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A survey on offline scheduling with rejection

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An Erratum to this article was published on 23 January 2015

Abstract

In classical deterministic scheduling problems, it is assumed that all jobs have to be processed. However, in many practical cases, mostly in highly loaded make-to-order production systems, accepting all jobs may cause a delay in the completion of orders which in turn may lead to high inventory and tardiness costs. Thus, in such systems, the firm may wish to reject the processing of some jobs by either outsourcing them or rejecting them altogether. The field of scheduling with rejection provides schemes for coordinated sales and production decisions by grouping them into a single model. Since scheduling problems with rejection are very interesting both from a practical and a theoretical point of view, they have received a great deal of attention from researchers over the last decade. The purpose of this survey is to offer a unified framework for offline scheduling with rejection by presenting an up-to-date survey of the results in this field. Moreover, we highlight the close connection between scheduling with rejection and other fields of research such as scheduling with controllable processing times and scheduling with due date assignment, and include some new results which we obtained for open problems.

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References

  • Alidaee, B., & Ahmadian, A. (1993). Two parallel machine sequencing problems involving controllable job processing times. European Journal of Operational Research, 70(3), 335–341.

    Article  Google Scholar 

  • Angel, E., Bampis, E., & Kononov, A. (2001). A FPTAS for approximating the unrelated parallel machines scheduling problem with costs. Lecture Notes in Computer Science, 2161, 194–205.

    Article  Google Scholar 

  • Bechman, A., Janiak, A., & Kovalyov, M. Y. (2002). Minimizing the total weighted completion time of deteriorating jobs. Information Processing Letters, 81(2), 81–84.

    Article  Google Scholar 

  • Bartal, Y., Leonardi, S., Marchetti-Spaccamela, A., Sgall, J., & Stougie, L. (2000). Multiprocessor scheduling with rejection. SIAM Journal of Discrete Mathematics, 13(1), 64–78.

    Article  Google Scholar 

  • Bilgintürk, Z., Oğuz, C., & Salman, S. (2007). Order acceptance and scheduling decisions in make-to-order systems. In 5th Multidisciplinary International Scheduling Conference: Theory and Applications, Paris, France.

  • Cao, Z., Wang, Z., Zhang, Y., & Liu, S. (2006). On several scheduling problems with rejection or discretely compressible processing times. Lecture Notes in Computer Science, 3959, 90–98.

    Article  Google Scholar 

  • Cao, Z., & Yang, X. (2009). A PTAS for parallel batch scheduling with rejection and dynamic job arrivals. Theoretical Computer Science, 410, 2732–2745.

    Article  Google Scholar 

  • Cao, Z., & Zhang, Y. (2007). Scheduling with rejection and non-identical job arrivals. Journal of Systems Science and Complexity, 20, 529–535.

    Article  Google Scholar 

  • Cesaret, B., Oğuz, C., & Salman, F. S. (2012). A tabu search algorithm for order acceptance and scheduling. Computers and Operations Research, 39(6), 1197–1205.

    Article  Google Scholar 

  • Cheng, Y., & Sun, S. (2009). Scheduling linear deteriorating jobs with rejection on a single machine. European Journal of Operational Research, 194(1), 18–27.

    Google Scholar 

  • Choi, B. C., Yoon, S. H., & Chung, S. J. (2007). Minimizing maximum completion time in a proportionate flow shop with one machine of different speed. European Journal of Operational Research, 176(2), 964–974.

    Article  Google Scholar 

  • Choi, B. C., & Chung, J. (2011). Two-machne flow shop schedulng problem with an outsourcing option. European Journal of Operational Research, 213, 66–72.

    Article  Google Scholar 

  • Chudak, F. (1999). A min-sum 1.5-approximation algorithm for scheduling unrelated parallel machines. Journal of Scheduling, 2(2), 73–77.

    Article  Google Scholar 

  • De, P., Ghosh, J. B., & Wells, C. E. (1991). Optimal delivery time quotation and order sequencing. Decision Sciences, 22(2), 379–390.

    Google Scholar 

  • Engels, D. W., Karger, D. R., Kolliopoulos, S. G., Sengupta, S., Uma, R. N., & Wein, J. (2003). Techniques for scheduling with rejection. Journal of Algorithms, 49(1), 175–191.

    Article  Google Scholar 

  • Gaspar, N., & Shabtay, D. (2010). Various special cases of the multiple-machine flow-shop scheduling problem with rejection. Working Paper.

  • Garey, M. R., & Johnson, D. S. (1979). Computers and intractability: A guide to the theory of \(\cal NP\) -completeness. San Francisco: Freeman.

  • Ghosh, J. B. (1997). Job selection in a heavily loaded shop. Computers and Operations Research, 24(2), 141–145.

    Article  Google Scholar 

  • Gonzalez, T., & Sahni, S. (1976). Open shop scheduling to minimize finish time. Journal of Association of Computing Machinery, 23(4), 665–679.

    Article  Google Scholar 

  • Gordon, V., Proth, J. M., & Chu, C. B. (2002). A survey of the state-of-the-art of common due date assignment and scheduling research. European Journal of Operational Research, 139(1), 1–25.

    Google Scholar 

  • Gordon, V., Proth, J. M., & Chu, C. B. (2002). Due date assignment and scheduling: SLK, TWK and other due date assignment models. Production Planning and Control, 13(2), 117–132.

    Article  Google Scholar 

  • Gordon, V., Proth, J. M., & Strusevich, V. A. (2004). Scheduling with due date assignment. In J. Y.-T. Leung (Ed.), Handbook of scheduling (pp. 21-1-21-22). Boca Raton, FL: CRC Press.

  • Graham, R. L., Lawler, E. L., & Lenstra, J. K. (1979). Optimization and approximation in deterministic sequencing and scheduling: A survey. Annals of Discrete Mathematics, 4, 287–326.

    Article  Google Scholar 

  • Guerrero, H. H., & Kern, G. M. (1988). How to more effectively accept and refuse orders. Production and Inventory Management, 29(4), 59–63.

    Google Scholar 

  • Gurel, S., & Akturk, M. S. (2007). Scheduling parallel CNC machines with time/cost trade-off considerations. Computers and Operations Research, 34(9), 2774–2789.

    Article  Google Scholar 

  • Hoogeveen, H., Skutella, M., & Woeginger, G. J. (2003). Preemptive scheduling with rejection. Mathematical Programming, 94(3), 361–374.

    Article  Google Scholar 

  • Hoogeveen, H. (2005). Multicriteria scheduling. European Journal of Operational Research, 167, 592–623.

    Article  Google Scholar 

  • Jansen, K., & Porkolab, L. (1999). Improved approximation schemes for scheduling unrelated parallel machines. In STOC ’99 Proceedings of the Thirty-First Annual ACM Symposium on Theory of Computing, Atlanta (pp. 408–417).

  • Józefowska, J., Jurisch, B., & Kubiak, W. (1994). Scheduling shops to minimize the weighted number of late jobs. Operations Research Letters, 16, 277–283.

    Article  Google Scholar 

  • Kaminsky, P., & Hochbaum, D. (2004). Due date quotation models and algorithms. In J. Y.-T. Leung (Ed.), Handbook of scheduling (pp. 20-1–20-22). Boca Raton, FL: CRC Press.

  • Karp, R. M. (1972). Reducibility among combinatorial problems. In R. E. Miller & J. W. Thatcher (Eds.), Complexity of computer computations (pp. 85–103). New York: Plenum Press.

  • Kellerer, H., Pferschy, U., & Pisinger, D. (2004). Knapsack problems. Berlin: Springer.

    Book  Google Scholar 

  • Khuller, S., & Mestre, J. (2008). An optimal incremental algorithm for minimizing lateness with rejection. Lecture Notes in Computer Science, 5193, 601–610.

    Article  Google Scholar 

  • Koulamas, C. (2010). A faster algorithm for a due date assignment problem with tardy jobs. Operations Research Letters, 38(2), 127–128.

    Article  Google Scholar 

  • Lawler, E. L., & Moore, J. M. (1969). A functional equation and its application to resource allocation and sequencing problems. Management Science, 16(1), 77–84.

    Article  Google Scholar 

  • Lawler, E. L. (1973). Optimal sequencing of a single machine subject to precedence constraints. Operations Research, 26, 544–546.

    Google Scholar 

  • Lawler, E. L., & Lenstra, J. K. (1982). Recent developments in deterministic sequencing and scheduling: A survey. In J. K. Lenstra & A. H. G. Rinnooy Kan (Eds.), Deterministic and stochastic scheduling (pp. 35–73). Dordrecht: Dempster, Reidel.

  • Leung, J. Y. T., & Li, C. L. (2008). Scheduling with processing time restriction: A survey. International Journal of Production Economics, 116(2), 251–262.

    Article  Google Scholar 

  • Li, X., & Feng, H. (2010). Minimize the sum of total completion time and total rejection penalties on a single batching machine. In Procedding of the International Conference on Information, Engineering (pp. 200–202).

  • Lin, J. H., & Vitter, J. S. (1992). \(\varepsilon \)-Approximation algorithms with minimum packing constraint violation. In STOC ’92 Proceedings of the Twenty-Fourth Annual ACM Symposium on Theory of Computing (pp. 771–782).

  • Li, S., & Yuan, J. (2010). Parallel-machine scheduling with deteriorating jobs and rejection. Theoretical Computer Science, 411, 3642–3650.

    Article  Google Scholar 

  • Lu, L., Cheng, T. C. E., Yuan, J., & Zhang, L. (2009). Bounded single-machine parallel-batch scheduling with release dates and rejection. Computers and Operations Research, 36(10), 2748–2751.

    Article  Google Scholar 

  • Lu, L., Zhang, L., & Yuan, J. (2008). The unbounded parallel batch machine scheduling with release dates and rejection to minimize makespan. Theoretical Computer Science, 396, 283–289.

    Article  Google Scholar 

  • Miao, C., Zhang, Y., & Wang, C. (2010). Bounded parallel-batch scheduling on unrelated parallel machines. Lecture Notes in Computer Science, 6124, 220–228.

    Article  Google Scholar 

  • Moghaddam, A., Yalaoui, F., Amodeo, L., Karimi, B., & Jolai, F. (2010). Developing a technique for a bi-objective scheduling model with rejection by simulated annealing. In MOSIM’10, Proceedings of the Eight International Conference of Modeling and Simulation, Hammamet.

  • Mosheiov, G. (2003). Scheduling unit processing time jobs on an \(m\)-machine flow shop. Journal of the Operational Research Society, 54(4), 437–441.

    Google Scholar 

  • Mosheiov, G., & Oron, D. (2005). A note on flow-shop and job-shop batch scheduling with identical processing-time jobs. European Journal of Operational Research, 161(1), 285–291.

    Article  Google Scholar 

  • Mosheiov, G., & Sarig, A. (2009). Scheduling and due-date assignment problems with job rejection. Foundations of Computing and Decision Sciences, 34(3), 193–208.

    Google Scholar 

  • McGovern, G., & Quelch, J. (2005). Outsourcing marketing. Harvard Business Review, 83, 2–3.

    Google Scholar 

  • Nobibon, F. T., & Leus, R. (2011). Exact algorithms for a generalization of the order acceptance and scheduling problem in a single-machine environment. Computers and Operations Research, 38(10), 367–378.

    Article  Google Scholar 

  • Oğuz, C., Salman, S., & Bilgintürk, Z. (2010). Order acceptance and scheduling decisions in make-to-order systems. International Journal of Production Economics, 125(1), 200–211.

    Article  Google Scholar 

  • Orlin, J. B., Schulz, A. S., & Sengupta, S. (2000). \(\varepsilon \)-Optimization schemes and L-Bit precision: Alternative perspectives in combinatorial optimization. In STOC ’00 Proceedings of the Thirty-Two Annual ACM Symposium on Theory of Computing.

  • Panwalker, S. S., Dudek, R. A., & Smith, M. L. (1973). Sequencing research and the industrial problem. In S. E. Elmaghraby (Ed.), Symposium on the theory of scheduling and its applications (pp. 29–38). Berlin: Springer.

    Chapter  Google Scholar 

  • Papadimitriou, C. H., & Yannakakis, M. (2000). On the approximability of trade-offs and optimal access of web sources. In Proceedings 41th Annual IEEE Symposium on Foundations of Computer Science, Redondo Beach, CA, USA (pp. 86–92).

  • Phillips, C. A., Uma, R. N., & Wein, J. (2000). Off-line admission control for general scheduling problems. Journal of Scheduling, 3, 365–381.

    Article  Google Scholar 

  • Pinedo, M. (2008). Scheduling: Theory, algorithms and systems (3rd ed.). Upper Saddle River, NJ: Prentice-Hall.

    Google Scholar 

  • Rom, W. O., & Slotnick, S. A. (2009). Order acceptance using genetic algorithms. Computers and Operations Research, 36(5), 1758– 1767.

    Google Scholar 

  • Rothkopf, M. H. (1966). Scheduling independent tasks on parallel processors. Management Science, 12(5), 437–447.

    Article  Google Scholar 

  • Sahni, S. (1976). Algorithms for scheduling independent tasks. Journal of the ACM, 23(1), 116–127.

    Article  Google Scholar 

  • Schulz, A. S., & Skutella, M. (1997). Random-based scheduling: New approximations and LP lower bounds. Lecture Notes in Computer Science, 1269, 119–133.

    Article  Google Scholar 

  • Schulz, A. S., & Skutella, M. (1997). Scheduling-LPs bear probabilities: Randomized approximations for min-sum criteria. Lecture Notes in Computer Science, 1284, 416–429.

    Article  Google Scholar 

  • Sengupta, S. (2003). Algorithms and approximation schemes for minimum lateness/tardiness scheduling with rejection. Lecture Notes in Computer Science, 2748, 79–90.

    Article  Google Scholar 

  • Shabtay, D., & Steiner, G. (2006). Two due date assignment problems in scheduling a single machine. Operations Research Letters, 34(6), 683–691.

    Article  Google Scholar 

  • Shabtay, D., & Steiner, G. (2007). A survey of scheduling with controllable processing times. Discrete Applied Mathematics, 155(13), 1643–1666.

    Article  Google Scholar 

  • Shabtay, D., Gaspar, N., & Yedidsion, L. (2012). A bicriteria approach to scheduling a single machine with rejection and positional penalties. Journal of Combinatorial Optimization, 23(4), 395–424.

    Google Scholar 

  • Shabtay, D., & Gaspar, N. (2012). Two-machine flow-shop with rejection. Computers and Operations Research, 39(5), 1087–1096.

    Article  Google Scholar 

  • Shakhlevich, N., Hoogeveen, H., & Pinedo, M. (1998). Minimizing total weighted completion time in a proportionate flow shop. Journal of Scheduling, 1(3), 157–168.

    Article  Google Scholar 

  • Shmoys, D. B., & Tardos, E. (1993). An approximation algorithm for the generalized assignment problem. Mathematical Programming, 62, 461–474.

    Article  Google Scholar 

  • Slotnick, S. A., & Morton, T. E. (1996). Selecting jobs for a heavily loaded shop with lateness penalties. Computers and Operations Research, 23(2), 131–140.

    Article  Google Scholar 

  • Slotnick, S. A., & Morton, T. E. (2007). Order acceptance with weighted tardiness. Computers and Operations Research, 34, 3029–3042.

    Google Scholar 

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

    Article  Google Scholar 

  • Steiner, G., & Zhang, R. (2011). Revised delivery-time quotation in scheduling with tardiness penalties. Operations Research, 59, 1504–1511.

    Google Scholar 

  • T’kindt, V., & Billaut, J.-C. (2006). Multicriteria scheduling: Theory, models and algorithms (2nd ed.). Berlin: Springer.

    Google Scholar 

  • T’kindt, V., & Della Croce, F. (2007). Enumeration of Pareto optima for a flowshop scheduling problem with two criteria. INFORMS Journal of Computing, 19(1), 64–72.

    Article  Google Scholar 

  • Trick, M. A. (1994). Scheduling multiple variable-speed machines. Operations Research, 42(2), 234–248.

    Article  Google Scholar 

  • Yang, B., & Geunes, J. (2007). A single resource scheduling problem with job-selection flexibility, tardiness costs and controllable processing times. Computers and Industrial Engineering, 53, 420–432.

    Article  Google Scholar 

  • Zhang, S., Cao, Z., & Zhang Y. (2009a). Scheduling with rejection to minimize the total weighted completion time. In ISORA’09 (pp. 111–114).

  • Zhang, L., Lu, L., & Yuan, J. (2009b). Single machine scheduling with release dates and rejection. European Journal of Operational Research, 198(3), 975–978.

    Google Scholar 

  • Zhang, L., Lu, L., & Yuan, J. (2010). Single-machine scheduling under the job rejection constraint. Theoretical Computer Science, 411, 1877–1882.

    Article  Google Scholar 

  • Zhang, Y., Ren, J., & Wang, C. (2009c). Scheduling with rejection to minimize the makespan. Lecture Notes in Computer Science, 5573, 411–420.

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Acknowledgments

We would like to thank the anonymous referees for their helpful and valuable comments which greatly helped us to improve the quality of this survey paper.

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Authors and Affiliations

  1. Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer Sheva, Israel

    Dvir Shabtay, Nufar Gaspar & Moshe Kaspi

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  1. Dvir Shabtay
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  2. Nufar Gaspar
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  3. Moshe Kaspi
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Correspondence to Dvir Shabtay.

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An erratum to this article is available at http://dx.doi.org/10.1007/s10951-015-0417-1.

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Shabtay, D., Gaspar, N. & Kaspi, M. A survey on offline scheduling with rejection. J Sched 16, 3–28 (2013). https://doi.org/10.1007/s10951-012-0303-z

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