IBM Case

INDIAN INSTITUTE OF MANAGEMENT
AHMEDABAD • INDIA

Research and Publications

Minimizing Customer Waiting Costs for Rental
Vehicle Providers using Threshold Reservation Policies
Jennifer A. Pazour
Debjit Roy
W.P. No. 2012-12-05
December 2012

✏
✓
The main objective of the Working Paper series of IIMA is to help faculty members, research staff, and doctoral students to speedily share their research findings with professional colleagues and to test out their research findings at the pre-publication stage.
✒
✑

INDIAN INSTITUTE OF MANAGEMENT
AHMEDABAD – 380015
INDIA

W.P. No. 2012-12-05

Page No. 1

IIMA • INDIA

Research and Publications

Minimizing Customer Waiting Costs for Rental Vehicle
Providers using Threshold Reservation Policies
Jennifer A. Pazour
Debjit Roy

Abstract: Vehicle rental providers offer differentiated services to reserve and walk-in customers. In this research, we study one such service differentiation strategy, a vehicle threshold policy, which is to hold vehicles for reserve class customers in anticipation of their future arrivals. To consider the impact that vehicle threshold policies have on reserve and walk-in customer waiting times, we model a rental depot as a multi-class non-work-conserving semi-open queue with stochastic inputs. For exponential and deterministic service time distributions, we identify the optimal threshold quantity for stationary customer arrivals using closed-form expressions for the expected waiting times of both customer classes. For non-stationary customer arrivals, we develop different threshold policies and analyze their performance using a detailed simulation model. Through numerical testing, we provide insights into recommended threshold policies that can be applied to improve the profitability of a rental provider.

Keywords: Transportation; Vehicle rental system; Customer service differentiation; Semi-open non-work conserving queue; Priority threshold queuing

References: [1] Altman, E., Jimenez, T., and Koole, G., “On Optimal Call Admission Control in a ResourceSharing System,” IEEE Transactions on Communications, 49, 9, 1659–1668 (2001). [2] Auto Rental News, “2011 U.S. Car Rental Market, Auto Rental News, Fact Book 2012,” (2011), http : //www.autorentalnews.com/f cr esources/Editorial/ARN − 6.pdf . [3] Barcelo, F., Casares, V., and Paradells, J., “M/D/C Queue with Priority: Application to Trunked Mobile Radio Systems,” Electronics Letters, 32, 1644–1645 (1996). Operations (2011), [5] Busse, M., and Swinkels, J., “Enterprise Rent-A-Car,” Technical Report KEL612, Kellogg School of Management (2012). [6] Carroll, W. J., and Grimes, R. C., “Evolutionary Change in Product Mangement: Experiences in the Car Rental Industry,” Interfaces, 25, 5, 84–104 (1995). [7] Fink, A., and Reiners, T., “Modeling and Solving the Short-Term Car Rental Logistics Problem,” Transportation Research Part E, 42, 272–292 (2006). [8] Gans, N., and Savin, S., “Pricing and Capacity Rationing for Rentals with Uncertain Durations,” Management Science, 53, 3, 390–407 (2007). (2011). W.P. No. 2012-12-05 Page No [10] Green, L., and Kolesar, P., “The Pointwise Stationary Approximation for Queues with Nonstationary Arrivals,” Management Science, 37, 1, 84–97 (1991). [11] Green, L., Kolesar, P., and Soares, J., “Improving the SIPP Approach for Staffing Service Systems that have Cyclic Demands,” Operations Research, 49, 4, 549–564 (2001). Operational Research, 164, 2, 341–353 (2005). [13] Helm, J. E., AhmadBeygi, S., and Van Oyen, M. P., “Design and Analysis of Hospital Admission Control for Operational Effectiveness,” Production and Operations Management, 20, 3 (2011). Rental port SIC 7514, HighBeam Business (2012), of Operational Research, 198, 2, 545–556 (2009). [16] Lee, D.-S., and Sengupta, B., “Queueing Analysis of a Threshold Based Priority Scheme for ATM Networks,” IEEE/ACM Transactions on Networking, 1, 6, 709–717 (1993). [17] Miller, B. L., “A Queuing Reward System with Several Customer Classes,” Management Science, 16, 3, 234–245 (1969). [18] Ormeci, L., Burnetas, A., and van der Wal, J., “Admissions Policies to a Two-Class Loss System,” Stochastic Models, 17, 513–539 (2001). [19] Papier, F., and Thonemann, U. W., “Queuing Models for Sizing and Structuring Rental Fleets,” Transportation Science, 42, 3, 302–317 (2008). [20] Papier, F., and Thonemann, U. W., “Capacity Rationing in Stochastic Rental Systems with Advance Demand Information,” Operations Research, 58, 274–288 (2010). [21] Papier, F., and Thonemann, U. W., “Capacity Rationing in Rental Systems with Two Customer Classes and Batch Arrivals,” Omega, 39, 73–85 (2011). W.P. No. 2012-12-05 Page No