Abstract
This study considers a two-machine flowshop with a limited waiting time constraint between the two machines and sequence-dependent setup times on the second machine. These characteristics are motivated from semiconductor manufacturing systems. The objective of this scheduling problem is to minimize the total tardiness. In this study, a mixed-integer linear programming formulation was provided to define the problem mathematically and used to find optimal solutions using a mathematical programming solver, CPLEX. As CPLEX required a significantly long computation time because this problem is known to be NP-complete, a genetic algorithm was proposed to solve the problem within a short computation time. Computational experiments were performed to evaluate the performance of the proposed algorithm and the suggested GA outperformed the other heuristics considered in the study.
Highlights
Setup time refers to the time required for preparation before processing jobs
A two-machine flowshop scheduling problem with sequence-dependent setup times (SDSTs) to minimize the makespan is very similar to the typical travel salesman problem (TSP) [4], and dynamic programming methods [5, 6] and branch and bound algorithms [7, 8] have been proposed to obtain optimal solutions for the problem
Since finding optimal solutions of the flowshop problem with SDST requires considerably long computation times, recent studies have focused on development of metaheuristic algorithms: genetic algorithms [9,10,11], variable neighborhood search algorithm [12], migrating bird optimization algorithm [13], discrete artificial bee colony optimization [14], iterated greedy algorithm [15,16,17], and local search based heuristic algorithm [18]
Summary
The considered scheduling problem is described in more detail, and a mixed-integer linear programming formulation is presented. ere are n jobs to be processed in the two-machine flowshop with a limited waiting time constraint and sequence-dependent setup times on the second machine. The considered scheduling problem is described in more detail, and a mixed-integer linear programming formulation is presented. Ere are n jobs to be processed in the two-machine flowshop with a limited waiting time constraint and sequence-dependent setup times on the second machine. Only permutation schedules are considered; that is, job sequences on the two machines are the same. Note that permutation schedules are dominant in a typical two-machine flowshop with regular measures, including total tardiness. Completion times and tardiness of the jobs in a given sequence are computed as follows: c[1]1 p[1]1,. Constraints (9)–(12) define the start time of each job in the considered flowshop. Constraints (13)–(15) define the relationship between xir and yijr for sequencedependent setup times. Constraints (16) and (17) compute the completion time and tardiness of jobs. Constraints (18) and (19) define the domain of the decision variables
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