Theory and Methodology Formulating and solving production planning problems (original) (raw)

Production planning problems frequently involve the assignment of jobs or operations to machines. The simplest model of this problem is the well known assignment problem (AP). However, due to simplifying assumptions this model does not provide implementable solutions for many actual production planning problems. Extensions of the simple assignment model known as the generalized assignment problem (GAP) and the multi-resource generalized assignment problem (MRGAP) have been developed to overcome this diculty. This paper presents an extension of the (MRGAP) to allow splitting individual batches across multiple machines, while considering the eect of setup times and setup costs. The extension is important for many actual production planning problems, including ones in the injection molding industry and in the metal cutting industry. We formulate models which are logical extensions of previous models which ignored batch splitting for the problem we address. We then give dierent formulations and suggest adaptations of a genetic algorithm (GA) and simulated annealing (SA). A systematic evaluation of these algorithms, as well as a Lagrangian relaxation (LR) approach, is presented. Ó 0377-2217/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII S 0 3 7 7 -2 2 1 7 ( 9 7 ) 0 0 3 9 4 -9