Fuzzy optimization-based scheduling of identical machines with possible breakdown

Underlying each production system are activities fraught with uncertainty; for example, uncertain future demand, machine breakdowns, and processing time estimates for one-of-a-kind parts. These uncertain events can cause any detailed schedule to become outdated, and the effects may propagate throughout the schedule, affecting product delivery dates. Scheduling algorithms considering future uncertainties could improve the quality of schedules and, as a result, smooth the production of the system. As a step towards incorporating uncertainties in the scheduling consideration, this paper presents a fuzzy optimization methodology for scheduling single operation parts on identical machines with possible breakdowns. A fuzzy optimization formulation is first developed. A Lagrangian relaxation technique is used to decompose the problem into part-level subproblems and a fuzzy membership subproblem. The Lagrange multipliers are then updated by using a subgradient method. To evaluate the performance of the resulting algorithm in a dynamic environment, fuzzy simulation is developed. Preliminary testing results show that, with possible machine breakdowns, this algorithm outperforms the deterministic one