Makine uygunluk kısıtlaması ve sıra bağımlı kurulum süresi ile özdeş olmayan paralel makine çizelgeleme problemi için tabu arama algoritması

Abstract

 Formulate the unrelated parallel machine scheduling problem  Consideration of availability constraint and sequencedependent setup time  Propose a tabu search algorithm to solve the formulated model.Figure A. Gantt chart for unrelated parallel machine scheduling problem Purpose:The main purpose of this study is to formulate the unrelated parallel machine scheduling problem with machine eligibility restrictions and sequence-dependent setup time and propose the efficient meta -heuristic algorithm to solve the problem. Theory and Methods:Firstly a mix-integer mathematical model has been addressed for the unrelated parallel machine scheduling problem with following assumptions; machines are unavailable at certain time intervals for maintenance activities, machines have the ability to perform just a certain series of tasks and the setup time of the machines depends on the order of the jobs. Then, due to the complexity of the addressed problem, a Tabu Search (TS) algorithm is proposed to solve large-scale problems. In order to evaluate the performance of the proposed TS algorithm, various test problems with different sizes are generated randomly. Finally, the relative percentage deviation (RPD) is used to compare the results. Results:To evaluate the efficiency of the applied TS algorithm, 60 test problems are generated randomly and classified into three categories as small, medium and large scale problems. Due to the random nature of the tabu search algorithm, each of the generated problems are solved five times and the minimum, average and maximum values of the results are reported. According to the obtained results, 14 problems out of 60 are solved in a short time with the mathematical model and the optimum solution is obtained. In all solved problems, the optimum solution is also obtained at least once with the TS algorithm. For the other 46 problems, the feasible solution obtained from the mathematical model is compared with the results of the TS algorithm. According to the comparison results, it is seen that the proposed TS algorithm achieves better results in terms of both solution time and solution quality. Conclusion:In most studies that have addressed the parallel machine scheduling problem so far, it is assumed that the machines are available during the entire planning period. Although this assumption is true in some cases, it is not true in many practical situations. Therefore, it is important to formulate the scheduling of jobs considering the machine eligibility restrictions. In this study, in addition to the identified constraints, it is aimed to minimize total tardiness and earliness to close this gap in the literature. In addition, the suggested TS algorithm for solving the problem is shown a superior performance.