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Optimal Capacity Rationing Policy for a Container Leasing System with Multiple Kinds of Customers and Substitutable Containers

Author

Listed:
  • Xufeng Yang

    (School of Economics and Management, Beijing Jiaotong University, Beijing 100044, China)

  • Juliang Zhang

    (School of Economics and Management, Beijing Jiaotong University, Beijing 100044, China)

  • Wen Jiao

    (Centre for Simulation, Analytics and Modelling, University of Exeter Business School, Exeter EX4 4PU, United Kingdom)

  • Hong Yan

    (College of Management, Zhejiang Shuren University, Hangzhou 310015, China)

Abstract

In this paper, we consider a container leasing firm that has elementary and premium containers, which are downward substitutable and for use by elementary contract customers (ECCs), premium contract customers (PCCs), as well as walk-in customers (WICs). ECCs can be satisfied by elementary containers or premium ones at discounted prices while PCCs only accept premium containers. WICs can be satisfied by any type of container at different prices. The objective is to maximise the expected total rental revenue by managing its limited capacity. We formulate this problem as a discrete-time Markov Decision Process and show the submodularity and concavity of the value function. Based on this, we show that the optimal policy can be characterised by a series of rationing thresholds, a series of substitution thresholds and a priority threshold, all of which depend on the system states. We further give conditions under which the optimal policy can be simplified. Numerical experiments are conducted to show the impact of the substitution of two items on the revenue, to compare the performance of the optimal policy with those of the commonly used policies and to investigate the influence of arrival rates on the optimal policy. Last, we extend the basic model to consider different rental durations, ECCs’ acceptance behaviour and endogenous prices for WICs.

Suggested Citation

  • Xufeng Yang & Juliang Zhang & Wen Jiao & Hong Yan, 2023. "Optimal Capacity Rationing Policy for a Container Leasing System with Multiple Kinds of Customers and Substitutable Containers," Management Science, INFORMS, vol. 69(3), pages 1468-1485, March.
    • Handle: RePEc:inm:ormnsc:v:69:y:2023:i:3:p:1468-1485
    DOI: 10.1287/mnsc.2022.4425
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    References listed on IDEAS

    as
    1. Steinhardt, Claudius & Gönsch, Jochen, 2012. "Integrated revenue management approaches for capacity control with planned upgrades," European Journal of Operational Research, Elsevier, vol. 223(2), pages 380-391.
    2. Noah Gans & Sergei Savin, 2007. "Pricing and Capacity Rationing for Rentals with Uncertain Durations," Management Science, INFORMS, vol. 53(3), pages 390-407, March.
    3. Albert Y. Ha, 2000. "Stock Rationing in an M/E k /1 Make-to-Stock Queue," Management Science, INFORMS, vol. 46(1), pages 77-87, January.
    4. Liu, Shudong & Song, Miao & Tan, Kok Choon & Zhang, Changyong, 2015. "Multi-class dynamic inventory rationing with stochastic demands and backordering," European Journal of Operational Research, Elsevier, vol. 244(1), pages 153-163.
    5. Scott Fay & Jinhong Xie, 2008. "Probabilistic Goods: A Creative Way of Selling Products and Services," Marketing Science, INFORMS, vol. 27(4), pages 674-690, 07-08.
    6. Richard F. Serfozo, 1979. "Technical Note—An Equivalence Between Continuous and Discrete Time Markov Decision Processes," Operations Research, INFORMS, vol. 27(3), pages 616-620, June.
    7. Raymond K. Cheung & Chuen-Yih Chen, 1998. "A Two-Stage Stochastic Network Model and Solution Methods for the Dynamic Empty Container Allocation Problem," Transportation Science, INFORMS, vol. 32(2), pages 142-162, May.
    8. Yongbo Xiao & Jian Chen, 2014. "Evaluating the potential effects from probabilistic selling of similar products," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(8), pages 604-620, December.
    9. Lang, Jan Christian, 2009. "Production and inventory management with substitutions," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 42531, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    10. MILLER, Bruce L., 1969. "A queueing reward system with several customer classes," LIDAM Reprints CORE 41, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. Felix Papier, 2016. "Managing Electricity Peak Loads in Make-To-Stock Manufacturing Lines," Production and Operations Management, Production and Operations Management Society, vol. 25(10), pages 1709-1726, October.
    12. S Benigno & F Guerriero & G Miglionico, 2012. "A revenue management approach to address a truck rental problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 63(10), pages 1421-1433, October.
    13. Sergei V. Savin & Morris A. Cohen & Noah Gans & Ziv Katalan, 2005. "Capacity Management in Rental Businesses with Two Customer Bases," Operations Research, INFORMS, vol. 53(4), pages 617-631, August.
    14. Övünç Yılmaz & Pelin Pekgün & Mark Ferguson, 2017. "Would You Like to Upgrade to a Premium Room? Evaluating the Benefit of Offering Standby Upgrades," Manufacturing & Service Operations Management, INFORMS, vol. 19(1), pages 1-18, February.
    15. Zheng, Jianfeng & Sun, Zhuo & Zhang, Fangjun, 2016. "Measuring the perceived container leasing prices in liner shipping network design with empty container repositioning," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 94(C), pages 123-140.
    16. Bruce L. Miller, 1969. "A Queueing Reward System with Several Customer Classes," Management Science, INFORMS, vol. 16(3), pages 234-245, November.
    17. Guillermo Gallego & Robert Phillips, 2004. "Revenue Management of Flexible Products," Manufacturing & Service Operations Management, INFORMS, vol. 6(4), pages 321-337, January.
    18. Chun†Miin (Jimmy) Chen & Douglas J. Thomas, 2018. "Inventory Allocation in the Presence of Service†Level Agreements," Production and Operations Management, Production and Operations Management Society, vol. 27(3), pages 553-577, March.
    19. Liu, Cong & Jiang, Zhibin & Liu, Liming & Geng, Na, 2013. "Solutions for flexible container leasing contracts with options under capacity and order constraints," International Journal of Production Economics, Elsevier, vol. 141(1), pages 403-413.
    20. Jeffrey I. McGill & Garrett J. van Ryzin, 1999. "Revenue Management: Research Overview and Prospects," Transportation Science, INFORMS, vol. 33(2), pages 233-256, May.
    21. 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.
    22. Donald M. Topkis, 1968. "Optimal Ordering and Rationing Policies in a Nonstationary Dynamic Inventory Model with n Demand Classes," Management Science, INFORMS, vol. 15(3), pages 160-176, November.
    23. Jiao, Wen & Yan, Hong & Pang, King-Wah, 2016. "Nonlinear pricing for stochastic container leasing system," Transportation Research Part B: Methodological, Elsevier, vol. 89(C), pages 1-18.
    24. Zelin Zhang & Kissan Joseph & Ramanathan Subramaniam, 2015. "Probabilistic Selling in Quality-Differentiated Markets," Management Science, INFORMS, vol. 61(8), pages 1959-1977, August.
    25. Övünç Yılmaz & Pelin Pekgün & Mark Ferguson, 2017. "Would You Like to Upgrade to a Premium Room? Evaluating the Benefit of Offering Standby Upgrades," Manufacturing & Service Operations Management, INFORMS, vol. 19(1), pages 1-18, February.
    26. Chen, Shaoxiang & Gallego, Guillermo & Li, Michael Z.F. & Lin, Bing, 2010. "Optimal seat allocation for two-flight problems with a flexible demand segment," European Journal of Operational Research, Elsevier, vol. 201(3), pages 897-908, March.
    27. Francis de Véricourt & Fikri Karaesmen & Yves Dallery, 2001. "Assessing the Benefits of Different Stock-Allocation Policies for a Make-to-Stock Production System," Manufacturing & Service Operations Management, INFORMS, vol. 3(2), pages 105-121, December.
    28. Li, Jing-An & Leung, Stephen C.H. & Wu, Yue & Liu, Ke, 2007. "Allocation of empty containers between multi-ports," European Journal of Operational Research, Elsevier, vol. 182(1), pages 400-412, October.
    29. David Sayah & Stefan Irnich, 2019. "Optimal booking control in revenue management with two substitutable resources," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(2), pages 189-222, April.
    30. Song, Dong-Ping & Dong, Jing-Xin, 2012. "Cargo routing and empty container repositioning in multiple shipping service routes," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1556-1575.
    31. Steven Nahmias & W. Steven Demmy, 1981. "Operating Characteristics of an Inventory System with Rationing," Management Science, INFORMS, vol. 27(11), pages 1236-1245, November.
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