Heuristics for the Hybrid Flow Shop Scheduling Problem with Sequence-Dependent Setup times

Abstract

This paper considers the hybrid flow shop scheduling problem with two types of sequence-dependent setup times, one depending on the order of jobs and the other depending on both the order of jobs and the machines where the jobs are allocated. Three constructive heuristic algorithms based on the NEH algorithm are developed with the object of minimizing the total energy consumption cost. The first algorithm, called EPRA, obtains the order of jobs using the energy consumption cost based on the processing time. The second algorithm, called ESRA, obtains the order of jobs using the energy consumption cost based on the setup time. The third algorithm, called ESPRA, takes advantage of both EPRA and ESRA by constructing fictitious jobs with ESRA and acquiring the sequence of fictitious jobs with EPRA. Due to the drawback of NEH algorithm for the FFS problem proposed in this paper, all three heuristic algorithms use EST rules to allocate the jobs to the machines. Two lower bounds are developed to evaluate the heuristic algorithms proposed in this paper. A computational experiment based on the split-plot design is developed to carry out the factor analysis, algorithm analysis, lower bounds analysis, and CPU running time analysis. The analysis reveals that all main factor interactions except the algorithm are significant; the ESPRA algorithm is generally outstanding among the three algorithms; LB1 is better than LB2; the CPU running time of ESPRA algorithm is significantly reduced compared to those of EPRA and ESST algorithms.