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Optimal Planning of a Multi-Station System with Sojourn Time Constraints

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  • Marcos Singer
  • Patricio Donoso
  • José Noguer

Abstract

This paper studies a dynamic production system where multiple products must visit stations where inventories are constrained by maximum and minimum sojourn times with neither negative flow nor backlog being allowed. A resource availability constraint limits the aggregate throughput of the stations. The objective is to minimize the sum of flow and inventory cost. The problem is broken down into several single-product serial systems that serve as subroutines of a Lagrangian relaxation routine. This model is implemented in a spreadsheet so that it can be used by the officials of a Chilean institution for planning the operations and defining the optimal allocation of resources. Copyright Springer Science + Business Media, Inc. 2005

Suggested Citation

  • Marcos Singer & Patricio Donoso & José Noguer, 2005. "Optimal Planning of a Multi-Station System with Sojourn Time Constraints," Annals of Operations Research, Springer, vol. 138(1), pages 203-222, September.
    • Handle: RePEc:spr:annopr:v:138:y:2005:i:1:p:203-222:10.1007/s10479-005-2454-1
    DOI: 10.1007/s10479-005-2454-1
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    References listed on IDEAS

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    1. Michael Pinedo & Marcos Singer, 1999. "A shifting bottleneck heuristic for minimizing the total weighted tardiness in a job shop," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(1), pages 1-17, February.
    2. A.J. Ganesh, 1998. "Large deviations of the sojourn time for queues in series," Annals of Operations Research, Springer, vol. 79(0), pages 3-26, January.
    3. A. Auslender & R. Cominetti & M. Haddou, 1997. "Asymptotic Analysis for Penalty and Barrier Methods in Convex and Linear Programming," Mathematics of Operations Research, INFORMS, vol. 22(1), pages 43-62, February.
    4. Yang, Jun & Yan, Houmin & Sethi, Suresh P., 1999. "Optimal production planning in pull flow lines with multiple products," European Journal of Operational Research, Elsevier, vol. 119(3), pages 582-604, December.
    5. Fangruo Chen, 1998. "Stationary Policies in Multiechelon Inventory Systems with Deterministic Demand and Backlogging," Operations Research, INFORMS, vol. 46(3-supplem), pages 26-34, June.
    6. James R. Bradley & Bruce C. Arntzen, 1999. "The Simultaneous Planning of Production, Capacity, and Inventory in Seasonal Demand Environments," Operations Research, INFORMS, vol. 47(6), pages 795-806, December.
    7. Tayfur Altiok, 2000. "Tandem queues in bulk port operations," Annals of Operations Research, Springer, vol. 93(1), pages 1-14, January.
    8. Stephen C. Graves & David B. Kletter & William B. Hetzel, 1998. "A Dynamic Model for Requirements Planning with Application to Supply Chain Optimization," Operations Research, INFORMS, vol. 46(3-supplem), pages 35-49, June.
    9. Singer, Marcos & Donoso, Patricio & Poblete, Francisco, 2002. "Semi-autonomous planning using linear programming in the Chilean General Treasury," European Journal of Operational Research, Elsevier, vol. 140(2), pages 517-529, July.
    10. M Singer & P Donoso & S Jara, 2002. "Fleet configuration subject to stochastic demand: an application in the distribution of liquefied petroleum gas," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 53(9), pages 961-971, September.
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    Cited by:

    1. Singer, Marcos & Donoso, Patricio, 2006. "Strategic decision-making at a steel manufacturer assisted by linear programming," Journal of Business Research, Elsevier, vol. 59(3), pages 387-390, March.
    2. Singer, Marcos & Donoso, Patricio, 2008. "Empirical validation of an activity-based optimization system," International Journal of Production Economics, Elsevier, vol. 113(1), pages 335-345, May.
    3. Kung-Jeng Wang & Yu-Siang Lin, 2012. "Optimal inventory replenishment strategy for deteriorating items in a demand-declining market with the retailer’s price manipulation," Annals of Operations Research, Springer, vol. 201(1), pages 475-494, December.

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