Abstract
We consider a single-machine scheduling problem, in which the job processing times are controllable or compressible. The performance criteria are the compression cost and the number of tardy jobs. For the problem, where no tardy jobs are allowed and the objective is to minimize the total compression cost, we present a strongly polynomial time algorithm. For the problem to construct the trade-off curve between the number of tardy jobs and the maximum compression cost, we present a polynomial time algorithm. Furthermore, we extend the problem to the case of discrete controllable processing times, where the processing time of a job can only take one of several given discrete values. We show that even some special cases of the discrete controllable version with the objective of minimizing the total compression cost are NP-hard, but the general case is solvable in pseudo-polynomial time. Moreover, we present a strongly polynomial time algorithm to construct the trade-off curve between the number of tardy jobs and the maximum compression cost for the discrete controllable version.
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References
Chen, Z.-L., Lu, Q., & Tang, G. C. (1997). Single machine scheduling with discretely controllable processing times. Operations Research Letters, 21, 69–76.
Cheng, T. C. E., Chen, Z.-L., & Li, C.-L. (1996). Single-machine scheduling with trade-off between number of tardy jobs and resource allocation. Operations Research Letters, 19, 237–242.
De, P., Dunne, E. J., Ghosh, J. B., & Wells, C. E. (1995). The discrete time-cost trade-off problem revisited. European Journal of Operational Research, 81, 225–238.
De, P., Dunne, E. J., Ghosh, J. B., & Wells, C. E. (1997). Complexity of the discrete time-cost trade-off problem for project networks. Operations Research, 45, 302–306.
Daniels, R. L., & Sarin, R. K. (1989). Single machine scheduling with controllable processing times and number of jobs tardy. Operations Research, 37, 981–984.
Garey, M. R., & Johnson, D. S. (1978). Computers and intractability: a guide to the theory of NP-hardness. San Francisco: Freeman.
Martello, S., & Toth, P. (1990). Knapsack problems: algorithm and computer implementations. Chichester: Wiley.
Moore, J. M. (1968). An n job, one-machine sequencing algorithm for minimizing the number of late jobs. Management Science, 15, 102–109.
Nowicki, E., & Zdrzalka, S. (1990). A survey of results for sequencing problems with controllable processing times. Discrete Applied Mathematics, 25, 271–287.
Skutella, M. (1998). Approximation algorithms for the discrete time-cost trade-off problem. Mathematics of Operations Research, 23, 909–929.
Van Wassenhove, L. N., & Baker, K. R. (1982). A bicriterion approach to time/cost trade-offs in sequencing. European Journal of Operational Research, 11, 48–54.
Vickson, R. G. (1980a). Choosing the job sequence and processing times to minimize total processing plus flow cost on a single machine. Operations Research, 28, 1155–1167.
Vickson, R. G. (1980b). Two single machine sequencing problems involving controllable job processing times. IIE Transactions, 12, 258–262.
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This research was supported by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of the MOE, China, and the National Natural Science Foundation of China (10271110). The third author was supported in part by The Hong Kong Polytechnic University under a grant from the ASD in China Business Services.
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He, Y., Wei, Q. & Cheng, T.C.E. Single-machine scheduling with trade-off between number of tardy jobs and compression cost. J Sched 10, 303–310 (2007). https://doi.org/10.1007/s10951-007-0027-7
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DOI: https://doi.org/10.1007/s10951-007-0027-7