Scheduling Problem

Scheduling has been a popular area of research during the past four decades. Its object is to determine the sequence for processing jobs on a given set of machines. The need for scheduling arises from the limited resources available to the decision-maker. Researchers have studied this problem from many different perspectives. To satisfy reality, we consider the processing times as fuzzy numbers. To the best of our knowledge, scheduling with learning effects and fuzzy processing times on parallel machines has never been studied. The possibility measure will be used to rank the fuzzy numbers. Two heuristic algorithms, are proposed. Computational experiments have been conducted to evaluate their performance. We have developed memetic algorithms (MA, a hybrid genetic algorithm) by combining a genetic algorithm and the greedy heuristic using the pairwise exchange method and the insert method, the simulated annealing algorithm, the genetic algorithms, the heuristic algorithms, and the branch-and-bound algorithm to solve the the scheduling problem. Preliminary computational experiments demonstrate the efficiency and performance of the proposed memetic algorithm.