IDEAS home Printed from https://ideas.repec.org/a/eee/proeco/v268y2024ics0925527323003249.html
   My bibliography  Save this article

A continuous approximation location-inventory model with exact inventory costs and nonlinear delivery lead time penalties

Author

Listed:
  • Straubert, Christian

Abstract

Most existing location-inventory models use exact locations (coordinates) for warehouses and customers but use simple approximations for inventory costs. A different approach is presented in this paper. While the locations are loosely modeled using a continuous approximation approach, a reorder point, order quantity inventory model with exact costs is used. Exact expressions for the transport time distribution and backorder time distribution (for Poisson demand) are combined with an exogenously given warehouse fulfillment time and form the delivery lead time. Customers perceive a long delivery lead time negatively. This creates a dynamic between the number of stocking locations used (which affects the transport time and cost) and the inventory policy (which affects the backorder time and inventory costs) because both influence the delivery lead time. Furthermore, we are able to model a nonlinear customer perception of the delivery lead time. Based on the presented model, the general characteristics and mechanisms of such a location-inventory problem are investigated. Among other things, we show for many probability distributions that the average backorder time per backorder is convex and that our model is quasi-convex, which allows for a wide range of optimization methods.

Suggested Citation

  • Straubert, Christian, 2024. "A continuous approximation location-inventory model with exact inventory costs and nonlinear delivery lead time penalties," International Journal of Production Economics, Elsevier, vol. 268(C).
  • Handle: RePEc:eee:proeco:v:268:y:2024:i:c:s0925527323003249
    DOI: 10.1016/j.ijpe.2023.109092
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0925527323003249
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ijpe.2023.109092?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. Yanhui Li & Mengmeng Lu & Bailing Liu, 2014. "A Two-Stage Algorithm for the Closed-Loop Location-Inventory Problem Model Considering Returns in E-Commerce," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-9, September.
    2. W. Karl Kruse, 1981. "Technical Note—Waiting Time in a Continuous Review ( s , S ) Inventory System with Constant Lead Times," Operations Research, INFORMS, vol. 29(1), pages 202-207, February.
    3. Emre Berk & Ayhan Özgür Toy, 2023. "A serial inventory system with lead-time-dependent backordering: A reduced-state approximation," IISE Transactions, Taylor & Francis Journals, vol. 55(3), pages 259-270, March.
    4. Escalona, P. & Marianov, V. & Ordóñez, F. & Stegmaier, R., 2018. "On the effect of inventory policies on distribution network design with several demand classes," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 111(C), pages 229-240.
    5. Hsiao, Ming-Hsiung, 2009. "Shopping mode choice: Physical store shopping versus e-shopping," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 45(1), pages 86-95, January.
    6. Parlar, Mahmut & Rempala, Ryszarda, 1992. "A stochastic inventory problem with piecewise quadratic costs," International Journal of Production Economics, Elsevier, vol. 26(1-3), pages 327-332, February.
    7. Mahesh Nagarajan & S. Rajagopalan, 2008. "Inventory Models for Substitutable Products: Optimal Policies and Heuristics," Management Science, INFORMS, vol. 54(8), pages 1453-1466, August.
    8. Holzapfel, Andreas & Kuhn, Heinrich & Sternbeck, Michael G., 2018. "Product allocation to different types of distribution center in retail logistics networks," European Journal of Operational Research, Elsevier, vol. 264(3), pages 948-966.
    9. Soham Ghosh & Mamta Sahare & Sujay Mukhoti, 2021. "A New Generalized Newsvendor Model with Random Demand and Cost Misspecification," Springer Books, in: Bikas Kumar Sinha & Srijib Bhusan Bagchi (ed.), Strategic Management, Decision Theory, and Decision Science, pages 211-245, Springer.
    10. Escalona, P. & Ordóñez, F. & Marianov, V., 2015. "Joint location-inventory problem with differentiated service levels using critical level policy," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 83(C), pages 141-157.
    11. Kaan Unnu & Jennifer Pazour, 2022. "Evaluating on-demand warehousing via dynamic facility location models," IISE Transactions, Taylor & Francis Journals, vol. 54(10), pages 988-1003, July.
    12. Schuster Puga, Matías & Minner, Stefan & Tancrez, Jean-Sébastien, 2019. "Two-stage supply chain design with safety stock placement decisions," International Journal of Production Economics, Elsevier, vol. 209(C), pages 183-193.
    13. Hongtao Zhang, 1998. "A Note on the Convexity of Service-Level Measures of the (r, q) System," Management Science, INFORMS, vol. 44(3), pages 431-432, March.
    14. Bailing Liu & Hui Chen & Yanhui Li & Xiang Liu, 2015. "A Pseudo-Parallel Genetic Algorithm Integrating Simulated Annealing for Stochastic Location-Inventory-Routing Problem with Consideration of Returns in E-Commerce," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-15, March.
    15. Yu-Chung Tsao & Qinhong Zhang & Tsung-Hui Chen, 2016. "Multi-item distribution network design problems under volume discount on transportation cost," International Journal of Production Research, Taylor & Francis Journals, vol. 54(2), pages 426-443, January.
    16. Sara Ceschia & Margaretha Gansterer & Simona Mancini & Antonella Meneghetti, 2023. "The on-demand warehousing problem," International Journal of Production Research, Taylor & Francis Journals, vol. 61(10), pages 3152-3170, May.
    17. Yu-Chung Tsao, 2016. "Designing a supply chain network for deteriorating inventory under preservation effort and trade credits," International Journal of Production Research, Taylor & Francis Journals, vol. 54(13), pages 3837-3851, July.
    18. Paterson, Colin & Kiesmüller, Gudrun & Teunter, Ruud & Glazebrook, Kevin, 2011. "Inventory models with lateral transshipments: A review," European Journal of Operational Research, Elsevier, vol. 210(2), pages 125-136, April.
    19. Erik Brynjolfsson & Michael D. Smith, 2000. "Frictionless Commerce? A Comparison of Internet and Conventional Retailers," Management Science, INFORMS, vol. 46(4), pages 563-585, April.
    20. Shin, Hojung & Park, Soohoon & Lee, Euncheol & Benton, W.C., 2015. "A classification of the literature on the planning of substitutable products," European Journal of Operational Research, Elsevier, vol. 246(3), pages 686-699.
    21. Tsao, Yu-Chung & Mangotra, Divya & Lu, Jye-Chyi & Dong, Ming, 2012. "A continuous approximation approach for the integrated facility-inventory allocation problem," European Journal of Operational Research, Elsevier, vol. 222(2), pages 216-228.
    22. Awi Federgruen & Yu-Sheng Zheng, 1992. "An Efficient Algorithm for Computing an Optimal (r, Q) Policy in Continuous Review Stochastic Inventory Systems," Operations Research, INFORMS, vol. 40(4), pages 808-813, August.
    23. Fichtinger, Johannes & Chan, Claire (Wan-Chuan) & Yates, Nicola, 2019. "A joint network design and multi-echelon inventory optimisation approach for supply chain segmentation," International Journal of Production Economics, Elsevier, vol. 209(C), pages 103-111.
    24. Gary D. Eppen, 1979. "Note--Effects of Centralization on Expected Costs in a Multi-Location Newsboy Problem," Management Science, INFORMS, vol. 25(5), pages 498-501, May.
    25. Carlos F. Daganzo, 2005. "Logistics Systems Analysis," Springer Books, Springer, edition 0, number 978-3-540-27516-9, July.
    26. Shuai Deng & Yanhui Li & Hao Guo & Bailing Liu, 2016. "Solving a Closed-Loop Location-Inventory-Routing Problem with Mixed Quality Defects Returns in E-Commerce by Hybrid Ant Colony Optimization Algorithm," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-12, June.
    27. Mahar, Stephen & Bretthauer, Kurt M. & Venkataramanan, M.A., 2009. "The value of virtual pooling in dual sales channel supply chains," European Journal of Operational Research, Elsevier, vol. 192(2), pages 561-575, January.
    28. Reza Zanjirani Farahani & Hannaneh Rashidi Bajgan & Behnam Fahimnia & Mohamadreza Kaviani, 2015. "Location-inventory problem in supply chains: a modelling review," International Journal of Production Research, Taylor & Francis Journals, vol. 53(12), pages 3769-3788, June.
    29. Pujari, Nikhil A. & Hale, Trevor S. & Huq, Faizul, 2008. "A continuous approximation procedure for determining inventory distribution schemas within supply chains," European Journal of Operational Research, Elsevier, vol. 186(1), pages 405-422, April.
    30. Ansari, Sina & Başdere, Mehmet & Li, Xiaopeng & Ouyang, Yanfeng & Smilowitz, Karen, 2018. "Advancements in continuous approximation models for logistics and transportation systems: 1996–2016," Transportation Research Part B: Methodological, Elsevier, vol. 107(C), pages 229-252.
    31. Arthur M. Geoffrion, 1976. "The Purpose of Mathematical Programming is Insight, Not Numbers," Interfaces, INFORMS, vol. 7(1), pages 81-92, November.
    32. Wang, Ziping & Yao, Dong-Qing & Huang, Peiqing, 2007. "A new location-inventory policy with reverse logistics applied to B2C e-markets of China," International Journal of Production Economics, Elsevier, vol. 107(2), pages 350-363, June.
    33. Tsao, Yu-Chung & Lu, Jye-Chyi, 2012. "A supply chain network design considering transportation cost discounts," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(2), pages 401-414.
    34. Bernhard Fleischmann, 2016. "The impact of the number of parallel warehouses on total inventory," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(4), pages 899-920, October.
    35. Kim, Nayeon & Montreuil, Benoit & Klibi, Walid & Zied Babai, M., 2023. "Network inventory deployment for responsive fulfillment," International Journal of Production Economics, Elsevier, vol. 255(C).
    36. Paul Zipkin, 1986. "Inventory Service-Level Measures: Convexity and Approximation," Management Science, INFORMS, vol. 32(8), pages 975-981, August.
    37. Langevin, André & Mbaraga, Pontien & Campbell, James F., 1996. "Continuous approximation models in freight distribution: An overview," Transportation Research Part B: Methodological, Elsevier, vol. 30(3), pages 163-188, June.
    38. Lina Johansson & Fredrik Olsson, 2017. "Quantifying sustainable control of inventory systems with non-linear backorder costs," Annals of Operations Research, Springer, vol. 259(1), pages 217-239, December.
    39. Gerchak, Yigal & Wang, Shaun, 1997. "Liquid asset allocation using "newsvendor" models with convex shortage costs," Insurance: Mathematics and Economics, Elsevier, vol. 20(1), pages 17-21, June.
    Full references (including those not matched with items on IDEAS)

    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. Ansari, Sina & Başdere, Mehmet & Li, Xiaopeng & Ouyang, Yanfeng & Smilowitz, Karen, 2018. "Advancements in continuous approximation models for logistics and transportation systems: 1996–2016," Transportation Research Part B: Methodological, Elsevier, vol. 107(C), pages 229-252.
    2. Yu-Chung Tsao & Qinhong Zhang & Tsung-Hui Chen, 2016. "Multi-item distribution network design problems under volume discount on transportation cost," International Journal of Production Research, Taylor & Francis Journals, vol. 54(2), pages 426-443, January.
    3. Chowdhury, Sudipta & Emelogu, Adindu & Marufuzzaman, Mohammad & Nurre, Sarah G. & Bian, Linkan, 2017. "Drones for disaster response and relief operations: A continuous approximation model," International Journal of Production Economics, Elsevier, vol. 188(C), pages 167-184.
    4. Darmawan, Agus & Wong, Hartanto & Thorstenson, Anders, 2021. "Supply chain network design with coordinated inventory control," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 145(C).
    5. Holzapfel, Andreas & Potoczki, Tobias & Kuhn, Heinrich, 2023. "Designing the breadth and depth of distribution networks in the retail trade," International Journal of Production Economics, Elsevier, vol. 257(C).
    6. Lei, Chao & Ouyang, Yanfeng, 2018. "Continuous approximation for demand balancing in solving large-scale one-commodity pickup and delivery problems," Transportation Research Part B: Methodological, Elsevier, vol. 109(C), pages 90-109.
    7. Soham Ghosh & Sujay Mukhoti, 2023. "Non-parametric generalised newsvendor model," Annals of Operations Research, Springer, vol. 321(1), pages 241-266, February.
    8. Transchel, Sandra, 2017. "Inventory management under price-based and stockout-based substitution," European Journal of Operational Research, Elsevier, vol. 262(3), pages 996-1008.
    9. Awi Federgruen & Min Wang, 2013. "Monotonicity properties of a class of stochastic inventory systems," Annals of Operations Research, Springer, vol. 208(1), pages 155-186, September.
    10. Fan, Hongqiang & Yun, Lifen & Li, Xiaopeng, 2022. "A linear-time crystal-growth algorithm for discretization of continuum approximation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 161(C).
    11. Escalona, P. & Marianov, V. & Ordóñez, F. & Stegmaier, R., 2018. "On the effect of inventory policies on distribution network design with several demand classes," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 111(C), pages 229-240.
    12. Dasci, Abdullah & Huang, Rongbing, 2017. "A continuous approximation method for dynamic pricing problem under costly price modifications," Omega, Elsevier, vol. 72(C), pages 38-49.
    13. Tsao, Yu-Chung & Lu, Jye-Chyi, 2012. "A supply chain network design considering transportation cost discounts," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(2), pages 401-414.
    14. Vipul Agrawal & Sridhar Seshadri, 2000. "Distribution free bounds for service constrained (Q, r) inventory systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(8), pages 635-656, December.
    15. Vinayak Deshpande & Morris A. Cohen & Karen Donohue, 2003. "A Threshold Inventory Rationing Policy for Service-Differentiated Demand Classes," Management Science, INFORMS, vol. 49(6), pages 683-703, June.
    16. Yu-Chung Tsao & Vu-Thuy Linh & Jye-Chyi Lu & Vincent Yu, 2018. "A supply chain network with product remanufacturing and carbon emission considerations: a two-phase design," Journal of Intelligent Manufacturing, Springer, vol. 29(3), pages 693-705, March.
    17. Tsao, Yu-Chung & Mangotra, Divya & Lu, Jye-Chyi & Dong, Ming, 2012. "A continuous approximation approach for the integrated facility-inventory allocation problem," European Journal of Operational Research, Elsevier, vol. 222(2), pages 216-228.
    18. Liu, Baolong & Papier, Felix, 2022. "Remanufacturing of multi-component systems with product substitution," European Journal of Operational Research, Elsevier, vol. 301(3), pages 896-911.
    19. Ang, Marcus & Song, Jing-Sheng & Wang, Mingzheng & Zhang, Hanqin, 2013. "On properties of discrete (r, q) and (s, T) inventory systems," European Journal of Operational Research, Elsevier, vol. 229(1), pages 95-105.
    20. James F. Campbell & Morton E. O'Kelly, 2012. "Twenty-Five Years of Hub Location Research," Transportation Science, INFORMS, vol. 46(2), pages 153-169, May.

    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:proeco:v:268:y:2024:i:c:s0925527323003249. 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/ijpe .

    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.