Computationally efficient solution of a multiproduct, two-stage distribution-location problem

A two-stage distribution planning problem, in which customers are to be served with different commodities from a number of plants, through a number of intermediate warehouses is addressed. The possible locations for the warehouses are given. For each location, there is an associated fixed cost for opening the warehouse concerned, as well as an operating cost and a maximum capacity. The demand of each customer for each commodity is known, as are the shipping costs from a plant to a possible warehouse and thereafter to a customer. It is required to choose the locations for opening warehouses and to find the shipping schedule such that the total cost is minimized. The problem is modelled as a mixed-integer programming problem and solved by branch and bound. The lower bounds are calculated through solving a minimum-cost, multicommodity network flow problem with capacity constraints. Results of extensive computational experiments are given.