Distributed permutation flowshop scheduling problem with total completion time objective
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Distributed permutation flowshop scheduling problem with total completion time objective Arshad Ali1 · Yuvraj Gajpal2 · Tarek Y. Elmekkawy3 Accepted: 21 October 2020 © Operational Research Society of India 2020
Abstract This paper considers the distributed permutation flowshop scheduling problem (DPFSP) which is an extension of permutation flowshop scheduling problem (PFSP). In DPFSP, there are multiple parallel factories instead of one factory as in PFSP. Each factory consists of same number of machines, and jobs can be processed in either of the factories to perform all necessary operations. This paper considers DPFSP for minimizing the total completion time objective. An MILP formulation is developed to find the optimal solution. To solve the problem, a metaheuristic, tabu search (TS) is proposed. Numerical experiments are performed on benchmark problem instances from the literature, and results of the proposed method are compared with current metaheuristics in the literature for this problem. The tabu search outperforms all existing metaheuristics in terms of solution quality. Keywords Parallel flowshop · Distributed permutation flowshop · Tabu search · Total completion time · Scheduling · Metaheuristics
* Arshad Ali [email protected] Yuvraj Gajpal [email protected] Tarek Y. Elmekkawy [email protected] 1
Department of Mechanical Engineering, University of Manitoba, Winnipeg, MB R3T 5V6, Canada
2
Department of Supply Chain Management, Asper School of Business, University of Manitoba, Winnipeg, MB R3T 5V4, Canada
3
Department of Mechanical and Industrial Engineering, Qatar University, 2713 Doha, Qatar
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1 Introduction Scheduling deals with the allocation of resources, typically machines, to tasks (commonly referred to as jobs) over time with the goal of optimizing a given objective [29]. Optimal efficiency can be achieved by scheduling jobs proficiently. In a conventional manufacturing plant, jobs are usually scheduled by some skilled persons using their self-developed rules. Extensive study on scheduling led researchers to develop different models and methods for specific production environments. The permutation flowshop problem (PFSP) is one of these manufacturing environments, where a series of operations are performed on every job in the same sequence. All jobs follow the same route, as the machines are placed in the same sequence [8]. The PFSP is one of the widely studied problems in the area of scheduling. According to three field notations in scheduling, PFSP for the total completion time objective function can be denoted as F/permu/∑cj. A generalization of PFSP was introduced by Naderi and Ruiz (2010) [25] to address the problem of multiple parallel flowshops. This problem is named as distributed permutation flowshop or DPFSP, because it distributes jobs to different factories. In DPFSP, there are multiple parallel factories, instead of one factory as in PFSP. Each factory consists of same number of machines, and any job can be processed in any of th
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