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Single-machine scheduling with workload-dependent tool change durations and equal processing time jobs to minimize total completion time

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Abstract

We consider a single-machine tool change scheduling problem where tool change durations are workload-dependent. The processing times of all the jobs are the same. The objective is to determine the number of tool change activities, the start time and the completion time of each tool change activity jointly and schedule all the jobs to the machine such that the total completion time of the jobs is minimized. For the case where the tool change duration function is concave, we present a linear time optimal algorithm. For the case where the tool change duration function is convex, we convert it into a convex integer quadratic programming problem with fixed dimension and then propose two polynomial time algorithms for it. We also study some special cases for which optimal schedules can be obtained directly. For the case where the tool change duration function is linear, we present all the optimal schedules.

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References

  • Akturk, M. S., Ghosh, J. B., & Gunes, E. D. (2003). Scheduling with tool changes to minimize total completion time: A study of heuristics and their performance. Naval Research Logistics, 50(1), 15–30.

    Article  Google Scholar 

  • Akturk, M. S., Ghosh, J. B., & Gunes, E. D. (2004). Scheduling with tool changes to minimize total completion time: Basic results and SPT performance. European Journal of Operational Research, 157(3), 784–790.

    Article  Google Scholar 

  • Akturk, M. S., Ghosh, J. B., & Kayan, R. K. (2007). Scheduling with tool changes to minimize total completion time under controllable machining conditions. Computers & Operations Research, 34(7), 2130–2146.

    Article  Google Scholar 

  • Baptiste, P., & Schieber, B. (2003). A note on scheduling tall/small multiprocessor tasks with unit processing time to minimize maximum tardiness. Journal of Scheduling, 6(4), 395–404.

    Article  Google Scholar 

  • Baptiste, P., & Timkovsky, V. G. (2001). On preemption redundancy in scheduling unit processing time jobs on two parallel machines. Operations Research Letters, 28(5), 205–212.

    Article  Google Scholar 

  • Birks, M., & Fung, S. P. Y. (2013). Temperature aware online algorithms for scheduling equal length jobs. Theoretical Computer Science, 508, 54–65.

    Article  Google Scholar 

  • Blazewicz, J., Ecker, K., Kis, T., Potts, C. N., Tanas, M., & Whitehead, J. (2010). Scheduling of coupled tasks with unit processing times. Journal of Scheduling, 13(5), 453–461.

    Article  Google Scholar 

  • Brucker, P., & Shakhlevich, N. V. (2016). Necessary and sufficient optimality conditions for scheduling unit time jobs on identical parallel machines. Journal of Scheduling, 19, 659–685.

    Article  Google Scholar 

  • Chen, J. S. (2008). Optimization models for the tool change scheduling problem. Omega, 36(5), 888–894.

    Article  Google Scholar 

  • Gerstl, E., & Mosheiov, G. (2013a). Due-window assignment problems with unit-time jobs. Applied Mathematics and Computation, 220, 487–495.

    Article  Google Scholar 

  • Gerstl, E., & Mosheiov, G. (2013b). Due-window assignment with identical jobs on parallel uniform machines. European Journal of Operational Research, 229(1), 41–47.

    Article  Google Scholar 

  • Gerstl, E., & Mosheiov, G. (2013c). An improved algorithm for due-window assignment on parallel identical machines with unit-time jobs. Information Processing Letters, 113(19), 754–759.

    Article  Google Scholar 

  • Graham, R. L., Lawler, E. L., Lenstra, J. K., & Kan, A. R. (1979). Optimization and approximation in deterministic sequencing and scheduling: A survey. Annals of Discrete Mathematics, 5, 287–326.

    Article  Google Scholar 

  • Heinz, S. (2005). Complexity of integer quasiconvex polynomial optimization. Journal of Complexity, 21(4), 543–556.

    Article  Google Scholar 

  • Hemmecke, R., Köppe, M., Lee, J., & Weismantel, R. (2010). Nonlinear integer programming. In 50 years of integer programming 1958–2008 (pp. 561–618). New York, NY: Springer.

  • Jackson, J. R. (1956). An extension of Johnson’s results on job IDT scheduling. Naval Research Logistics Quarterly, 3(3), 201–203.

    Article  Google Scholar 

  • Janiak, A., Janiak, W., Kovalyov, M. Y., & Werner, F. (2012). Soft due window assignment and scheduling of unit-time jobs on parallel machines. 4OR, 10(4), 347–360.

    Article  Google Scholar 

  • Johnson, S. M. (1954). Optimal two-and three-stage production schedules with setup times included. Naval Research Logistics Quarterly, 1(1), 61–68.

    Article  Google Scholar 

  • Lenstra, H. W, Jr. (1983). Integer programming with a fixed number of variables. Mathematics of Operations Research, 8(4), 538–548.

    Article  Google Scholar 

  • Li, C. L., Mosheiov, G., & Yovel, U. (2008). An efficient algorithm for minimizing earliness, tardiness, and due-date costs for equal-sized jobs. Computers & Operations Research, 35(11), 3612–3619.

    Article  Google Scholar 

  • Li, W., Yuan, J., & Yang, S. (2014). Online scheduling of incompatible unit-length job families with lookahead. Theoretical Computer Science, 543, 120–125.

    Article  Google Scholar 

  • Luo, T., Xu, Y., Luo, L., & He, C. (2014). Semi-online scheduling with two gos levels and unit processing time. Theoretical Computer Science, 521, 62–72.

    Article  Google Scholar 

  • Luo, W., Cheng, T. E., & Ji, M. (2015). Single-machine scheduling with a variable maintenance activity. Computers & Industrial Engineering, 79, 168–174.

    Article  Google Scholar 

  • Luo, W., & Ji, M. (2015). Scheduling a variable maintenance and linear deteriorating jobs on a single machine. Information Processing Letters, 115(1), 33–39.

    Article  Google Scholar 

  • Mosheiov, G., & Shadmon, M. (2001). Minmax earliness-tardiness costs with unit processing time jobs. European Journal of Operational Research, 130(3), 638–652.

    Article  Google Scholar 

  • Mosheiov, G., & Yovel, U. (2006). Minimizing weighted earliness-tardiness and due-date cost with unit processing-time jobs. European Journal of Operational Research, 172(2), 528–544.

    Article  Google Scholar 

  • Oron, D., Shabtay, D., & Steiner, G. (2015). Single machine scheduling with two competing agents and equal job processing times. European Journal of Operational Research, 244(1), 86–99.

    Article  Google Scholar 

  • Pinedo, M. L. (2012). Scheduling: Theory, algorithms, and systems (4th ed.). New York, NY: Springer.

    Book  Google Scholar 

  • Qi, X. (2007). A note on worst-case performance of heuristics for maintenance scheduling problems. Discrete Applied Mathematics, 155(3), 416–422.

    Article  Google Scholar 

  • Qi, X., Chen, T., & Tu, T. (1999). Scheduling the maintenance on a single machine. Journal of the Operational Research Society, 50, 1071–1078.

    Article  Google Scholar 

  • Quilliot, A., & Chrétienne, P. (2013). Homogeneously non-idling schedules of unit-time jobs on identical parallel machines. Discrete Applied Mathematics, 161(10), 1586–1597.

    Article  Google Scholar 

  • Rodriguez, C. E. P., & de Souza, G. F. M. (2010). Reliability concepts applied to cutting tool change time. Reliability Engineering & System Safety, 95(8), 866–873.

    Article  Google Scholar 

  • Sarin, S. C., & Prakash, D. (2004). Equal processing time bicriteria scheduling on parallel machines. Journal of Combinatorial Optimization, 8(3), 227–240.

    Article  Google Scholar 

  • Shabtay, D., & Karhi, S. (2012a). An asymptotically optimal online algorithm to minimize the total completion time on two multipurpose machines with unit processing times. Discrete Optimization, 9(4), 241–248.

    Article  Google Scholar 

  • Shabtay, D., & Karhi, S. (2012b). Online scheduling of two job types on a set of multipurpose machines with unit processing times. Computers & Operations Research, 39(2), 405–412.

    Article  Google Scholar 

  • Smith, W. E. (1956). Various optimizers for single-stage production. Naval Research Logistics Quarterly, 3(1–2), 59–66.

    Article  Google Scholar 

  • Tuong, N. H., & Soukhal, A. (2010). Due dates assignment and JIT scheduling with equal-size jobs. European Journal of Operational Research, 205(2), 280–289.

    Article  Google Scholar 

  • Xu, D., Liu, M., Yin, Y., & Hao, J. (2013). Scheduling tool changes and special jobs on a single machine to minimize makespan. Omega-International Journal of Management Science, 41(2), 299–304.

    Article  Google Scholar 

  • Xu, D., Wan, L., Liu, A., & Yang, D. L. (2015). Single machine total completion time scheduling problem with workload-dependent maintenance duration. Omega-International Journal of Management Science, 52, 101–106.

    Article  Google Scholar 

  • Xu, D., Yin, Y., & Li, H. (2010). Scheduling jobs under increasing linear machine maintenance time. Journal of Scheduling, 13(4), 443–449.

    Article  Google Scholar 

  • Xu, Z., & Xu, D. (2015). Single-machine scheduling with preemptive jobs and workload-dependent maintenance durations. Operational Research, 15(3), 423–436.

    Article  Google Scholar 

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Acknowledgements

We thank the referees for their valuable comments which improved the paper substantially. This research was supported by the National Natural Science Foundation of China (71201022).

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Authors and Affiliations

  1. School of Science, East China University of Technology, Nanchang, 330013, Jiangxi, People’s Republic of China

    Zhijun Xu & Dehua Xu

  2. Department of Mathematics, Tongji University, Shanghai, 200092, People’s Republic of China

    Zhijun Xu

  3. School of International Economics and Business, Nanjing University of Finance & Economics, Nanjing, 210023, Jiangsu, People’s Republic of China

    Dehua Xu

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  1. Zhijun Xu
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Correspondence to Dehua Xu.

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Xu, Z., Xu, D. Single-machine scheduling with workload-dependent tool change durations and equal processing time jobs to minimize total completion time. J Sched 21, 461–482 (2018). https://doi.org/10.1007/s10951-017-0543-z

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