Minimizing the Total Weighted Completion Time of a Single Machine With Flexible Maintenance

Shenquan Huang,Fuh-Der Chou,Hongming Zhou,Ya-Chih Tsai,Yarong Chen

doi:10.1109/access.2019.2937812

Abstract

This paper investigates the NP-hard problem of scheduling $n$ jobs on a single machine, where the machine must be stopped periodically for maintenance after a certain continuous working time. The objective is to minimize the total weighted completion time. Two-phase heuristic algorithms are proposed: in the first phase, initial solutions are obtained by WSPT or look-ahead (LA) algorithms; then, in the second phase, the solutions are improved through improvement procedures. Additionally, a mixed integer programming (MIP) model and a branch and bound (BAB) algorithm are developed. The results of computational experiments demonstrate that when the number of jobs is less than or equal to 20, the BAB is competitive compared with an MIP model implemented in a commercial solver because in most instances the former can obtain optimal solutions faster. The results also indicate that the LA algorithm significantly outperforms the WSPT algorithm in terms of the solution quality, and the proposed improvement procedure is evidently useful in refining the solution quality for both the WSPT and LA algorithms.

Highlights

In scheduling, one well-known problem that has been a recent research focus is integrating job production with maintenance activity scheduling
We consider a more general case of recurring flexible maintenance activities that extends the work of Mosheiov and Sarig [36]. For this more practical problem, we provide a mixed integer programming (MIP) model, and a branch and bound (BAB) method, to obtain optimal solutions for reference solutions because there are no benchmark solutions for the same problems in the literature
This study investigated the problem of scheduling a single machine with machine unavailability periods to minimize the total weighted completion time

Summary

INTRODUCTION

One well-known problem that has been a recent research focus is integrating job production with maintenance activity scheduling. For the second type of PM, Qi et al [21] considered the single-machine problem to minimize the total completion time They developed several heuristics and a branch and bound (BAB) algorithm in their study. Sbihi and Varnier [22] considered both types of flexible maintenance, and their objective was to minimize the maximum tardiness They proposed a heuristic and a BAB algorithm for the two single-machine problems. Cui and Lu [24] were the first researchers to simultaneously consider flexible maintenance and job release dates in a single machine problem They proposed a mixed integer programming (MIP) model, a heuristic and a branch and bound algorithm to minimize the makespan.

NOTATION

MATHEMATICAL FORMULATION

AN ILLUSTRATIVE EXAMPLE

COMPUTATIONAL EXPERIMENTS

CONCLUSION