Scheduling to minimize expected completion time in flowshop plants with uncertain processing times

Abstract We present a Mixed Integer Linear Programming (MILP) model for the scheduling of flowshop plants with uncertain processing times in order to minimize the expected completion time. The uncertainty in processing times, modeled using discrete probability density functions, results in a combinatorially explosive state-space. Model sizes and solution times increase exponentially with the number of scenarios and multiperiod formulations cannot handle even modestly large problems. We use an activity network to represent a schedule, which enables us to derive an analytical expression for the expected completion time. The nonlinear optimization model is reformulated as an MILP using exact linearization techniques to yield rigorous optimal schedules. Numerical results show that the solution times for the proposed method are several orders of magnitude smaller than those for multiperiod models.