A Network Approach to a Multi-Facility, Multi-Product Production Scheduling Problem Without Backordering

A multi-product, multi-facility production scheduling problem is considered over a finite planning horizon. The horizon consists of discrete production periods during each of which at most one product can be assigned to each facility. Product demand rates are assumed to be constant over a period but not necessarily identical in all periods. All demands must be met without allowing backorders. The problem objective is to determine an assignment of products to facilities over the horizon which minimizes the sum of production and inventory carrying charges. The problem is formulated as a network flow problem for which efficient solution procedures are known. However, for an important special case a single pass algorithm is given which is more efficient than the standard flow algorithms.