Scheduling optimization under uncertainty - an alternative approach

The prevalent approach to the treatment of processing time uncertainties in production scheduling problems is through the use of probabilistic models. Apart from requiring detailed information about probability distribution functions, this approach also has the drawback that the computational expense of solving these models is very high. In this work, we present a non-probabilistic treatment of scheduling optimization under uncertainty, where we describe the imprecision and uncertainty in the task durations using concepts from fuzzy set theory. We first provide a brief review on the fuzzy set approach, comparing it with the probabilistic approach. We then present mixed integer linear programming (MILP) models derived from applying this approach to two different problems-flowshop scheduling and new product development process scheduling-and show how they can be used to predict most likely, optimistic and pessimistic values of metrics such as the makespan. Results indicate that these MILP models are computationally tractable for reasonably sized problems. We also describe tabu search implementations in order to handle larger problems. (C) 2002 Elsevier Science Ltd. All rights reserved.