The economic lot scheduling problem: A pure genetic search approach

Abstract

The economic lot scheduling problem (ELSP) is the challenge of accommodating several products to be produced on a single machine in a cyclical pattern. A solution involves determining the repetitive production schedule for N products with a goal of minimizing the total of setup and holding costs. We develop the genetic lot scheduling (GLS) procedure. This method combines an extended solution structure with a new item scheduling approach, allowing a greater number of potential schedules to be considered while being the first to explicitly state the assignment of products to periods as part of the solution structure. We maintain efficient solution feasibility determination, a problematic part of ELSP solution generation and a weakness of several other methods, by employing simple but effective sequencing rules that create “nested” schedules. We create a binary chromosomal representation of the new problem formulation and utilize a genetic algorithm to efficiently search for low cost ELSP solutions. The procedure is applied to a benchmark problem suite from the literature, including Bomberger's stamping problem [Bomberger, A dynamic programming approach to a lot scheduling problem. Management Science 1966; 12:778–84], a problem that has been under investigation since the mid 1960's. The genetic lot scheduling procedure produces impressive results, including the best solutions obtained to date on some problems. Scope and purpose The need to utilize a single facility to produce several items is a common situation. We study the fundamental form of this situation, the economic lot scheduling problem (ELSP). The ELSP involves determining the minimal cost production schedule for several items that must be produced on a single machine while meeting all demands for each product. Setup costs and times are incurred each time the machine is changed (setup) to produce a different item. Holding costs are incurred based on the average amount of an item held in inventory. We must determine how much of each item should be made in each production run as well as the order of production. Examples of ELSP situations include producing several different colors of paint on the same equipment, and producing several types of stamped metal parts with the same stamping press. Since the ELSP is NP-complete, research, dating back to the 1950's, has focused on developing efficient heuristics that yield quality solutions. Our purpose is to develop an efficient heuristic search procedure for the ELSP that addresses shortcomings of previous methods. We present an extended and more definitive solution structure than previous ELSP methods, one that allows a direct mapping of solution parameters to an implementable production schedule. In addition, we address solution feasibility testing issues and structure our problem formulation in a manner that allows efficient search via a genetic algorithm (GA). We create a non-hybridized GA-based procedure that produces ELSP solutions of excellent quality, in some cases the best solutions to date.