IDEAS home Printed from https://ideas.repec.org/a/inm/ormsom/v18y2016i3p429-444.html
   My bibliography  Save this article

Managing Rentals with Usage-Based Loss

Author

Listed:
  • Vincent W. Slaugh

    (School of Hotel Administration, Cornell University, Ithaca, New York 14853)

  • Bahar Biller

    (Global Research Center, General Electric, Niskayuna, New York 12309)

  • Sridhar R. Tayur

    (Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)

Abstract

Motivated by innovative rental business models, we study a rental system with random loss of inventory due to use. We utilize a discrete-time model in which the inventory level is chosen before the start of a finite rental season, and customers not immediately served are lost. Demand, rental durations, and rental unit lifetimes are stochastic; sample path coupling allows us to derive structural results that hold under limited distributional assumptions. Considering different “recirculation” rules (i.e., which unit to select to meet a demand), we prove the concavity of the expected profit function and identify the optimal recirculation rule under two different models of a rental unit’s state: the number of times rented out or its condition. We develop two upper bounds on the number of lost rental units and two heuristics for the inventory decision. Numerical study shows the following: (1) accounting for rental unit loss can increase the expected profit by 7% for a single season; (2) the optimal inventory level in response to increasing loss probability is nonmonotonic; (3) both heuristics perform well; and (4) choosing the optimal recirculation rule over a commonly used policy can increase the profit-maximizing service level by up to six percentage points.

Suggested Citation

  • Vincent W. Slaugh & Bahar Biller & Sridhar R. Tayur, 2016. "Managing Rentals with Usage-Based Loss," Manufacturing & Service Operations Management, INFORMS, vol. 18(3), pages 429-444, July.
    • Handle: RePEc:inm:ormsom:v:18:y:2016:i:3:p:429-444
    DOI: 10.1287/msom.2016.0576
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/msom.2016.0576
    Download Restriction: no
    File URL: https://libkey.io/10.1287/msom.2016.0576?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. Achal Bassamboo & Sunil Kumar & Ramandeep S. Randhawa, 2009. "Dynamics of New Product Introduction in Closed Rental Systems," Operations Research, INFORMS, vol. 57(6), pages 1347-1359, December.
    2. Linda V. Green & Peter J. Kolesar & João Soares, 2001. "Improving the Sipp Approach for Staffing Service Systems That Have Cyclic Demands," Operations Research, INFORMS, vol. 49(4), pages 549-564, August.
    3. Yue Zhang & Martin L. Puterman & Matthew Nelson & Derek Atkins, 2012. "A Simulation Optimization Approach to Long-Term Care Capacity Planning," Operations Research, INFORMS, vol. 60(2), pages 249-261, April.
    4. Noah Gans & Sergei Savin, 2007. "Pricing and Capacity Rationing for Rentals with Uncertain Durations," Management Science, INFORMS, vol. 53(3), pages 390-407, March.
    5. Opher Baron & Iman Hajizadeh & Joseph Milner, 2011. "Now Playing: DVD Purchasing for a Multilocation Rental Firm," Manufacturing & Service Operations Management, INFORMS, vol. 13(2), pages 209-226, April.
    6. Apurva Jain & Kamran Moinzadeh & Aussadavut Dumrongsiri, 2015. "Priority Allocation in a Rental Model with Decreasing Demand," Manufacturing & Service Operations Management, INFORMS, vol. 17(2), pages 236-248, May.
    7. Arie Harel, 1988. "Sharp Bounds and Simple Approximations for the Erlang Delay and Loss Formulas," Management Science, INFORMS, vol. 34(8), pages 959-972, August.
    8. Arie Harel, 1988. "Erratum to: Sharp Bounds and Simple Approximations for the Erlang Delay and Loss Formulas," Management Science, INFORMS, vol. 34(10), pages 1277-1277, October.
    9. 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).
    10. J. George Shanthikumar & David D. Yao, 1987. "Optimal Server Allocation in a System of Multi-Server Stations," Management Science, INFORMS, vol. 33(9), pages 1173-1180, September.
    11. Tang, Christopher S. & Deo, Sarang, 2008. "Rental price and rental duration under retail competition," European Journal of Operational Research, Elsevier, vol. 187(3), pages 806-828, June.
    12. 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.
    13. Bruce L. Miller, 1969. "A Queueing Reward System with Several Customer Classes," Management Science, INFORMS, vol. 16(3), pages 234-245, November.
    14. Eginhard J. Muth, 1979. "The Reversibility Property of Production Lines," Management Science, INFORMS, vol. 25(2), pages 152-158, February.
    15. William D. Whisler, 1967. "A Stochastic Inventory Model for Rented Equipment," Management Science, INFORMS, vol. 13(9), pages 640-647, May.
    16. Sridhar R. Tayur, 1993. "Structural Properties and a Heuristic for Kanban-Controlled Serial Lines," Management Science, INFORMS, vol. 39(11), pages 1347-1368, November.
    17. Siddharth Mahajan & Garrett van Ryzin, 2001. "Stocking Retail Assortments Under Dynamic Consumer Substitution," Operations Research, INFORMS, vol. 49(3), pages 334-351, June.
    18. Felix Papier & Ulrich W. Thonemann, 2010. "Capacity Rationing in Stochastic Rental Systems with Advance Demand Information," Operations Research, INFORMS, vol. 58(2), pages 274-288, April.
    19. M. Tainiter, 1964. "Some Stochastic Inventory Models for Rental Situations," Management Science, INFORMS, vol. 11(2), pages 316-326, November.
    20. Felix Papier & Ulrich W. Thonemann, 2008. "Queuing Models for Sizing and Structuring Rental Fleets," Transportation Science, INFORMS, vol. 42(3), pages 302-317, August.
    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. Felipe Caro & A. Gürhan Kök & Victor Martínez-de-Albéniz, 2020. "The Future of Retail Operations," Manufacturing & Service Operations Management, INFORMS, vol. 22(1), pages 47-58, January.
    2. Michiel A. J. uit het Broek & Ruud H. Teunter & Bram de Jonge & Jasper Veldman & Nicky D. Van Foreest, 2020. "Condition-Based Production Planning: Adjusting Production Rates to Balance Output and Failure Risk," Manufacturing & Service Operations Management, INFORMS, vol. 22(4), pages 792-811, July.
    3. Van der Heide, G. & Roodbergen, K.J. & Van Foreest, N.D., 2021. "Cross docking for libraries with a depot," European Journal of Operational Research, Elsevier, vol. 290(2), pages 749-765.
    4. Sridhar Tayur, 2017. "OM Forum—An Essay on Operations Management," Manufacturing & Service Operations Management, INFORMS, vol. 19(4), pages 526-533, October.

    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. Mohammad Firouz & Linda Li & Burcu B. Keskin, 2022. "Managing equipment rentals: Unreliable fleet, impatient customers, and finite commitment capacity," Production and Operations Management, Production and Operations Management Society, vol. 31(11), pages 3963-3981, November.
    2. Belleh Fontem, 2022. "An optimal stopping policy for car rental businesses with purchasing customers," Annals of Operations Research, Springer, vol. 317(1), pages 47-76, October.
    3. Apurva Jain & Kamran Moinzadeh & Aussadavut Dumrongsiri, 2015. "Priority Allocation in a Rental Model with Decreasing Demand," Manufacturing & Service Operations Management, INFORMS, vol. 17(2), pages 236-248, May.
    4. Pazour, Jennifer A. & Roy, Debjit, 2012. "Minimizing Customer Waiting Costs for Rental Vehicle Providers using Threshold Reservation Policies," IIMA Working Papers WP2012-12-05, Indian Institute of Management Ahmedabad, Research and Publication Department.
    5. Felix Papier & Ulrich W. Thonemann, 2010. "Capacity Rationing in Stochastic Rental Systems with Advance Demand Information," Operations Research, INFORMS, vol. 58(2), pages 274-288, April.
    6. Van der Heide, G. & Roodbergen, K.J. & Van Foreest, N.D., 2021. "Cross docking for libraries with a depot," European Journal of Operational Research, Elsevier, vol. 290(2), pages 749-765.
    7. Xufeng Yang & Wen Jiao & Juliang Zhang & Hong Yan, 2022. "Capacity management for a leasing system with different equipment and batch demands," Production and Operations Management, Production and Operations Management Society, vol. 31(7), pages 3004-3020, July.
    8. 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.
    9. Gabriel Zayas-Cabán & Mark E. Lewis, 2020. "Admission control in a two-class loss system with periodically varying parameters and abandonments," Queueing Systems: Theory and Applications, Springer, vol. 94(1), pages 175-210, February.
    10. Vibhanshu Abhishek & Jose A. Guajardo & Zhe Zhang, 2021. "Business Models in the Sharing Economy: Manufacturing Durable Goods in the Presence of Peer-to-Peer Rental Markets," Information Systems Research, INFORMS, vol. 32(4), pages 1450-1469, December.
    11. Leon Yang Chu & Zhixi Wan & Dongyuan Zhan, 2018. "Harnessing the Double-edged Sword via Routing: Information Provision on Ride-hailing Platforms," Working Papers 18-04, NET Institute.
    12. Papier, Felix & Thonemann, Ulrich W., 2011. "Capacity rationing in rental systems with two customer classes and batch arrivals," Omega, Elsevier, vol. 39(1), pages 73-85, January.
    13. Demet Batur & Jennifer K. Ryan & Zhongyuan Zhao & Mehmet C. Vuran, 2019. "Dynamic Pricing of Wireless Internet Based on Usage and Stochastically Changing Capacity," Manufacturing & Service Operations Management, INFORMS, vol. 21(4), pages 833-852, October.
    14. Eugene A. Feinberg & Fenghsu Yang, 2016. "Optimal pricing for a GI/M/k/N queue with several customer types and holding costs," Queueing Systems: Theory and Applications, Springer, vol. 82(1), pages 103-120, February.
    15. 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.
    16. Noah Gans & Sergei Savin, 2007. "Pricing and Capacity Rationing for Rentals with Uncertain Durations," Management Science, INFORMS, vol. 53(3), pages 390-407, March.
    17. Kyle Y. Lin, 2003. "Decentralized admission control of a queueing system: A game‐theoretic model," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(7), pages 702-718, October.
    18. Dong Li & Zhan Pang & Lixian Qian, 2023. "Bid price controls for car rental network revenue management," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 261-282, January.
    19. Kyle Y. Lin & Sheldon M. Ross, 2003. "Admission Control with Incomplete Information of a Queueing System," Operations Research, INFORMS, vol. 51(4), pages 645-654, August.
    20. E. Carrizosa & E. Conde & M. Muñoz-Márquez, 1998. "Admission Policies in Loss Queueing Models with Heterogeneous Arrivals," Management Science, INFORMS, vol. 44(3), pages 311-320, March.

    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:ormsom:v:18:y:2016:i:3:p:429-444. 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.