Abstract
In this paper, we consider a single-machine earliness-tardiness scheduling problem with due-date assignment, in which the processing time of a job is a function of its position in a sequence and its resource allocation. The due date assignment methods studied include the common due date, and the slack due date, which reflects equal waiting time allowance for the jobs. For each combination of due date assignment method and processing time function, we provide a polynomial-time algorithm to find the optimal job sequence, due date values, and resource allocations that minimize an integrated objective function, which includes earliness, tardiness, due date assignment, and total resource consumption costs.
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References
Adamopoulos G.I., Pappis C.P.: Single machine scheduling with flow allowances. J. Operat. Res. Soc. 47, 1280–1285 (1996)
Baker K.R., Scudder G.D.: Sequencing with earliness and tardiness penalties: a review. Operat. Res. 38, 22–36 (1990)
Biskup D.: Single-machine scheduling with learning considerations. Eur. J. Operat. Res. 115, 173–178 (1999)
Biskup D.: A state-of-the-art review on scheduling with learning effects. Eur. J. Operat. Res. 188, 315–329 (2008)
Dambreville F.: Cross-entropic learning of a machine for the decision in a partially observable universe. J. Global Optim. 37, 541–555 (2007)
Gordon V.S., Proth J.M., Chu C.B.: A survey of the state of- the-art of common due date assignment and scheduling research. Eur. J. Operat. Res. 139, 1–25 (2002)
Gordon V.S., Proth J.M., Chu C.B.: Due date assignment and scheduling: SLK, TWK and other due date assignment models. Product. Plan. Control 13, 117–132 (2002)
Floudas C.A., Pardalos P.M.: Encyclopedia of optimization, 2nd ed. Springer, Berlin (2009)
Graham R.L., Lawler E.L., Lenstra J.K., Rinnooy Kan A.H.G.: Optimization and approximation in deterministic sequencing and scheduling: a survey. Ann. Discret. Math. 5, 287–326 (1979)
Hadda H.: A (\({\frac{4}{3}}\))-approximation algorithm for a special case of the two machine flow shop problem with several availability constraints. Optim. Lett. 3, 583–592 (2009)
Hardy G.H., Littlewood J.E., Polya G.: Inequalities. Cambridge University Press, Cambridge (1934)
Lee C.-Y., Yu G.: Parallel-machine scheduling under potential disruption. Optim. Lett. 2, 27–37 (2008)
Leyvand Y., Shabtay D., Steiner G.: A unified approach for scheduling with convex resource consumption functions using positional penalties. Eur. J. Operat. Res. 206, 301–312 (2010)
Mosheiov G.: Scheduling problems with a learning effect. Eur. J. Operat. Res. 132, 687–693 (2001)
Mosheiov G., Sidney J.B.: Scheduling with general job-dependent learning curves. Eur. J. Operat. Res. 147, 665–670 (2003)
Panwalker S.S., Smith M.L., Seidmann A.: Common due-date assignment to minimize total penalty for the one machine scheduling problem. Operat. Res. 30, 391–399 (1982)
Panwalkar S.S., Rajagopalan R.: Single-machine sequencing with controllable processing times. Eur. J. Operat. Res. 59, 298–302 (1992)
Pardalos P.M., Resende M.G.C.: Handbook of applied optimization. Oxford University Press, Oxford (2002)
Pardalos P.M.: Complexity in numerical optimization. World Scientific, Singapore (1993)
Pinedo M.: Scheduling: theory, algorithms, and systems. Prentice-Hall, Upper Saddle River (2002)
Setamaa-Karkkainen A., Miettinen K., Vuori J.: Heuristic for a new multiobjective scheduling problem. Optim. Lett. 1, 213–225 (2007)
Shabtay D., Steiner G.: A survey of scheduling with controllable processing times. Discret. Appl. Math. 155, 1643–1666 (2007)
Shabtay D., Steiner G.: The single-machine earliness-tardiness scheduling problem with due date assignment and resource-dependent processing times. Ann. Operat. Res. 159, 25–40 (2008)
Wang J.-B., Li J.-X.: Single machine past-sequence-dependent setup times scheduling with general position-dependent and time-dependent learning effects. Appl. Math. Model. 35, 1388–1395 (2011)
Wang J.-B., Sun L.-H., Sun L.-Y.: Single machine scheduling with a learning effect and discounted costs. Int. J. Adv. Manuf. Technol. 49, 1141–1149 (2010)
Wang J.-B., Wang M.-Z.: Single machine multiple common due dates scheduling with general job-dependent learning curves. Comput. Math. Appl. 60, 2998–3002 (2010)
Wang J.-B., Wang M.-Z.: A revision of machine scheduling problems with a general learning effect. Math. Comput. Model. 53, 330–336 (2011)
Wang J.-B., Wang M.-Z.: Worst-case behavior of simple sequencing rules in flow shop scheduling with general position-dependent learning effects. Ann. Operat. Res. 191, 155–169 (2011)
Wang J.-B., Wang M.-Z.: Single-machine scheduling with nonlinear deterioration. Optim. Lett. 6, 87–98 (2012)
Wang, J.-B., Ji, P., Cheng, T.C.E., Wang, D.: Minimizing makespan in a two-machine flow shop with effects of deterioration and learning. Optim. Lett. doi:10.1007/s11590-011-0334-y
Wang, J.-B., Wang, X.-Y., Sun, L.-H., Sun, L.-Y.: Scheduling jobs with truncated exponential learning functions. Optim. Lett. doi:10.1007/s11590-011-0433-9
Wang D., Wang M.-Z., Wang J.-B.: Single-machine scheduling with learning effect and resource-dependent processing times. Comput. Indus. Eng. 59, 458–462 (2010)
Xu L.: Machine learning problems from optimization perspective. J. Global Optimiz. 47, 369–401 (2010)
Yin N., Wang X.-Y.: Single-machine scheduling with controllable processing times and learning effect. Int. J. Adv. Manuf. Technol. 54, 743–748 (2011)
Zhao C.-L., Tang H.-Y.: A note on two-machine no-wait flow shop scheduling with deteriorating jobs and machine availability constraints. Optim. Lett. 5, 183–190 (2011)
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Lu, YY., Li, G., Wu, YB. et al. Optimal due-date assignment problem with learning effect and resource-dependent processing times. Optim Lett 8, 113–127 (2014). https://doi.org/10.1007/s11590-012-0467-7
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DOI: https://doi.org/10.1007/s11590-012-0467-7