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A Facilities in Series Inventory Model with Nested Schedules

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  • Stephen F. Love

    (Oregon State University)

Abstract

We consider an n-period single-product inventory model with known requirements and separable concave production and storage costs. The model is a multi-echelon structure in which N facilities, labeled 1,...,N, are arranged in series. We show that if storage and production costs are respectively nondecreasing in order of facilities and nonincreasing in time, then an optimal schedule has the property that if in a given period, facility j produces, then facility j + 1 does also. This nested structure is exploited in an algorithm for finding an optimal schedule. The computational effort increases in proportion to the cube of the number of periods and linearly with the number of facilities. For the stationary infinite horizon case an algorithm yields a periodic optimal schedule.

Suggested Citation

  • Stephen F. Love, 1972. "A Facilities in Series Inventory Model with Nested Schedules," Management Science, INFORMS, vol. 18(5-Part-1), pages 327-338, January.
    • Handle: RePEc:inm:ormnsc:v:18:y:1972:i:5-part-1:p:327-338
    DOI: 10.1287/mnsc.18.5.327
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    Cited by:

    1. Chu, Chi-Leung & Leon, V. Jorge, 2009. "Scalable methodology for supply chain inventory coordination with private information," European Journal of Operational Research, Elsevier, vol. 195(1), pages 262-279, May.
    2. Ming Zhao & Minjiao Zhang, 2020. "Multiechelon Lot Sizing: New Complexities and Inequalities," Operations Research, INFORMS, vol. 68(2), pages 534-551, March.
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    4. Vroblefski, Mark & Ramesh, R. & Zionts, Stanley, 2000. "Efficient lot-sizing under a differential transportation cost structure for serially distributed warehouses," European Journal of Operational Research, Elsevier, vol. 127(3), pages 574-593, December.
    5. Brian Q. Rieksts & José A. Ventura & Yale T. Herer & Daning Sun, 2007. "Technical note: Worst‐case performance of power‐of‐two policies for serial inventory systems with incremental quantity discounts," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(5), pages 583-587, August.
    6. Martin Albrecht, 2017. "Coordination of dynamic lot-sizing in supply chains," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(3), pages 322-330, March.
    7. Anantaram Balakrishnan & Joseph Geunes, 2000. "Requirements Planning with Substitutions: Exploiting Bill-of-Materials Flexibility in Production Planning," Manufacturing & Service Operations Management, INFORMS, vol. 2(2), pages 166-185, January.
    8. Joseph Geunes & H. Edwin Romeijn & Kevin Taaffe, 2006. "Requirements Planning with Pricing and Order Selection Flexibility," Operations Research, INFORMS, vol. 54(2), pages 394-401, April.
    9. Zhang, Guoqing & Nishi, Tatsushi & Turner, Sarina D.O. & Oga, Keisuke & Li, Xindan, 2017. "An integrated strategy for a production planning and warehouse layout problem: Modeling and solution approaches," Omega, Elsevier, vol. 68(C), pages 85-94.
    10. Ozelkan, Ertunga C. & Cakanyildirim, Metin, 2007. "Resource downgrading," European Journal of Operational Research, Elsevier, vol. 177(1), pages 572-590, February.
    11. Yale T. Herer & Michal Tzur, 2001. "The dynamic transshipment problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(5), pages 386-408, August.
    12. Gautier Stauffer, 2018. "Approximation algorithms for k-echelon extensions of the one warehouse multi-retailer problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(3), pages 445-473, December.
    13. Voros, Jozsef, 1995. "Setup cost stability region for the multi-level dynamic lot sizing problem," European Journal of Operational Research, Elsevier, vol. 87(1), pages 132-141, November.
    14. Adeinat, Hamza & Ventura, Jose A., 2018. "Integrated pricing and supplier selection in a two-stage supply chain," International Journal of Production Economics, Elsevier, vol. 201(C), pages 193-202.
    15. Minjiao Zhang & Simge Küçükyavuz & Hande Yaman, 2012. "A Polyhedral Study of Multiechelon Lot Sizing with Intermediate Demands," Operations Research, INFORMS, vol. 60(4), pages 918-935, August.
    16. Zhang, Guoqing & Shang, Xiaoting & Alawneh, Fawzat & Yang, Yiqin & Nishi, Tatsushi, 2021. "Integrated production planning and warehouse storage assignment problem: An IoT assisted case," International Journal of Production Economics, Elsevier, vol. 234(C).
    17. Kimms, Alf & Drexl, Andreas, 1996. "Multi-level lot sizing: A literature survey," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 405, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    18. Adeinat, Hamza & Pazhani, Subramanian & Mendoza, Abraham & Ventura, Jose A., 2022. "Coordination of pricing and inventory replenishment decisions in a supply chain with multiple geographically dispersed retailers," International Journal of Production Economics, Elsevier, vol. 248(C).
    19. Sunil Chopra & M.R. Rao & Chih‐Yang Tsai, 1997. "Computational study of the multiechelon production planning problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(1), pages 1-19, February.
    20. Mendoza, Abraham & Ventura, José A., 2010. "A serial inventory system with supplier selection and order quantity allocation," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1304-1315, December.
    21. Hark-Chin Hwang & Wilco van den Heuvel & Albert P. M. Wagelmans, 2023. "Multilevel Lot-Sizing with Inventory Bounds," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1470-1490, November.
    22. Voros, Jozsef, 2002. "On the relaxation of multi-level dynamic lot-sizing models," International Journal of Production Economics, Elsevier, vol. 77(1), pages 53-61, May.
    23. Awi Federgruen & Michal Tzur, 1999. "Time‐partitioning heuristics: Application to one warehouse, multiitem, multiretailer lot‐sizing problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(5), pages 463-486, August.
    24. Merzifonluoglu, Yasemin & Geunes, Joseph, 2006. "Uncapacitated production and location planning models with demand fulfillment flexibility," International Journal of Production Economics, Elsevier, vol. 102(2), pages 199-216, August.

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