An heuristic algorithm for a multi-product, single machine capacitated production scheduling problem

Abstract

This paper develops a technique for solving a capacitated production scheduling problem representative of a paper forming manufacturing process. The process involves equipment set ups for which down time has both fixed and variable components. An objective of minimizing the total time required to produce given orders for each of the products is considered. The scheduling problem may be characterized as a non-linear, integer, optimization problem. While there is a variety of literature available concerning optimization and scheduling theory, very little of it is directly applicable to the problem investigated here. The algorithmic methods (and associated computer programs) that were used in this research were developed specifically to solve these problems in reasonable times. The proposed algorithm is shown to generate production schedules that exceeded the true optimal by no more than 5%. Scope and purpose This paper develops an algorithmic approach for solving a particular capacitated production scheduling problem that appears in paper forming and other industries employing similar manufacturing processes. Typical instances of the problem are so difficult (over 500 trillion possible schedules for seven products) as to be unsolvable by exact methods or current commercial software. This paper characterizes an heuristic algorithm capable of solving the problem in a reasonable amount of time. The heuristic algorithm is validated experimentally by comparing the heuristic solutions to those obtained with complete implicit enumeration on small test problems adapted from actual problem instances occurring at a company employing paper forming processes. This paper discusses algorithmic and heuristic approaches to solving a particular large scheduling problem. It also deals with computer implementations of and experimentation with these algorithms.