Transportation problem: Construction of starting solution 1

Transportation problem: Find an initial solution

Introduction

The transportation problem is a general problem for every company, especially in logistics, to get a balance between supply and demand quantity. That means, you have j locations which need the product x and i locations which could send it to each of these. The supply quantity is declared by the variable ai, the quantity of demand by the variable bj. A necessary condition for this is that the total supply is equal to the total demand. Furthermore the problem consists of an allocation of the quantity in a cost minimal way. That shows basically the theoretical problem.

Mathematical formulation of a general transportation problem

ai : supply quantity at location I (i=1,…,m)
bj : demand quantity at location j (j=1,…,n)
cij :transportation cost per unit from supply location i to demand location j
xij : transportation quantity from i to j