Abstract
This paper studies a flexible flowshop scheduling problem with step-deteriorating jobs and sequence-dependent setup times (FFSP-SDJ&SDST) where there are multiple unrelated parallel machines at each stage. The actual processing time of each job is modeled as a step function of its starting time. An integer programming model is first formulated with the objective of minimizing the total weighted completion time. Since this problem is NP-complete, it becomes an interesting and challenging topic to develop effective approximation algorithms for solving it. The artificial bee colony (ABC) algorithm has been successfully applied to solve both continuous and combinatorial optimization problems with the advantages of fewer control parameters and ease of implementation. So, an improved discrete artificial bee colony algorithm is proposed. In this algorithm, a dynamic generation mechanism of initial solutions is designed based on job permutation encoding. A genetic algorithm and a modified variable neighborhood search are introduced, respectively, to obtain new solutions for the employed and onlooker bees. A greedy heuristic is proposed to generate the solutions of the scout bees. Finally, to verify the performance of the proposed algorithm, an orthogonal test is performed to optimize the parameter settings. Simulation results on different scale problems demonstrate that the proposed algorithm is more effective compared against several presented algorithms from the existing literatures.
Highlights
Scheduling problem is one of key issues in many manufacturing systems
Ten random instances are generated. us, there are 360 small- and medium-sized instances and 240 large-sized instances to test these algorithms. e relative percentage increase (RPI) is defined as follows: RPI Oζ − Obest × 100, Obest where Oζ is the objective value obtained by different metaheuristic algorithm and Obest is the best objective value found by all algorithms
Erefore, average RPI (ARPI) can be computed and used as a performance measure to compare the performance of the algorithms
Summary
Scheduling problem is one of key issues in many manufacturing systems. Flexible flowshop scheduling problem (FFSP) widely arises in discrete industry and process industry such as semiconductors, electronics manufacturing, cosmetics, and pharmaceuticals [1]. To solve identical parallel machine scheduling, Guo et al [2] considered sequencedependent setup times and applied a hybrid discrete cuckoo algorithm to minimize total tardiness; Cheng et al [9] presented a modified weight-combination search algorithm and a variable neighborhood search to minimize total completion time. For two-stage FFSP with identical parallel machines at stage 1 and a single batching machine at stage 2, Gong and Tang [10] proposed a heuristic algorithm to minimize makespan plus the total penalty cost of batching-machine utilization ratio where the job processing time at stage 2 is a step function of its waiting time between the two stages
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