A genetic solution based on lexicographical goal programming for a multiobjective job shop with uncertainty

In this work we consider a multiobjective job shop problem with uncertain durations and crisp due dates. Ill-known durations are modelled as fuzzy numbers. We take a fuzzy goal programming approach to propose a generic multiobjective model based on lexicographical minimisation of expected values. To solve the resulting problem, we propose a genetic algorithm searching in the space of possibly active schedules. Experimental results are presented for several problem instances, solved by the GA according to the proposed model, considering three objectives: makespan, tardiness and idleness. The results illustrate the potential of the proposed multiobjective model and genetic algorithm.