Abstract
We consider the single-machine scheduling problem with job-dependent machine deterioration. In the problem, we are given a single machine with an initial nonnegative maintenance level, and a set of jobs each with a non-preemptive processing time and a machine deterioration. Such a machine deterioration quantifies the decrement in the machine maintenance level after processing the job. To avoid a machine breakdown, one should guarantee a nonnegative maintenance level at any time point, and whenever necessary, a maintenance activity must be allocated for restoring the machine maintenance level. The goal of the problem is to schedule the jobs and the maintenance activities such that the total completion time of jobs is minimized. There are two variants of maintenance activities: In the partial maintenance case, each activity can be allocated to increase the machine maintenance level to any level not exceeding the maximum; in the full maintenance case, every activity must be allocated to increase the machine maintenance level to the maximum. In a recent work, the problem in the full maintenance case was proven NP-hard; several special cases of the problem in the partial maintenance case were shown to be solvable in polynomial time, but the complexity of the general problem was left open. In this paper we first prove that the problem in the partial maintenance case is binary NP-hard, thus settling the open problem; we then design a 2-approximation algorithm and a branch-and-bound exact search algorithm. Computational experiments are conducted for the two algorithms to examine their practical performance.
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References
Bock, S., Briskorn, D., & Horbach, A. (2012). Scheduling flexible maintenance activities subject to job-dependent machine deterioration. Journal of Scheduling, 15, 565–578.
Chen, J.-S. (2008). Scheduling of non-resumable jobs and flexible maintenance activities on a single machine to minimize makespan. European Journal of Operation Research, 190, 90–102.
Garey, M. R., & Johnson, D. S. (1979). Computers and intractability: A guide to the theory of NP-completeness. San Francisco: W. H. Freeman and Company.
Kubzin, M. A., & Strusevich, V. A. (2006). Planning machine maintenance in two-machine shop scheduling. Operations Research, 54, 789–800.
Lee, C.-Y. (2004). Machine scheduling with availability constraints. In: J. Y.-T. Leung (Ed.), Handbook of scheduling: Algorithms, models and performance analysis, vol. 22 (pp. 1–13).
Lee, C.-Y., & Chen, Z.-L. (2000). Scheduling jobs and maintenance activities on parallel machines. Naval Research Logistics, 47, 145–165.
Lee, C.-Y., & Liman, S. (1992). Single machine flow-time scheduling with scheduled maintenance. Acta Informatica, 29, 375–382.
Luo, W., Chen, L., & Zhang, G. (2010). Approximation algorithms for scheduling with a variable machine maintenance. In: Proceedings of algorithmic aspects in information and management (AAIM 2010), LNCS 6124 (pp. 209–219).
Ma, Y., Chu, C., & Zuo, C. (2010). A survey of scheduling with deterministic machine availability constraints. Computers & Industrial Engineering, 58, 199–211.
Mosheiov, G., & Sarig, A. (2009). Scheduling a maintenance activity to minimize total weighted completion-time. Computers & Mathematics with Applications, 57, 619–623.
Qi, X. (2007). A note on worst-case performance of heuristics for maintenance scheduling problems. Discrete Applied Mathematics, 155, 416–422.
Qi, X., Chen, T., & Tu, F. (1999). Scheduling the maintenance on a single machine. Journal of the Operational Research Society, 50, 1071–1078.
Schmidt, G. (2000). Scheduling with limited machine availability. European Journal of Operational Research, 121, 1–15.
Sun, K., & Li, H. (2010). Scheduling problems with multiple maintenance activities and non-preemptive jobs on two identical parallel machines. International Journal of Production Economics, 124, 151–158.
Xu, D., Yin, Y., & Li, H. (2010). Scheduling jobs under increasing linear machine maintenance time. Journal of Scheduling, 13, 443–449.
Yang, S., & Yang, D. (2010). Minimizing the makespan on single-machine scheduling with aging effect and variable maintenance activities. Omega, 38, 528–533.
Acknowledgements
The authors are grateful to the reviewers’ valuable comments which improved the manuscript. W.L. was supported by K.C. Wong Magna Fund of Ningbo University, the China Scholarship Council (Grant No. 201408330402), the Humanities and Social Sciences Planning Foundation of the Ministry of Education (Grant No. 18YJA630077), Zhejiang Provincial Natural Science Foundation (Grant No. LY19A010005), Natural Science Foundation of China (Grant No. 11971252) and the Ningbo Natural Science Foundation (Grant No. 2018A610198). W.T. was supported in part by funds from the Office of the Vice President for Research & Economic Development at Georgia Southern University. G.L. was supported by NSERC Canada.
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An extended abstract appears in the Proceedings of ISAAC 2016. LIPICS, Volume 64.
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Luo, W., Xu, Y., Tong, W. et al. Single-machine scheduling with job-dependent machine deterioration. J Sched 22, 691–707 (2019). https://doi.org/10.1007/s10951-019-00622-w
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DOI: https://doi.org/10.1007/s10951-019-00622-w