a cost for shipping a car from a given factory to a given showroom. The objective is to minimize the total shipping cost while satisfying the demands and respecting supply.

In concrete terms, assume there are three factories and four showrooms. Here is the quantity that each factory can supply:

supply0 = 1000
supply1 = 850
supply2 = 1250

Each showroom has a fixed demand:

demand0 = 900
demand1 = 1200
demand2 = 600
demand3 = 400

Let nbSupply be the number of factories and nbDemand be the number of showrooms. Let x ij be the number of cars shipped from factory i to showroom j . The model is composed of nbDemand + nbSupply constraints that force all demands to be satisfied and all supplies to be shipped. Thus far, a model for our problem looks like this:

Minimize

subject to