Integral Approaches to Integrated Scheduling

Abstract

integration to achieve computational performance. We reconsider the widely used models and representations for production scheduling problems, we review optimization objectives and we discuss and propose efficient solution approaches to the production scheduling problem. Traditionally, machines are considered to be the only constraining resources when solving a production scheduling problem. This representation although resulting in high mathematical complexity, does not reflect the real problem. Many other constraining resources are needed in a production setting. Among these are material handling resources, buffers, route segments and intersections on a shop floor, labor, tools, pallets, fixtures and energy. Rich formulations considering these resources were presented in the literature together with corresponding solution approaches. These formulations are frequently referred to as the integrated scheduling problem. We provide an overview of these formulations within a proposed framework that builds on special characteristics of the different resources needed. Objective functions guiding optimization are also revisited for relevance analysis. Moreover, a generic cost function integrating different components is proposed. It unifies and complements, in some cases, most of the objective functions proposed in the literature. This rich picture is not without cost. The corresponding formulations result into very high mathematical complexity and exact solutions become difficult. Literature analysis as well as our research in this area reveals the importance of integral approaches to tackle such problems. Integral approaches may combine different methodologies whether at the level of the algorithm development subsuming one method into another or at the level of solvers cooperation for sharing information or at other levels of integration. Among methodologies considered and being integrated together are mathematical programming, constraint programming and metaheuristics. An integration scheme is proposed and performance of approaches is analyzed. The high cost of integration suggests a prudent approach to the integrated scheduling problem. Resources to integrate, objectives to consider and methodologies to use remain questions to answer according to the industrial reality studied. We conclude with a proposition of a methodology for diagnosis of a scheduling problem that allows tackling the problem, at first, by the most appropriate formulation. This methodology proposes