Handling soft constraints in hoist scheduling problems: the fuzzy approach

The Hoist Scheduling Problem (HSP) deals with the scheduling of hoists that move products between tanks in electroplating facilities that perform chemical surface treatments. In HSP, the gradual effect of soaking times (operation duration in tanks) on the quality of treatment can be represented by means of fuzzy sets: the satisfaction degree in a fuzzy interval models a quality evaluation of the chemical treatment. When temporal bounds are required, an implicit relaxation of these flexible constraints can thus be performed so as to meet the due-date. When the objective is rather a minimization of the makespan, a bi-criteria decision problem has to be dealt with that involves both the quality and the line throughput optimization. Rather than an aggregation of the two evaluations under the form of a single criterion, we propose a decision-support approach that quickly converges to a good trade-off between the two criteria.