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Minmax scheduling with job-classes and earliness-tardiness costs. (English) Zbl 1107.90022
Summary: We address scheduling problems with job-dependent due-dates and general (possibly nonlinear and asymmetric) earliness and tardiness costs. The number of distinct due-dates is substantially smaller than the number of jobs, thus jobs are partitioned to classes, where all jobs of a given class share a common due-date. We consider the settings of a single machine and parallel identical machines. Our objective is of a minmax type, i.e., we seek a schedule that minimizes the maximum earliness/tardiness cost among all jobs.We introduce a nonlinear program that needs to be solved in order to obtain an optimal solution for the single-machine case. The case of parallel identical machines is NP-hard even for two machines, linear costs and a single common due-date. We introduce an LPT-based (largest processing time first) heuristic and a simple lower bound on the optimal cost. Both the heuristic and the lower bound are asymptotically accurate under very general conditions. Our numerical tests indicate that the heuristic produces very close-to-optimal schedules in all settings.

90B35Scheduling theory, deterministic
Full Text: DOI
[1] Abdul-Razaq, T. S.; Potts, C. N.: Dynamic programming state space relaxation for single machine scheduling. Journal of operational research society 39, 141-152 (1988) · Zbl 0655.90034
[2] Federgruen, A.; Mosheiov, G.: Heuristics for multi-machine minmax scheduling problems with earliness and tardiness costs. Naval research logistics 44, 287-299 (1997) · Zbl 0890.90100
[3] Frenk, J. B. G.; Kan, A. H. G. Rinnooy: The asymptotic optimality of the LPT rule. Mathematics of operations research 12, 241-254 (1987) · Zbl 0632.90031
[4] Fry, T. D.; Armstrong, R. D.; Blackstone, J. H.: Minimizing weighted absolute deviation in single machine scheduling. IIE transactions 19, 445-450 (1987)
[5] Garey, M. R.; Tarjan, R. E.; Wilfong, G. T.: One processor scheduling with symmetric earliness and tardiness penalties. Mathematics of operations research 13, 330-348 (1988) · Zbl 0671.90033
[6] Ibaraki, T.; Nakamura, Y.: A dynamic programming method for single machine scheduling. European journal of operational research 76, 72-82 (1994) · Zbl 0806.90064
[7] Lakshminarayan, S.; Lakshmanan, R.; Papineau, R.; Rochette, R.: Optimal single-machine scheduling with earliness and tardiness penalties. Operations research 26, 1079-1082 (1978) · Zbl 0413.90031
[8] Lee, C. Y.; Choi, J. Y.: A genetic algorithm for job sequencing problems with distinct due-dates and general early-tardy penalty weights. Computers and operation research 22, 857-869 (1995) · Zbl 0838.90066
[9] Li, C. -L.; Chen, Z. -L.; Cheng, T. C. E.: A note on one processor scheduling with asymmetry earliness and tardiness penalties. Operations research letters 13, 33-46 (1993)
[10] Mazzini, R.; Armentano, V. A.: A heuristic for single machine scheduling with early and tardy cost. European journal of operational research 128, 129-146 (2001) · Zbl 0983.90021
[11] Oguz, C.; Dincer, C.: Single machine earliness -- tardiness scheduling problems using the equal-slack rule. Journal of operational research society 45, 589-594 (1994)
[12] Ow, P. S.; Morton, T. E.: The single machine early-tardy problem. Management science 35, 177-191 (1989) · Zbl 0666.90043
[13] Seidmann, A.; Panwalker, S. S.; Smith, M. L.: Optimal assignment of due-dates for a single processor scheduling problem. International journal of production research 19, 393-399 (1981)
[14] Sidney, J. B.: Optimal single-machine scheduling with earliness and tardiness penalties. Operations research 25, 62-69 (1977) · Zbl 0383.90055
[15] Szwarc, W.: Adjacent orderings in single machine scheduling with earliness and tardiness penalties. Naval research logistics 40, 229-243 (1993) · Zbl 0779.90048
[16] Ventura, J. A.; Radhakrishnan, S.: Single machine scheduling with symmetric earliness and tardiness penalties. European journal of operational research 144, 598-612 (2003) · Zbl 1012.90006
[17] Yano, C. A.; Kim, Y.: Algorithms for a class of single machine weighted tardiness and earliness problems. European journal of operational research 52, 167-178 (1991) · Zbl 0725.90041