Abstract
This article studies a scheduling problem of a two-machine flow shop with both time-dependent deteriorating jobs and sequence-independent setup time. It is assumed that the deterioration of processing time and setup time is of a linear increasing function with respect to the starting time. The objective is to minimize the total completion time of all jobs. For such a scheduling problem, a mixed integer programming model is developed to find an optimal solution for small-sized problems. For medium- and large-sized problems, a modified variable neighborhood search algorithm is presented. To improve the performance of the algorithm, a greedy algorithm is proposed to find a good initial solution. Also, lower bounds are presented for performance evaluation. Numerical experiments are used to evaluate the effectiveness and efficiency of the proposed method, and the results show that an optimal or near-optimal solution can be obtained.
Highlights
It is vitally important to optimally schedule a production system, and great attention has been paid to this issue, such as the studies in the literature.1–9 Among the production scheduling problems, in some production systems, the jobs to be scheduled are subject to deterioration,10–12 which complicates the scheduling problem
We evaluate the improvement made by the variable neighborhood search (VNS) with respect to the initial schedule obtained by the greedy algorithm
In order to determinate loopmax for the VNS, we examine the problem with its size being 20 (n = 20) since we can analyze the effect of loopmax by comparing with the optimal solution obtained via the mixed integer programming (MIP)
Summary
It is vitally important to optimally schedule a production system, and great attention has been paid to this issue, such as the studies in the literature. Among the production scheduling problems, in some production systems, the jobs to be scheduled are subject to deterioration, which complicates the scheduling problem. The studies done in the literature deal with a simple linear deterioration model that is different from the one in Wu and Lee and Ng et al.21 They proposed branch-and-bound algorithms or heuristics to minimize the make-span and total completion time of the jobs for a two-machine flow shop. Given a schedule p, for a two-machine flow shop with time-dependent deteriorating jobs and sequenceindependent deteriorating setup time, we can obtain the make-span and the total completion time, respectively. This work adopts VNS to solve the scheduling problem of a two-machine flow shop with both the jobs and setup time being deteriorated.
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