Abstract
Fully polynomial time approximation schemes for scheduling deteriorating jobs with nonlinear processing times on a single machine are given via an application of the K-approximation sets and functions technique.
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References
Cai, J.-Y., Cai, P., & Zhu, Y. (1998). On a scheduling problem of time deteriorating jobs. Journal of Complexity, 14, 190–209.
Díaz-Núñez, F., Halman, N., & Vásquez, Ó. (2019). The TV advertisements scheduling problem. Optimization Letters, 13, 81–94.
Fontan, F., Lemaire, P., & Brauner, N. (2018). Complexity of scheduling tasks with processing time dependent profit. HAL Archives-ouvertes. Available from https://hal.archives-ouvertes.fr/hal-01947847. Accessed 23 Dec 2018.
Gawiejnowicz, S. (2008). Time-dependent scheduling. Berlin: Springer.
Halman, N., Kellerer, H., & Strusevich, V. (2018a). Approximation schemes for a non-separable non-linear boolean programming problems under nested knapsack constraints. European Journal of Operational Research, 2, 435–447.
Halman, N., Klabjan, D., Li, C.-L., Orlin, J., & Simchi-Levi, D. (2014). Fully polynomial time approximation schemes for stochastic dynamic programs. SIAM Journal on Discrete Mathematics, 28, 1725–1796.
Halman, N., Klabjan, D., Mostagir, M., Orlin, J., & Simchi-Levi, D. (2009). A fully polynomial time approximation scheme for single-item stochastic inventory control with discrete demand. Mathematics of Operations Research, 34, 674–685.
Halman, N., Kovalyov, M., Quilliot, A., Shabtay, D., & Zofi, M. (2019). Bi-criteria path problem with minimum length and maximum survival probability. OR Spectrum, 41(2), 469–489.
Halman, N., Nannicini, G., & Orlin, J. (2018b). On the complexity of energy storage problems. Discrete Optimization, 28, 31–53.
Kovalyov, M. Y., & Kubiak, W. (1998). A fully polynomial approximation scheme for minimizing makespan of deteriorating jobs. Journal of Heuristics, 3, 287–297.
Kovalyov, M. Y., & Kubiak, W. (2012). A generic FPTAS for partition type optimisation problems. International Journal of Planning and Scheduling, 1, 209–233.
Kubiak, W., & van de Velde, S. L. (1998). Scheduling deteriorating jobs to minimize makespan. Naval Research Logistics, 45, 511–523.
Sedding, H. A. (2018). Scheduling non-monotonous convex piecewise-linear time-dependent processing times of a uniform shape. In Proceedings of the second international workshop on dynamic scheduling problems (pp. 79–84). Available from https://iwdsp2018.wmi.amu.edu.pl/wp-content/uploads/2018/09/iwdsp2018.pdf. Accessed June 2018.
Smith, W. E. (1956). Various optimizers for single-stage production. Naval Research Logistics Quarterly, 3, 59–66.
Acknowledgements
This work is supported in part by the Israel Science Foundation, Grant No. 399/17, and by the United States–Israel Binational Science Foundation (BSF), Jerusalem, Israel. The author thanks the anonymous referees for their valuable comments and Stanislaw Gawiejnowicz for fruitful discussions.
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Halman, N. A technical note: fully polynomial time approximation schemes for minimizing the makespan of deteriorating jobs with nonlinear processing times. J Sched 23, 643–648 (2020). https://doi.org/10.1007/s10951-019-00616-8
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DOI: https://doi.org/10.1007/s10951-019-00616-8