IBM Case

Topics: Customer, Customer service, Queueing theory Pages: 30 (11833 words) Published: October 27, 2014

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. ✒

AHMEDABAD – 380015

W.P. No. 2012-12-05

Page No. 1


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 systems.



Vehicle rental providers operate a fleet of vehicles that are rented to customers who are temporary in need of a vehicle for a fee. Vehicle rental markets are growing worldwide, with the United States’ market witnessing an 8.8% increase in revenue growth in 2011 from $20.6B in 2010 [2]. Notable large rental providers include Enterprise, Hertz, and Avis with a fleet size of 920,861, 320,000, and 285,000 vehicles, respectively.

Rental providers serve a wide range of customer needs and rental periods (generally ranging from a few hours to a few weeks). Customers rent vehicles for business travel, for leisure travel, for a replacement vehicle due to accidents or vehicle maintenance, and for use as a primary vehicle. Customers, who plan their travel in advance, reserve vehicles whereas customers with last-minute 1 Jennifer A. Pazour, Department of Industrial Engineering and Management Systems, University of Central Florida, Orlando, FL 32816,

2 Debjit Roy, Indian Institute of Management Ahmedabad, Gujarat-380015, India, Email:

W.P. No. 2012-12-05

Page No. 2


Research and Publications

travel requirements may walk-in at a depot to rent a vehicle without a reservation. Therefore, customers can be broadly classified into two classes: reserve and walk-in. Reserve customers place a vehicle reservation either directly with a rental provider or through a third-party travel site. Reservations provide a benefit to customers by increasing the chance that a vehicle will be available when the customer arrives and to vehicle providers through increased sales and for planning purposes. However, reservations require holding idle vehicles, which can reduce fleet utilizations especially when customers’ arrival times vary from the information provided in their reservation (either by not arriving to pick up their vehicle or by arriving late). Walk-in customers arrive to the rental depot...

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 : // 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).
[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).
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).
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
Continue Reading

Please join StudyMode to read the full document

You May Also Find These Documents Helpful

  • ibm case study 2007 Essay
  • IBM Case Study Essay
  • Ibm Case Study Essay
  • Ibm Case Study Essay
  • Ibm Case Study Research Paper
  • Ibm Case Study Essay
  • Ibm Case Study Essay
  • Essay about IBM case study

Become a StudyMode Member

Sign Up - It's Free