Abstract
We consider various single machine scheduling problems in which the processing time of a job depends either on its position in a processing sequence or on its start time. We focus on problems of minimizing the makespan or the sum of (weighted) completion times of the jobs. In many situations we show that the objective function is priority-generating, and therefore the corresponding scheduling problem under series-parallel precedence constraints is polynomially solvable. In other situations we provide counter-examples that show that the objective function is not priority-generating.
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References
Alidaee, B., & Womer, N. K. (1999). Scheduling with time dependent processing times: review and extensions. Journal of the Operational Research Society, 50, 711–720.
Bachman, A., Janiak, A., & Kovalyov, M. Y. (2002). Minimizing the total weighted completion time of deteriorating jobs. Information Processing Letters, 81, 81–84.
Biskup, D. (1999). Single-machine scheduling with learning considerations. European Journal of Operational Research, 115, 173–178.
Biskup, D. (2008). A state-of-the-art review on scheduling with learning effects. European Journal of Operational Research, 188, 315–329.
Browne, S., & Yechiali, U. (1990). Scheduling deteriorating jobs on a single processor. Operations Research, 38, 495–498.
Burdyuk, V. Y., & Reva, V. N. (1980). A method for optimizing functions over permutations under constraints. Kibernetika (Kiev), 1, 99–103 (in Russian).
Cheng, T. C. E., Ding, Q., & Lin, B. M. T. (2004). A concise survey of scheduling with time-dependent processing times. European Journal of Operational Research, 152, 1–13.
Cheng, T. C. E., & Kovalyov, M. Y. (1994). Scheduling with learning effects on job processing times (Working paper no. 06/94). Faculty of Business and Information Systems, The Hong Kong Polytechnic University.
Cheng, M.-B., & Sun, S.-L. (2006). The single-machine scheduling problems with deteriorating jobs and learning effect. Journal of Zhejiang University-Science A, 7, 597–601.
Crauwels, H. A. J., Potts, C. N., & Van Wassenhove, L. N. (1997). Local search heuristics for single machine scheduling with batch set-up times to minimize total weighted completion time. Annals of Operations Research, 70, 261–279.
Crauwels, H. A. J., Hariri, A. M. A., Potts, C. N., & Van Wassenhove, L. N. (1998). Branch and bound algorithms for single-machine scheduling with batch set-up times to minimize total weighted completion time. Annals of Operations Research, 83, 59–76.
Gawiejnowicz, S., & Pankovska, L. (1995). Scheduling jobs with varying processing times. Information Processing Letters, 54, 175–178.
Gordon, V. S., & Shafransky, Y. M. (1978). Optimal ordering with series-parallel precedence constraints. Doklady Akademii Nauk BSSR, 22, 244–247 (in Russian).
Gordon, V. S., Proth, J.-M., & Strusevich, V. A. (2005). Single machine scheduling and due date assignment under series-parallel precedence constraints. Central European Journal of Operations Research, 13, 15–35.
Ho, K. I.-J., Leung, J. Y.-T., & Wei, W.-D. (1993). Complexity of scheduling tasks with time dependent execution times. Information Processing Letters, 48, 315–320.
Janiak, A., & Kovalyov, M. Y. (2006). Scheduling in a contaminated area: a model and polynomial algorithms. European Journal of Operational Research, 173, 125–132.
Kuo, W.-H., & Yang, D.-L. (2006a). Minimizing the makespan in a single machine scheduling problem with a time-based learning effect. Information Processing Letters, 97, 64–67.
Kuo, W.-H., & Yang, D.-L. (2006b). Minimizing the total completion time in a single-machine scheduling problem with a time-dependent learning effect. European Journal of Operational Research, 174, 1184–1190.
Lawler, E. L. (1978). Sequencing jobs to minimize total weighted completion time subject to precedence constraints. Annals of Discrete Mathematics, 2, 75–90.
Lawler, E. L., & Sivazlian, B. D. (1978). Minimization of time-varying costs in single-machine sequencing. Operations Research, 26, 563–569.
Lawler, E. L., Lenstra, J. K., Rinnooy Kan, A. H. G., & Shmoys, D. B. (1993). Sequencing and scheduling: algorithms and complexity. In S. C. Graves, A. H. G. Rinnooy, & P. H. Zipkin (Eds.), Handbooks in operations research and management science : Vol. 4. Logistics of production and inventory (pp. 445–522). Amsterdam: North-Holland.
Möhring, R. H., & Rademacher, F. J. (1985). Generalized results on the polynomiality of certain weighted sum scheduling problems. Methods of Operations Research, 49, 405–417.
Monma, C. L., & Sidney, J. B. (1979). Sequencing with series-parallel precedence constraints. Mathematics of Operations Research, 4, 215–234.
Monma, C. L., & Sidney, J. B. (1987). Optimal sequencing via modular decomposition: characterization of sequencing functions. Mathematics of Operations Research, 12, 22–31.
Mosheiov, G. (1996). Λ-shaped policies to schedule deteriorating jobs. Journal of the Operational Research Society, 47, 1184–1191.
Mosheiov, G. (2001). Scheduling problems with a learning effect. European Journal of Operational Research, 132, 687–693.
Mosheiov, G. (2005). A note on scheduling deteriorating jobs. Mathematical and Computer Modelling, 41, 883–886.
Ng, C. T., Cheng, T. C. E., Bachman, A., & Janiak, A. (2002). Three scheduling problems with deteriorating jobs to minimize the total completion time. Information Processing Letters, 81, 327–333.
Reva, V. N. (1979). On an algorithm for optimizing functions over the permutations of a partially ordered set. In Actual Problems of computers and programming (pp. 92–95). Dnepropetrovsk (in Russian).
Rothkopf, M. E. (1966). Scheduling independent tasks on parallel processors. Management Science, 12, 437–447.
Shafransky, Y. M. (1978a). On optimal sequencing for deterministic systems with a tree-like partial order. Vestsi Akademii Navuk BSSR, Seria Fizika-Matematychnykh Navuk, 2, 120 (in Russian).
Shafransky, Y. M. (1978b). Optimization for deterministic scheduling systems with a tree-like partial order. Vestsi Akademii Navuk BSSR, Seria Fizika-Matematychnykh Navuk, 2, 119 (in Russian).
Shafransky, Y. M. (1980). On a problem of minimizing functions over a set of permutations of partially ordered elements, part I. Vestsi Akademii Navuk BSSR, Seria Fizika-Matematychnykh Navuk, 5, 132 (in Russian).
Sidney, J. B., & Steiner, G. (1986). Optimal sequencing by modular decomposition: polynomial algorithms. Operations Research, 34, 606–612.
Smith, W. E. (1956). Various optimizers for single stage production. Naval Research Logistics Quarterly, 3, 59–66.
Tanaev, V. S. (1965). Some objective functions of a single-stage production. Doklady Akademii Nauk BSSR, 9, 11–14 (in Russian).
Tanaev, V. S., Gordon, V. S., & Shafransky, Y. M. (1984). Scheduling theory. Single-stage systems. Moscow: Nauka (in Russian); translated into English by Kluwer Academic, Dordrecht, 1994.
Valdes, J. R., Tarjan, E., & Lawler, E. L. (1982). The recognition of series-parallel digraphs. SIAM Journal on Computing, 11, 361–370.
Wang, J.-B., Ng, C. T., & Cheng, T. C. E. (2008). Single-machine scheduling with deteriorating jobs under a series-parallel graph constraint. Computers and Operations Research, 35, 2684–2693.
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Gordon, V.S., Potts, C.N., Strusevich, V.A. et al. Single machine scheduling models with deterioration and learning: handling precedence constraints via priority generation. J Sched 11, 357–370 (2008). https://doi.org/10.1007/s10951-008-0064-x
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DOI: https://doi.org/10.1007/s10951-008-0064-x