IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v268y2018i2p569-581.html
   My bibliography  Save this article

Control of a continuous production inventory system with production quantity restrictions

Author

Listed:
  • Klosterhalfen, Steffen T.
  • Holzhauer, Falk
  • Fleischmann, Moritz

Abstract

Motivated by a real-world application in the chemical industry, we consider the problem of controlling a production asset that has to run continuously around the clock. This requirement causes minimum and maximum production quantities per period, resulting from the minimally and maximally feasible production rates. Our goal in this paper is to find a good control rule for this production inventory setting. To this end, we first show that the setting is analytically equivalent to a periodic-review inventory system with an order band, for which a modified base-stock policy is optimal. We then develop an iterative solution algorithm to approximate the optimal base-stock level under a predefined service-level target. This algorithm is easily implementable in a spreadsheet software tool with additional Visual Basic for Applications coding. In a numerical study, we find that the approximation works very well for a broad set of parameters. In contrast, simple rules-of-thumb such as the usage of a “standard” base-stock level that does not consider the order band may result in severe errors. Either the chosen base-stock level is too low, causing the service-level target to be undershot (by up to 40% in our analyzed settings), or it is too high, resulting in an overshoot of the service-level target and thus in excessive inventory. In the real-world application example, the new solution approach identifies an inventory saving potential of about 17%.

Suggested Citation

  • Klosterhalfen, Steffen T. & Holzhauer, Falk & Fleischmann, Moritz, 2018. "Control of a continuous production inventory system with production quantity restrictions," European Journal of Operational Research, Elsevier, vol. 268(2), pages 569-581.
  • Handle: RePEc:eee:ejores:v:268:y:2018:i:2:p:569-581
    DOI: 10.1016/j.ejor.2018.02.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221718300961
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ejor.2018.02.001?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. G. J. Van Houtum & W. H. M. Zijm, 2000. "On the relationship between cost and service models for general inventory systems," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 54(2), pages 127-147, July.
    2. Kiesmüller, G.P. & de Kok, A.G. & Dabia, S., 2011. "Single item inventory control under periodic review and a minimum order quantity," International Journal of Production Economics, Elsevier, vol. 133(1), pages 280-285, September.
    3. Zhou, Bin & Zhao, Yao & Katehakis, Michael N., 2007. "Effective control policies for stochastic inventory systems with a minimum order quantity and linear costs," International Journal of Production Economics, Elsevier, vol. 106(2), pages 523-531, April.
    4. A. Federgruen & P. Zipkin, 1986. "An Inventory Model with Limited Production Capacity and Uncertain Demands II. The Discounted-Cost Criterion," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 208-215, May.
    5. de Kok, A. G., 1987. "Approximations for operating characteristics in a production-inventory model with variable production rate," European Journal of Operational Research, Elsevier, vol. 29(3), pages 286-297, June.
    6. Stephen C. Graves & Julian Keilson, 1981. "The Compensation Method Applied to a One-Product Production/Inventory Problem," Mathematics of Operations Research, INFORMS, vol. 6(2), pages 246-262, May.
    7. Doshi, Bharat T., 1978. "Two-mode control of Brownian Motion with quadratic loss and switching costs," Stochastic Processes and their Applications, Elsevier, vol. 6(3), pages 277-289, February.
    8. Paul Glasserman & Sridhar Tayur, 1994. "The Stability of a Capacitated, Multi-Echelon Production-Inventory System Under a Base-Stock Policy," Operations Research, INFORMS, vol. 42(5), pages 913-925, October.
    9. A. G. de Kok, 1985. "Approximations for a Lost-Sales Production/Inventory Control Model with Service Level Constraints," Management Science, INFORMS, vol. 31(6), pages 729-737, June.
    10. Özgür Yazlali & Feryal Erhun, 2009. "Dual-supply inventory problem with capacity limits on order sizes and unrestricted ordering costs," IISE Transactions, Taylor & Francis Journals, vol. 41(8), pages 716-729.
    11. A. Federgruen & P. Zipkin, 1986. "An Inventory Model with Limited Production Capacity and Uncertain Demands I. The Average-Cost Criterion," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 193-207, May.
    12. Stephen C. Graves, 1982. "The Application of Queueing Theory to Continuous Perishable Inventory Systems," Management Science, INFORMS, vol. 28(4), pages 400-406, April.
    13. Janssen, Fred & de Kok, Ton, 1999. "A two-supplier inventory model," International Journal of Production Economics, Elsevier, vol. 59(1-3), pages 395-403, March.
    14. Scheller-Wolf, Alan & Tayur, Sridhar, 2009. "Risk sharing in supply chains using order bands--Analytical results and managerial insights," International Journal of Production Economics, Elsevier, vol. 121(2), pages 715-727, October.
    15. Jim (Junmin) Shi & Michael N. Katehakis & Benjamin Melamed & Yusen Xia, 2014. "Production-Inventory Systems with Lost Sales and Compound Poisson Demands," Operations Research, INFORMS, vol. 62(5), pages 1048-1063, October.
    16. de Kok, A. G. & Tijms, H. C. & van der Duyn Schouten, F. A., 1985. "Inventory levels to stop and restart a single machine producing one product," European Journal of Operational Research, Elsevier, vol. 20(2), pages 239-247, May.
    17. Doshi, Bharat T., 1978. "Controlled one dimensional diffusions with switching costs--average cost criterion," Stochastic Processes and their Applications, Elsevier, vol. 8(2), pages 211-227, December.
    18. Nicky D. Van Foreest & Jacob Wijngaard, 2014. "On Optimal Policies for Production-Inventory Systems with Compound Poisson Demand and Setup Costs," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 517-532, May.
    19. R. G. Vickson, 1986. "A Single Product Cycling Problem Under Brownian Motion Demand," Management Science, INFORMS, vol. 32(10), pages 1336-1345, October.
    20. Roman Kapuściński & Sridhar Tayur, 1998. "A Capacitated Production-Inventory Model with Periodic Demand," Operations Research, INFORMS, vol. 46(6), pages 899-911, December.
    21. van Houtum, G. J. & Inderfurth, K. & Zijm, W. H. M., 1996. "Materials coordination in stochastic multi-echelon systems," European Journal of Operational Research, Elsevier, vol. 95(1), pages 1-23, November.
    22. Paul Glasserman & Sridhar Tayur, 1995. "Sensitivity Analysis for Base-Stock Levels in Multiechelon Production-Inventory Systems," Management Science, INFORMS, vol. 41(2), pages 263-281, February.
    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. Muriel, Ana & Chugh, Tammana & Prokle, Michael, 2022. "Efficient algorithms for the joint replenishment problem with minimum order quantities," European Journal of Operational Research, Elsevier, vol. 300(1), pages 137-150.

    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. Wang, Xun & Disney, Stephen M. & Ponte, Borja, 2023. "On the stationary stochastic response of an order-constrained inventory system," European Journal of Operational Research, Elsevier, vol. 304(2), pages 543-557.
    2. Ioannis Ch. Paschalidis & Yong Liu, 2003. "Large Deviations-Based Asymptotics for Inventory Control in Supply Chains," Operations Research, INFORMS, vol. 51(3), pages 437-460, June.
    3. Han Zhu, 2022. "A simple heuristic policy for stochastic inventory systems with both minimum and maximum order quantity requirements," Annals of Operations Research, Springer, vol. 309(1), pages 347-363, February.
    4. Gavirneni, Srinagesh, 2006. "Price fluctuations, information sharing, and supply chain performance," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1651-1663, November.
    5. Rodney P. Parker & Roman Kapuscinski, 2004. "Optimal Policies for a Capacitated Two-Echelon Inventory System," Operations Research, INFORMS, vol. 52(5), pages 739-755, October.
    6. Jian Yang & Xiangtong Qi & Yusen Xia, 2005. "A Production-Inventory System with Markovian Capacity and Outsourcing Option," Operations Research, INFORMS, vol. 53(2), pages 328-349, April.
    7. Woonghee Tim Huh & Ganesh Janakiraman & Mahesh Nagarajan, 2016. "Capacitated Multiechelon Inventory Systems: Policies and Bounds," Manufacturing & Service Operations Management, INFORMS, vol. 18(4), pages 570-584, October.
    8. Jian Yang & Zhaoqiong Qin, 2007. "Capacitated Production Control with Virtual Lateral Transshipments," Operations Research, INFORMS, vol. 55(6), pages 1104-1119, December.
    9. Xinxin Hu & Izak Duenyas & Roman Kapuscinski, 2008. "Optimal Joint Inventory and Transshipment Control Under Uncertain Capacity," Operations Research, INFORMS, vol. 56(4), pages 881-897, August.
    10. Rodney P. Parker & Roman Kapuściński, 2011. "Managing a Noncooperative Supply Chain with Limited Capacity," Operations Research, INFORMS, vol. 59(4), pages 866-881, August.
    11. Yang, Jian & Qi, Xiangtong & Xia, Yusen & Yu, Gang, 2006. "Inventory control with Markovian capacity and the option of order rejection," European Journal of Operational Research, Elsevier, vol. 174(1), pages 622-645, October.
    12. Iida, Tetsuo, 2002. "A non-stationary periodic review production-inventory model with uncertain production capacity and uncertain demand," European Journal of Operational Research, Elsevier, vol. 140(3), pages 670-683, August.
    13. Xiuli Chao & Sridhar Seshadri & Michael Pinedo, 2008. "Optimal capacity in a coordinated supply chain," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(2), pages 130-141, March.
    14. Jim (Junmin) Shi & Michael N. Katehakis & Benjamin Melamed & Yusen Xia, 2014. "Production-Inventory Systems with Lost Sales and Compound Poisson Demands," Operations Research, INFORMS, vol. 62(5), pages 1048-1063, October.
    15. Woonghee Tim Huh & Ganesh Janakiraman & Mahesh Nagarajan, 2010. "Technical Note ---Capacitated Serial Inventory Systems: Sample Path and Stability Properties Under Base-Stock Policies," Operations Research, INFORMS, vol. 58(4-part-1), pages 1017-1022, August.
    16. Gavirneni, Srinagesh, 2001. "Benefits of co-operation in a production distribution environment," European Journal of Operational Research, Elsevier, vol. 130(3), pages 612-622, May.
    17. Saif Benjaafar & David Chen & Rowan Wang, 2017. "Managing Production-Inventory Systems with Scarce Resources," Manufacturing & Service Operations Management, INFORMS, vol. 19(2), pages 216-229, May.
    18. Jim Shi, 2022. "Optimal continuous production-inventory systems subject to stockout risk," Annals of Operations Research, Springer, vol. 317(2), pages 777-804, October.
    19. Xiuli Chao & Xiting Gong & Cong Shi & Chaolin Yang & Huanan Zhang & Sean X. Zhou, 2018. "Approximation Algorithms for Capacitated Perishable Inventory Systems with Positive Lead Times," Management Science, INFORMS, vol. 64(11), pages 5038-5061, November.
    20. van Houtum, G. J. & Inderfurth, K. & Zijm, W. H. M., 1996. "Materials coordination in stochastic multi-echelon systems," European Journal of Operational Research, Elsevier, vol. 95(1), pages 1-23, November.

    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:eee:ejores:v:268:y:2018:i:2:p:569-581. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: http://www.elsevier.com/locate/eor .

    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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.