A Decomposition Based Procedure for Production Scheduling in Job-Shops with Negligible Setup Times

Abstract

In short term planning of production in a discrete parts manufacturing system, a major problem is to decide on the maximum number of prespecified items that can be produced with limited shared resources, when all the items have a demand dependence in the form of bill-of- materials. The inventory carrying costs and the variation in the unit production costs from period to period become relatively unimportant in case of short planning horizons (such as one month, with periods taken to be one shift). When the total number of interacting items (such as raw materials, semifinished parts, subassemblies, finished goods, etc. ) is in the order of thousands, with considerable number of shared resources (such as machines, work centres, etc. ), the resulting model has a very large number of constraints and variables. Inclusion of the setup costs (or setup times), because of the introduced nonconvexity, makes the solution of the mathematical program infeasible from practical and computational viewpoint for short term planning purposes. Even the exclusion of the setup costs results in a large scale linear program.