Efficient solution of a multi-commodity, two-stage distribution problem with constraints on assignment of customers to distribution centres

A two-stage, distribution-planning problem is addressed. Customers are to be served with different commodities from a number of plants, through a number of intermediate distribution centres (DCs). The possible locations for the DCs are given. For each location, there is a fixed cost for opening the DC concerned, as well as an operating cost and a maximum capacity. The demand of each customer for each commodity is known, as well as shipping costs throughout. There are also two additional important requirements. First, each customer must be served with all the products it requires from a single distribution centre. Secondly, it must be possible to ascertain the plant origin of each product quantity delivered. The objective is to choose the locations for opening DCs such that the total cost is minimised. The problem is modelled as a mixed-integer-programming problem and solved by branch and bound. Lower bounds are calculated through a series of structural transformations. Much of the power of the solution scheme also stems from frequent generation of good upper bounds. Results of extensive computational experiments are given and discussed.