Warehouse Location Problem

In the Warehouse Location problem (WLP), a company considers opening warehouses at some candidate locations in order to supply its existing stores.

Each possible warehouse has the same maintenance cost, and a capacity designating the maximum number of stores that it can supply.

Each store must be supplied by exactly one open warehouse. The supply cost to a store depends on the warehouse.

The objective is to determine which warehouses to open, and which of these warehouses should supply the various stores, such that the sum of the maintenance and supply costs is minimized.

See this page for more details.

Input data

We consider here the following input (in java):

// number of warehouses
int W = 5;
// number of stores
int S = 10;
// maintenance cost
int C = 30;
// capacity of each warehouse
int[] K = new int[]{1, 4, 2, 1, 3};
// matrix of supply costs, store x warehouse
int[][] P = new int[][]{
    {20, 24, 11, 25, 30},
    {28, 27, 82, 83, 74},
    {74, 97, 71, 96, 70},
    {2, 55, 73, 69, 61},
    {46, 96, 59, 83, 4},
    {42, 22, 29, 67, 59},
    {1, 5, 73, 59, 56},
    {10, 73, 13, 43, 96},
    {93, 35, 63, 85, 46},
    {47, 65, 55, 71, 95}};

mathematical model>>