Abstract
This paper concerns a due-date matching problem in a single-stage manufacturing system. Given a finite sequence of jobs and their service order, and given the delivery due date of each job, the problem is to choose the jobs release (arrival) times so as to match as closely as possible their completion times to their respective due dates. The system is modelled as a deterministic single-server FIFO queue with an output buffer for storing jobs whose service is completed prior to their due dates. The output buffer has a finite capacity; when it is full, the server is being blocked. Associated with each job there is a convex cost function penalizing its earliness as well as tardiness. The due-date matching problem is cast as an optimal control problem, whose objective is to minimize the sum of the above cost functions by the choice of the jobs arrival (release) times. Time-box upper-bound and lower-bound constraints are imposed on the jobs output (delivery) times. The optimal-control setting brings to bear on the development of fast and efficient algorithms having intuitive geometric appeal and potential for online implementation.
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References
K. R. Baker G. D. Scudder (1990) ArticleTitleSequencing with Earliness and Tardiness Penalties: A Review. Operations Research. 38 22–36
C. G. Cassandras D. L. Pepyne Y. Wardi (2001) ArticleTitleOptimal Control of a Class of Hybrid Systems. IEEE Transactions on Automatic Control. 46 398–415 Occurrence Handle10.1109/9.911417
A. Di Febbraro R. Minciardi S. Sacone (2002) ArticleTitleOptimal Control Laws for Lot-Sizing and Timing of Jobs on a Single Production Facility. IEEE Transactions on Automatic Control. 47 1613–1623 Occurrence Handle10.1109/TAC.2002.803527
Wagneur E., and Sriskandarajah C., DEDS with State-Dependent Event Durations Look–Ahead Policies and Scheduling Proceedings of the 31st IEEE Conference on Decision and Control, Tucson, Arizona:413–418, 1992.
G. Mosheiov M. Shadmon (2001) ArticleTitleMinmax Earliness-Tardiness Costs with Unit Processing Time Jobs. European Journal of Operational Research. 130 638–652 Occurrence Handle10.1016/S0377-2217(99)00432-4
M. Gazarik Y. Wardi (1998) ArticleTitleOptimal Release Times in a Single Server: An Optimal Control Perspective. IEEE Transactions on Automatic Control. 43 998–1002 Occurrence Handle10.1109/9.701110
Y. Wardi C. G. Cassandras D. L. Pepyne (2001) ArticleTitleA Backward Algorithm for Computing Optimal Controls for Single-Stage Manufacturing Systems. International Journal on Production Research. 39 369–393 Occurrence Handle10.1080/00207540010004313
Y. Cho C. G. Cassandras D. L. Pepyne (2001) ArticleTitleForward Decomposition Algorithms for Optimal Control of a Class of Hybrid Systems. International Journal on Robust and Nonlinear Control. 11 497–513 Occurrence Handle10.1002/rnc.595
P. Chretienne F. Sourd (2003) ArticleTitlePERT Scheduling with Convex Cost Functions. Journal of Theoretical Computer Science. 292 145–164 Occurrence Handle10.1016/S0304-3975(01)00220-1
Moon J., and Wardi Y. (2003). Optimal Control of Completion Times in Single-Stage Max-Plus Systems Proceedings of the Conference on Analysis and Design of Hybrid Systems, St. Malo, France:307–312
Moon J., and Wardi Y.(2003). Optimal Release Times in Single-Stage Manufacturing Systems with Blocking: Optimality Conditions and Numerical Algorithms Technical Memorandum, School of Electrical and Computer Engineering. Institute of Technology, Georgia
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Communicated by W. B. Gong
Research supported in part by the National Science Foundation under Grant ECS-9979693 and by the Georgia Tech Manufacturing Research Center under Grant B01-D06.
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Moon, J., Wardi, Y. Optimal Release Times in Single-Stage Manufacturing Systems with Blocking: Optimal Control Perspective. J Optim Theory Appl 125, 653–672 (2005). https://doi.org/10.1007/s10957-005-2094-2
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DOI: https://doi.org/10.1007/s10957-005-2094-2