Technical Note - A Production-Scheduling Problem with Batch Processing

This note considers a multiple-facility, multiple-product, production-scheduling problem with backordering over a finite planning horizon that consists of discrete production periods during each of which at most one product can be assigned to each facility. Product demands in each period are assumed to be known but not necessarily the same in all periods. The problem objective is to determine an assignment of products to facilities that meets all product demands on a first-come, first-served basis and minimizes the sum of production, inventory, and backordering charges over the horizon. This problem is formulated as a linear, mixed integer program and then transformed into an all-integer program that can be solved using any of the very efficient algorithms for finding minimal-cost network flows.