Abstract
In this paper we propose to solve a single machine scheduling problem which has to undergo a periodic preventive maintenance. The objective is to minimize the weighted sum of the completion times. This criterion is defined as one of the most important objectives in practice but has not been studied so far for the considered problem. As the problem is proven to be NP-hard, and a mathematical model is proposed in the literature, we propose to use General Variable Neighborhood Search algorithm to solve this problem in order to obtain near optimal solutions for the large-sized instances in a small amount of computational time.
Highlights
For manufacturing companies, the largest part of the investment is dedicated to production systems which must be in operating conditions as often as possible
99.33 91.04 91.81 80.12 69.38 96.34 88.16 92.76 98.25 86.69 79.16 77.85 79.36 80.25 81.20 81.52 82.72 83.30 84.27 columns three and five represent the ratio between the optimal value returned by the mixed linear integer programming (MILP) (ValueMILP) and the objective function value returned by the General Variable Neighborhood Search (GVNS) (ValueGVNS) respectively, between the lower bound (ValueLBbest ) and (ValueGVNS)
In this paper we studied the single machine scheduling problem with periodic maintenance
Summary
The largest part of the investment is dedicated to production systems which must be in operating conditions as often as possible. Wen-Jinn et al [8] proposed a heuristic to solve the single-machine scheduling problem with periodic maintenance for the preemptive case They minimized the total flow time and the maximum tardiness simultaneously. Benmansour et al [6] investigated the single machine scheduling problem with periodic maintenance in order to minimize the weighted sum of maximum earliness and maximum tardiness costs They proved the NP-hardness of this problem and proposed an efficient heuristic to solve it. Luo et al [27] investigated a single-machine scheduling problem with workload-dependent maintenance duration with the aim of minimizing the total weighted completion time They proposed a (2+ )-approximation algorithm and a fully polynomial time approximation scheme to solve the problem.
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