Fuzzy modeling of single machine scheduling problems including the learning effect

Abstract

In this chapter, we consider the single machine scheduling problem including uncertain parameters and position based learning effect with the aim to minimize the weighted sum of jobs completion times. Due to the ill-known quantities within the model, the determination procedures of optimal solutions in the conventional way is not an affordable task and more elaborated frameworks should be developed. In this context, we introduce two solution approaches for the proposed fuzzy scheduling problem in order to obtain an exact or a satisfactory near optimal solution. The first approach is based on the extension of the well-known Smith’s rule resulting in a polynomial algorithm with a complexity O(nlog(n)). However, a severe constraint on jobs (fuzzy agreeability concept) should be satisfied in this case. The second approach based on optimization methods is built upon the assumption of unequal fuzzy release dates in addition to the absence of fuzzy agreeability constraint. Three trajectory based metaheuristics (Simulated annealing, taboo search and kangaroo search) are implemented and applied to solve the resulting problem. For the proposed methods throughout the chapter, several numerical experimentations jointly with statistical deductions are provided.