IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v46y2000i8p1159-1169.html
   My bibliography  Save this article

Dynamic Economic Lot Size Model with Perishable Inventory

Author

Listed:
  • Vernon Ning Hsu

    (School of Management, George Mason University, Fairfax, Virginia 22030)

Abstract

This paper considers an economic lot size (ELS) model for perishable products where an inventory stock's deterioration rate and its carrying cost in each period depend on the age of the stock. We discuss situations where the traditional ELS models are not applicable, and propose a new model with general concave production and inventory cost functions. We explore the structural properties of the optimal solutions and use them to develop a dynamic programming algorithm which solves the problem in polynomial time. We also consider special cases of the general model which are solvable with reduced computational complexities.

Suggested Citation

  • Vernon Ning Hsu, 2000. "Dynamic Economic Lot Size Model with Perishable Inventory," Management Science, INFORMS, vol. 46(8), pages 1159-1169, August.
    • Handle: RePEc:inm:ormnsc:v:46:y:2000:i:8:p:1159-1169
    DOI: 10.1287/mnsc.46.8.1159.12021
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.46.8.1159.12021
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.46.8.1159.12021?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Albert Wagelmans & Stan van Hoesel & Antoon Kolen, 1992. "Economic Lot Sizing: An O(n log n) Algorithm That Runs in Linear Time in the Wagner-Whitin Case," Operations Research, INFORMS, vol. 40(1-supplem), pages 145-156, February.
    2. Thomas E. Morton, 1978. "Note--An Improved Algorithm for the Stationary Cost Dynamic Lot Size Model with Backlogging," Management Science, INFORMS, vol. 24(8), pages 869-873, April.
    3. Uday S. Karmarkar & Sham Kekre & Sunder Kekre, 1987. "The Dynamic Lot-Sizing Problem with Startup and Reservation Costs," Operations Research, INFORMS, vol. 35(3), pages 389-398, June.
    4. Harvey M. Wagner & Thomson M. Whitin, 1958. "Dynamic Version of the Economic Lot Size Model," Management Science, INFORMS, vol. 5(1), pages 89-96, October.
    5. Gabriel R. Bitran & Horacio H. Yanasse, 1982. "Computational Complexity of the Capacitated Lot Size Problem," Management Science, INFORMS, vol. 28(10), pages 1174-1186, October.
    6. Steven Nahmias, 1982. "Perishable Inventory Theory: A Review," Operations Research, INFORMS, vol. 30(4), pages 680-708, August.
    7. Gary D. Eppen & F. J. Gould & B. Peter Pashigian, 1969. "Extensions of the Planning Horizon Theorem in the Dynamic Lot Size Model," Management Science, INFORMS, vol. 15(5), pages 268-277, January.
    8. Willard I. Zangwill, 1969. "A Backlogging Model and a Multi-Echelon Model of a Dynamic Economic Lot Size Production System--A Network Approach," Management Science, INFORMS, vol. 15(9), pages 506-527, May.
    9. Kirk R. Karwan & Joseph B. Mazzola & Richard C. Morey, 1988. "Production lot sizing under setup and worker learning," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(2), pages 159-175, April.
    10. Dong X. Shaw & Albert P. M. Wagelmans, 1998. "An Algorithm for Single-Item Capacitated Economic Lot Sizing with Piecewise Linear Production Costs and General Holding Costs," Management Science, INFORMS, vol. 44(6), pages 831-838, June.
    11. Van Wassenhove, Luk N. & Vanderhenst, Pieter, 1983. "Planning production in a bottleneck department," European Journal of Operational Research, Elsevier, vol. 12(2), pages 127-137, February.
    12. Edward Zabel, 1964. "Some Generalizations of an Inventory Planning Horizon Theorem," Management Science, INFORMS, vol. 10(3), pages 465-471, April.
    13. Michal Tzur, 1996. "Learning in Setups: Analysis, Minimal Forecast Horizons, and Algorithms," Management Science, INFORMS, vol. 42(12), pages 1732-1743, December.
    14. Willard I. Zangwill, 1968. "Minimum Concave Cost Flows in Certain Networks," Management Science, INFORMS, vol. 14(7), pages 429-450, March.
    15. Willard I. Zangwill, 1966. "A Deterministic Multi-Period Production Scheduling Model with Backlogging," Management Science, INFORMS, vol. 13(1), pages 105-119, September.
    16. Kenneth R. Baker & Paul Dixon & Michael J. Magazine & Edward A. Silver, 1978. "An Algorithm for the Dynamic Lot-Size Problem with Time-Varying Production Capacity Constraints," Management Science, INFORMS, vol. 24(16), pages 1710-1720, December.
    17. S. Rajagopalan, 1992. "Deterministic Capacity Expansion Under Deterioration," Management Science, INFORMS, vol. 38(4), pages 525-539, April.
    18. Suresh Chand & Suresh P. Sethi, 1990. "A Dynamic Lot Sizing Model with Learning in Setups," Operations Research, INFORMS, vol. 38(4), pages 644-655, August.
    19. Joseph D. Blackburn & Howard Kunreuther, 1974. "Planning Horizons for the Dynamic Lot Size Model with Backlogging," Management Science, INFORMS, vol. 21(3), pages 251-255, November.
    20. Awi Federgruen & Michal Tzur, 1991. "A Simple Forward Algorithm to Solve General Dynamic Lot Sizing Models with n Periods in 0(n log n) or 0(n) Time," Management Science, INFORMS, vol. 37(8), pages 909-925, August.
    21. van Hoesel, Stan & Wagelmans, Albert & Moerman, Bram, 1994. "Using geometric techniques to improve dynamic programming algorithms for the economic lot-sizing problem and extensions," European Journal of Operational Research, Elsevier, vol. 75(2), pages 312-331, June.
    22. M. Florian & J. K. Lenstra & A. H. G. Rinnooy Kan, 1980. "Deterministic Production Planning: Algorithms and Complexity," Management Science, INFORMS, vol. 26(7), pages 669-679, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lee, Chia-Yen & Charles, Vincent, 2022. "A robust capacity expansion integrating the perspectives of marginal productivity and capacity regret," European Journal of Operational Research, Elsevier, vol. 296(2), pages 557-569.
    2. Jian Zhang & Shuang He & Juliang Zhang & T. C. Edwin Cheng, 2020. "Purchase and retrieval competition for seasonal produce," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(3), pages 161-184, April.
    3. Fuying Jing & Zirui Lan, 2017. "Forecast horizon of multi-item dynamic lot size model with perishable inventory," PLOS ONE, Public Library of Science, vol. 12(11), pages 1-15, November.
    4. Önal, Mehmet & Romeijn, H.Edwin & Sapra, Amar & van den Heuvel, Wilco, 2015. "The economic lot-sizing problem with perishable items and consumption order preference," European Journal of Operational Research, Elsevier, vol. 244(3), pages 881-891.
    5. Brahimi, Nadjib & Absi, Nabil & Dauzère-Pérès, Stéphane & Nordli, Atle, 2017. "Single-item dynamic lot-sizing problems: An updated survey," European Journal of Operational Research, Elsevier, vol. 263(3), pages 838-863.
    6. Wang, Gang & Lei, Lei, 2012. "Polynomial-time solvable cases of the capacitated multi-echelon shipping network scheduling problem with delivery deadlines," International Journal of Production Economics, Elsevier, vol. 137(2), pages 263-271.
    7. Andrea Raiconi & Julia Pahl & Monica Gentili & Stefan Voß & Raffaele Cerulli, 2017. "Tactical Production and Lot Size Planning with Lifetime Constraints: A Comparison of Model Formulations," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(05), pages 1-24, October.
    8. Sazvar, Z. & Mirzapour Al-e-hashem, S.M.J. & Govindan, K. & Bahli, B., 2016. "A novel mathematical model for a multi-period, multi-product optimal ordering problem considering expiry dates in a FEFO system," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 93(C), pages 232-261.
    9. Chung-Lun Li & Vernon Ning Hsu & Wen-Qiang Xiao, 2004. "Dynamic Lot Sizing with Batch Ordering and Truckload Discounts," Operations Research, INFORMS, vol. 52(4), pages 639-654, August.
    10. Qiu, Yuzhuo & Qiao, Jun & Pardalos, Panos M., 2019. "Optimal production, replenishment, delivery, routing and inventory management policies for products with perishable inventory," Omega, Elsevier, vol. 82(C), pages 193-204.
    11. Jing, Fuying & Chao, Xiangrui, 2022. "Forecast horizons for a two-echelon dynamic lot-sizing problem," Omega, Elsevier, vol. 110(C).
    12. Jans, R.F. & Degraeve, Z., 2005. "Modeling Industrial Lot Sizing Problems: A Review," ERIM Report Series Research in Management ERS-2005-049-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    13. Z Shen & M Dessouky & F Ordonez, 2011. "Perishable inventory management system with a minimum volume constraint," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(12), pages 2063-2082, December.
    14. Leon Yang Chu & Vernon Ning Hsu & Zuo‐Jun Max Shen, 2005. "An economic lot‐sizing problem with perishable inventory and economies of scale costs: Approximation solutions and worst case analysis," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(6), pages 536-548, September.
    15. Fan, Jie & Ou, Jinwen, 2023. "On dynamic lot sizing with bounded inventory for a perishable product," Omega, Elsevier, vol. 119(C).
    16. Jing, Fuying & Chao, Xiangrui, 2021. "A dynamic lot size model with perishable inventory and stockout," Omega, Elsevier, vol. 103(C).
    17. Liu, Hengyu & Zhang, Juliang & Zhou, Chen & Ru, Yihong, 2018. "Optimal purchase and inventory retrieval policies for perishable seasonal agricultural products," Omega, Elsevier, vol. 79(C), pages 133-145.
    18. Stefano Coniglio & Arie M. C. A. Koster & Nils Spiekermann, 2018. "Lot sizing with storage losses under demand uncertainty," Journal of Combinatorial Optimization, Springer, vol. 36(3), pages 763-788, October.
    19. Sadia Samar Ali & Haripriya Barman & Rajbir Kaur & Hana Tomaskova & Sankar Kumar Roy, 2021. "Multi-Product Multi Echelon Measurements of Perishable Supply Chain: Fuzzy Non-Linear Programming Approach," Mathematics, MDPI, vol. 9(17), pages 1-27, August.
    20. Pahl, Julia & Voß, Stefan, 2014. "Integrating deterioration and lifetime constraints in production and supply chain planning: A survey," European Journal of Operational Research, Elsevier, vol. 238(3), pages 654-674.
    21. Milind Dawande & Srinagesh Gavirneni & Yinping Mu & Suresh Sethi & Chelliah Sriskandarajah, 2010. "On the Interaction Between Demand Substitution and Production Changeovers," Manufacturing & Service Operations Management, INFORMS, vol. 12(4), pages 682-691, September.
    22. Behzadi, Golnar & O'Sullivan, Michael Justin & Olsen, Tava Lennon & Scrimgeour, Frank & Zhang, Abraham, 2017. "Robust and resilient strategies for managing supply disruptions in an agribusiness supply chain," International Journal of Production Economics, Elsevier, vol. 191(C), pages 207-220.
    23. Suresh Chand & Vernon Ning Hsu & Suresh Sethi, 2002. "Forecast, Solution, and Rolling Horizons in Operations Management Problems: A Classified Bibliography," Manufacturing & Service Operations Management, INFORMS, vol. 4(1), pages 25-43, September.
    24. Awi Federgruen & Joern Meissner, 2004. "Probabilistic Analysis of Multi-Item Capacitated Lot Sizing Problems," Working Papers MRG/0004, Department of Management Science, Lancaster University, revised Apr 2005.
    25. Brahimi, Nadjib & Dauzere-Peres, Stephane & Najid, Najib M. & Nordli, Atle, 2006. "Single item lot sizing problems," European Journal of Operational Research, Elsevier, vol. 168(1), pages 1-16, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Brahimi, Nadjib & Dauzere-Peres, Stephane & Najid, Najib M. & Nordli, Atle, 2006. "Single item lot sizing problems," European Journal of Operational Research, Elsevier, vol. 168(1), pages 1-16, January.
    2. Suresh Chand & Vernon Ning Hsu & Suresh Sethi, 2002. "Forecast, Solution, and Rolling Horizons in Operations Management Problems: A Classified Bibliography," Manufacturing & Service Operations Management, INFORMS, vol. 4(1), pages 25-43, September.
    3. Jans, Raf & Degraeve, Zeger, 2007. "Meta-heuristics for dynamic lot sizing: A review and comparison of solution approaches," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1855-1875, March.
    4. Chung-Lun Li & Qingying Li, 2016. "Polynomial-Time Solvability of Dynamic Lot Size Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(03), pages 1-20, June.
    5. Brahimi, Nadjib & Absi, Nabil & Dauzère-Pérès, Stéphane & Nordli, Atle, 2017. "Single-item dynamic lot-sizing problems: An updated survey," European Journal of Operational Research, Elsevier, vol. 263(3), pages 838-863.
    6. Stan van Hoesel & H. Edwin Romeijn & Dolores Romero Morales & Albert P. M. Wagelmans, 2005. "Integrated Lot Sizing in Serial Supply Chains with Production Capacities," Management Science, INFORMS, vol. 51(11), pages 1706-1719, November.
    7. Hark-Chin Hwang, 2010. "Economic Lot-Sizing for Integrated Production and Transportation," Operations Research, INFORMS, vol. 58(2), pages 428-444, April.
    8. Hark-Chin Hwang, 2009. "Inventory Replenishment and Inbound Shipment Scheduling Under a Minimum Replenishment Policy," Transportation Science, INFORMS, vol. 43(2), pages 244-264, May.
    9. Alper Atamtürk & Dorit S. Hochbaum, 2001. "Capacity Acquisition, Subcontracting, and Lot Sizing," Management Science, INFORMS, vol. 47(8), pages 1081-1100, August.
    10. van den Heuvel, W.J. & Wagelmans, A.P.M., 2003. "A geometric algorithm to solve the NI/G/NI/ND capacitated lot-sizing problem in O(T2) time," Econometric Institute Research Papers EI 2003-24, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    11. Hwang, Hark-Chin & Jaruphongsa, Wikrom, 2008. "Dynamic lot-sizing model for major and minor demands," European Journal of Operational Research, Elsevier, vol. 184(2), pages 711-724, January.
    12. Liu, X. & Tu, Yl., 2008. "Production planning with limited inventory capacity and allowed stockout," International Journal of Production Economics, Elsevier, vol. 111(1), pages 180-191, January.
    13. Mathieu Van Vyve, 2007. "Algorithms for Single-Item Lot-Sizing Problems with Constant Batch Size," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 594-613, August.
    14. Stan van Hoesel & H. Edwin Romeijn & Dolores Romero Morales & Albert P.M. Wagelmans, 2002. "Polynomial Time Algorithms for Some Multi-Level Lot-Sizing Problems with Production Capacities," Tinbergen Institute Discussion Papers 02-066/4, Tinbergen Institute.
    15. Awi Federgruen & Joern Meissner & Michal Tzur, 2007. "Progressive Interval Heuristics for Multi-Item Capacitated Lot-Sizing Problems," Operations Research, INFORMS, vol. 55(3), pages 490-502, June.
    16. Hark‐Chin Hwang & Wilco van den Heuvel, 2012. "Improved algorithms for a lot‐sizing problem with inventory bounds and backlogging," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(3‐4), pages 244-253, April.
    17. Goisque, Guillaume & Rapine, Christophe, 2017. "An efficient algorithm for the 2-level capacitated lot-sizing problem with identical capacities at both levels," European Journal of Operational Research, Elsevier, vol. 261(3), pages 918-928.
    18. H. Edwin Romeijn & Dolores Romero Morales & Wilco Van den Heuvel, 2014. "Computational complexity of finding Pareto efficient outcomes for biobjective lot‐sizing models," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(5), pages 386-402, August.
    19. van Hoesel, C.P.M. & Romeijn, H.E. & Romero Morales, M.D. & Wagelmans, A., 2002. "Polynomial time algorithms for some multi-level lot-sizing problems with production capacities," Research Memorandum 018, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    20. Jans, R.F. & Degraeve, Z., 2005. "Modeling Industrial Lot Sizing Problems: A Review," ERIM Report Series Research in Management ERS-2005-049-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:46:y:2000:i:8:p:1159-1169. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.