Abstract
Recently, several heuristics have been interested in scheduling problems, especially those that are difficult to solve via traditional methods, and these are called NP-hard problems. As a result, many methods have been proposed to solve the difficult scheduling problems; among those, effective methods are the tabu search algorithm (TS), which is characterized by its high ability to adapt to problems of the large size scale and ease of implementation and gives solution closest to the optimum, but even though those difficult problems are common in many industries, there are only a few numbers of previous studies interested in the scheduling of jobs on unrelated parallel machines. In this paper, a developed TS algorithm based on lower bound (LB) and exact algorithm (EA) solutions is proposed with the objective of minimizing the total completion time (makespan) of jobs on nonidentical parallel machines. The given solution via EA was suggested to enhance and assess the solution obtained from TS. Moreover, the LB algorithm was developed to evaluate the quality of the solution that is supposed to be obtained by the developed TS algorithm and, in addition, to reduce the period for searching for the optimal solution. Two numerical examples from previous studies from the literature have been solved using the developed TS algorithm. Findings show that the developed TS algorithm proved its superiority and speed in giving it the best solution compared to those solutions previously obtained from the literature.
Highlights
Scheduling plays an essential role in the management of production. e scheduling dictates what will be done, where, and with what resources [1]
We proposed an exact algorithm to be used as a base of comparison to measure the effectiveness of the two phases. en, the second phase established a lower bound that judges the optimality of the heuristic algorithm
Mathematical optimization techniques are suitable only for small-scale problems; they have limited applications in the case of a large-scale problem. us, the study efforts have focused on heuristic approaches
Summary
Scheduling plays an essential role in the management of production. e scheduling dictates what will be done, where, and with what resources [1]. E issue discussed in this paper is that independent jobs should be scheduled on nonidentical parallel machines to minimize the total completion time of the job “makespan.” ere are n separate jobs, each with its own processing time and can be processed on any m parallel machine that is nonidentical. E reason for presenting TS for minimizing the makespan in nonidentical parallel machines’ scheduling in this paper is that the solutions of the proposed method depend on the value of the lower bound to stop, unlike the previous TS methods, in which the solution iterations are predetermined to stop, even if they do not find the optimum solution. It can solve big scheduling problems quickly
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