Abstract
This paper deals with two-machine flowshop problems with deteriorating tasks, i.e. tasks whose processing times are a nondecreasing function that depend on the length of the waiting periods. We consider the so-called Restricted Problem. This problem can be defined as follows: for a given permutation of tasks, find an optimal placement on two machines so that the total completion time is minimized. We will show that the Restricted Problem is nontrivial. We give some properties for the optimal placement and we propose an optimal placement algorithm.
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Alidaee, B.: Single machine scheduling with nonlinear cost functions. Comput. Oper. Res. 18, 317–322 (1991)
Chen, Z.-L.: Parallel machine scheduling with time dependent processing times. Discrete Appl. Math. 70, 81–93 (1996)
Finke, G., Jiang, H.: A variant of the permutation flow shop model with variable processing times. Discrete Appl. Math. 76, 123–140 (1997)
Espinouse, M.-L., Finke, G., Jiang, H.: General flowshop models: job dependent capacities, job overlapping and deterioration. Int. Trans. Oper. Res. 9, 399–414 (2002)
Gupta, J.N.D., Gupta, S.K.: Single facility scheduling with nonlinear processing times. Comput. Ind. Eng. 14, 387–393 (1988)
Janiak, A.: General flow-shop scheduling with resource constraints. Int. J. Prod. Res. 26, 1089–1103 (1988)
Janiak, A.: Minimization of resource consumption under a given deadline in two-processor flow-shop scheduling problem. Inf. Process. Lett. 32, 101–112 (1989)
Mosheiov, G.: ∧-shaped policies to schedule deteriorating jobs. J. Oper. Res. Soc. 47, 1184–1191 (1996)
Mosheiov, G.: Multi-machine scheduling with linear deterioration. INFOR 36, 205–214 (1998)
Mosheiov, G.: Complexity analysis of job-shop scheduling with deteriorating jobs. Discrete Appl. Math. 117, 195–209 (2002)
Sriskandarajah, C., Goyal, S.K.: Scheduling of two-machine flowshop with processing time linearly dependent on job waiting-time. J. Oper. Res. Soc. 40, 907–921 (1989)
Sriskandarajah, C., Wagneur, E.: Hierarchical control of the two processor flow-shop with state-dependent processing time: complexity analysis and approximate algorithms. INFOR 29, 193–205 (1991)
Wagneur, E., Sriskandarajah, C.: Optimal control of a class of deds: flow-shops with state-dependent processing times. Discret. Event Dyn. Syst., Theory Appl. 3, 397–425 (1993)
Wagneur, E., Sriskandarajah, C.: The two-machine permutation flow-shops with state-dependent processing times. Nav. Res. Logist. 40, 697–717 (1993)
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Finke, G., Oulamara, A. Total Completion Time in a Two-machine Flowshop with Deteriorating Tasks. J Math Model Algor 6, 563–576 (2007). https://doi.org/10.1007/s10852-007-9057-6
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DOI: https://doi.org/10.1007/s10852-007-9057-6