IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v304y2023i2p543-557.html
   My bibliography  Save this article

On the stationary stochastic response of an order-constrained inventory system

Author

Listed:
  • Wang, Xun
  • Disney, Stephen M.
  • Ponte, Borja

Abstract

We investigate the stochastic response of a base stock inventory system where the order quantity is either upper- or lower-constrained. This system can represent many real-world settings: forbidden returns, minimum order quantities, and capacity constraints for example. We show that this problem can be translated into a stopping time problem where the distributions of orders and inventory can be represented by a countably infinite mixture of truncated and convoluted demand distributions. This result can be extended to the cases of arbitrary lead time and auto-correlated demand. A state space algorithm is developed to approximate the first- and second-order moments of the order quantity and inventory level. Via a numerical analysis, we investigate the performance of the approximation, as well as the operational and economic impact of the order constraint. In particular, the constraint impacts order and inventory variances via different combinations of the mixture and truncation effects. We show how tuning the constraint can improve the operational and financial performance of the inventory system by acting as a smoothing mechanism.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:304:y:2023:i:2:p:543-557
    DOI: 10.1016/j.ejor.2022.04.020
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221722003319
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2022.04.020?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. Wang, Xun & Disney, Stephen M., 2017. "Mitigating variance amplification under stochastic lead-time: The proportional control approach," European Journal of Operational Research, Elsevier, vol. 256(1), pages 151-162.
    2. 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.
    3. 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.
    4. Hau L. Lee & V. Padmanabhan & Seungjin Whang, 1997. "Information Distortion in a Supply Chain: The Bullwhip Effect," Management Science, INFORMS, vol. 43(4), pages 546-558, April.
    5. 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.
    6. Disney, Stephen M. & Gaalman, Gerard J.C. & Hedenstierna, Carl Philip T. & Hosoda, Takamichi, 2015. "Fill rate in a periodic review order-up-to policy under auto-correlated normally distributed, possibly negative, demand," International Journal of Production Economics, Elsevier, vol. 170(PB), pages 501-512.
    7. Borja Ponte & Xun Wang & David de la Fuente & Stephen M. Disney, 2017. "Exploring nonlinear supply chains: the dynamics of capacity constraints," International Journal of Production Research, Taylor & Francis Journals, vol. 55(14), pages 4053-4067, July.
    8. 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.
    9. Harvey,Andrew C., 1991. "Forecasting, Structural Time Series Models and the Kalman Filter," Cambridge Books, Cambridge University Press, number 9780521405737, October.
    10. Noblesse, Ann M. & Boute, Robert N. & Lambrecht, Marc R. & Van Houdt, Benny, 2014. "Characterizing order processes of continuous review (s,S) and (r,nQ) policies," European Journal of Operational Research, Elsevier, vol. 236(2), pages 534-547.
    11. Srinagesh Gavirneni & Roman Kapuscinski & Sridhar Tayur, 1999. "Value of Information in Capacitated Supply Chains," Management Science, INFORMS, vol. 45(1), pages 16-24, January.
    12. Chatfield, Dean C. & Pritchard, Alan M., 2013. "Returns and the bullwhip effect," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 49(1), pages 159-175.
    13. Disney, S. M. & Towill, D. R., 2003. "On the bullwhip and inventory variance produced by an ordering policy," Omega, Elsevier, vol. 31(3), pages 157-167, June.
    14. Retsef Levi & Robin O. Roundy & David B. Shmoys & Van Anh Truong, 2008. "Approximation Algorithms for Capacitated Stochastic Inventory Control Models," Operations Research, INFORMS, vol. 56(5), pages 1184-1199, October.
    15. Larsen, Erik R. & Morecroft, John D. W. & Thomsen, Jesper S., 1999. "Complex behaviour in a production-distribution model," European Journal of Operational Research, Elsevier, vol. 119(1), pages 61-74, November.
    16. Stephen M. Disney & Borja Ponte & Xun Wang, 2021. "Exploring the nonlinear dynamics of the lost-sales order-up-to policy," International Journal of Production Research, Taylor & Francis Journals, vol. 59(19), pages 5809-5830, October.
    17. John D. Sterman, 1989. "Modeling Managerial Behavior: Misperceptions of Feedback in a Dynamic Decision Making Experiment," Management Science, INFORMS, vol. 35(3), pages 321-339, March.
    18. Wang, Xun & Disney, Stephen M. & Wang, Jing, 2012. "Stability analysis of constrained inventory systems with transportation delay," European Journal of Operational Research, Elsevier, vol. 223(1), pages 86-95.
    19. Roman Kapuściński & Sridhar Tayur, 1998. "A Capacitated Production-Inventory Model with Periodic Demand," Operations Research, INFORMS, vol. 46(6), pages 899-911, December.
    20. Kelle, Peter & Milne, Alistair, 1999. "The effect of (s, S) ordering policy on the supply chain," International Journal of Production Economics, Elsevier, vol. 59(1-3), pages 113-122, March.
    21. Paul Glasserman, 1997. "Bounds and Asymptotics for Planning Critical Safety Stocks," Operations Research, INFORMS, vol. 45(2), pages 244-257, April.
    22. Carl R. Schultz, 1983. "Computing demand properties at the wholesale warehouse level," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 30(1), pages 37-48, March.
    23. Sterman, John D., 1989. "Misperceptions of feedback in dynamic decision making," Organizational Behavior and Human Decision Processes, Elsevier, vol. 43(3), pages 301-335, June.
    24. 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.
    25. Disney, Stephen M. & Maltz, Arnold & Wang, Xun & Warburton, Roger D.H., 2016. "Inventory management for stochastic lead times with order crossovers," European Journal of Operational Research, Elsevier, vol. 248(2), pages 473-486.
    26. Li Chen & Hau L. Lee, 2009. "Information Sharing and Order Variability Control Under a Generalized Demand Model," Management Science, INFORMS, vol. 55(5), pages 781-797, May.
    27. 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.
    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. Nuramilawahida Mat Ropi & Hawa Hishamuddin & Dzuraidah Abd Wahab & Wakhid Ahmad Jauhari & Fatin Amrina A. Rashid & Nor Kamaliana Khamis & Intan Fadhlina Mohamed & Mohd Anas Mohd Sabri & Mohd Radzi Abu, 2023. "Optimal Lot-Sizing Decisions for a Remanufacturing Production System under Spare Parts Supply Disruption," Mathematics, MDPI, vol. 11(19), pages 1-19, September.
    2. Manik Debnath & Sanat Kr. Mazumder & Md Billal Hossain & Arindam Garai & Csaba Balint Illes, 2023. "Optimal Base-Stock Inventory-Management Policies of Cement Retailers under Supply-Side Disruptions," Mathematics, MDPI, vol. 11(18), pages 1-34, September.
    3. Yang, Y. & Lin, J. & Hedenstierna, C.P.T. & Zhou, L., 2023. "The more the better? The impact of the number and location of product recovery options on the system dynamics in a closed-loop supply chain," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 175(C).

    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. Ponte, Borja & Costas, José & Puche, Julio & Pino, Raúl & de la Fuente, David, 2018. "The value of lead time reduction and stabilization: A comparison between traditional and collaborative supply chains," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 111(C), pages 165-185.
    2. Lin, Junyi & Huang, Hongfu & Li, Shanshan & Naim, Mohamed M., 2023. "On the dynamics of order pipeline inventory in a nonlinear order-up-to system," International Journal of Production Economics, Elsevier, vol. 266(C).
    3. Dominguez, Roberto & Cannella, Salvatore & Barbosa-Póvoa, Ana P. & Framinan, Jose M., 2018. "Information sharing in supply chains with heterogeneous retailers," Omega, Elsevier, vol. 79(C), pages 116-132.
    4. Ponte, Borja & Puche, Julio & Rosillo, Rafael & de la Fuente, David, 2020. "The effects of quantity discounts on supply chain performance: Looking through the Bullwhip lens," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 143(C).
    5. Wang, Xun & Disney, Stephen M., 2016. "The bullwhip effect: Progress, trends and directions," European Journal of Operational Research, Elsevier, vol. 250(3), pages 691-701.
    6. 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.
    7. 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.
    8. Qingkai Ji & Lijun Sun & Xiangpei Hu & Jing Hou, 2016. "Optimal policies of a two-echelon serial inventory system with general limited capacities," International Journal of Production Research, Taylor & Francis Journals, vol. 54(20), pages 6142-6155, October.
    9. K. Devika & A. Jafarian & A. Hassanzadeh & R. Khodaverdi, 2016. "Optimizing of bullwhip effect and net stock amplification in three-echelon supply chains using evolutionary multi-objective metaheuristics," Annals of Operations Research, Springer, vol. 242(2), pages 457-487, July.
    10. Cannella, Salvatore & Dominguez, Roberto & Ponte, Borja & Framinan, Jose M., 2018. "Capacity restrictions and supply chain performance: Modelling and analysing load-dependent lead times," International Journal of Production Economics, Elsevier, vol. 204(C), pages 264-277.
    11. 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.
    12. 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.
    13. 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.
    14. Altug, Mehmet Sekip & Muharremoglu, Alp, 2011. "Inventory management with advance supply information," International Journal of Production Economics, Elsevier, vol. 129(2), pages 302-313, February.
    15. Dejian Yu & Zhaoping Yan, 2021. "Knowledge diffusion of supply chain bullwhip effect: main path analysis and science mapping analysis," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(10), pages 8491-8515, October.
    16. Cannella, S. & Ciancimino, E. & Ashayeri, J., 2010. "On the Significance of Demand and Inventory Smoothing Interventions in Supply Chain," Other publications TiSEM 03de2e58-4ef5-40a3-96e1-6, Tilburg University, School of Economics and Management.
    17. Robert L. Bray & Haim Mendelson, 2012. "Information Transmission and the Bullwhip Effect: An Empirical Investigation," Management Science, INFORMS, vol. 58(5), pages 860-875, May.
    18. Luong, Huynh Trung, 2007. "Measure of bullwhip effect in supply chains with autoregressive demand process," European Journal of Operational Research, Elsevier, vol. 180(3), pages 1086-1097, August.
    19. Cannella, S. & Ciancimino, E. & Ashayeri, J., 2010. "On the Significance of Demand and Inventory Smoothing Interventions in Supply Chain," Discussion Paper 2010-126, Tilburg University, Center for Economic Research.
    20. Gavirneni, Srinagesh, 2006. "Price fluctuations, information sharing, and supply chain performance," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1651-1663, 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:304:y:2023:i:2:p:543-557. 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: 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. RePEc uses bibliographic data supplied by the respective publishers.