Exploiting process plan flexibility in production scheduling: A multi-objective approach

When solving a product/process design problem, we must exploit the available degrees of freedom to cope with a variety of issues. Alternative process plans can be generated for a given product, and choosing one of them has implications on manufacturing functions downstream, including planning/scheduling. Flexible process plans can be exploited in real time to react to machine failures, but they are also relevant for off-line scheduling. On the one hand, we should select a process plan in order to avoid creating bottleneck machines, which would deteriorate the schedule quality; on the other one we should aim at minimizing costs. Assessing the tradeoff between these possibly conflicting objectives is difficult; actually, it is a multi-objective problem, for which available scheduling packages offer little support. Since coping with a multi-objective scheduling problem with flexible process plans by an exact optimization algorithm is out of the question, we propose a hierarchical approach, based on a decomposition into a machine loading and a scheduling sub-problem. The aim of machine loading is to generate a set of efficient (non-dominated) solutions with respect to the load balancing and cost objectives, leaving to the user the task of selecting a compromise solution. Solving the machine loading sub-problem essentially amounts to selecting a process plan for each job and to routing jobs to the machines; then a schedule must be determined. In this paper we deal only with the machine loading sub-problem, as many scheduling methods are already available for the problem with fixed process plans. The machine loading problem is formulated as a bicriterion integer programming model, and two different heuristics are proposed, one based on surrogate duality theory and one based on a genetic descent algorithm. The heuristics are tested on a set of benchmark problems.