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Optimal Pricing of Priority Services

Author

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  • S. Rao

    (Queen's University, Kingston, Ontario, Canada)

  • E. R. Petersen

    (Queen's University, Kingston, Ontario, Canada)

Abstract

We consider the problem of a service facility that offers m different priority classes to its n customers, and sets a tariff (price-schedule) to maximize profit. Each customer must use the service facility and will select an output rate and the priority classes used to maximize profit. The problem is formulated as a noncooperative game. We show that equilibrium output rates and assignments to priority classes can be determined by solving the integrated system problem (ISP) that maximizes the joint profit of all agents. The service facility can be represented by a network, and ISP is a traffic assignment problem. A tariff schedule that induces each customer to select the integrated system output rate and assignment is said to be vertically efficient. We show that the server can select vertically efficient tariffs that result in an equilibrium. Optimal pricing for the special case where the service facility is modeled as a priority queue is discussed. Examples are included to illustrate the results.

Suggested Citation

  • S. Rao & E. R. Petersen, 1998. "Optimal Pricing of Priority Services," Operations Research, INFORMS, vol. 46(1), pages 46-56, February.
    • Handle: RePEc:inm:oropre:v:46:y:1998:i:1:p:46-56
    DOI: 10.1287/opre.46.1.46
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    References listed on IDEAS

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    1. Steven A. Lippman & Shaler Stidham, 1977. "Individual versus Social Optimization in Exponential Congestion Systems," Operations Research, INFORMS, vol. 25(2), pages 233-247, April.
    2. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
    3. Haim Mendelson & Seungjin Whang, 1990. "Optimal Incentive-Compatible Priority Pricing for the M/M/1 Queue," Operations Research, INFORMS, vol. 38(5), pages 870-883, October.
    4. E. R. Petersen, 1974. "Over-the-Road Transit Time for a Single Track Railway," Transportation Science, INFORMS, vol. 8(1), pages 65-74, February.
    5. Sanjeev Dewan & Haim Mendelson, 1990. "User Delay Costs and Internal Pricing for a Service Facility," Management Science, INFORMS, vol. 36(12), pages 1502-1517, December.
    6. Walter Y. Oi, 1971. "A Disneyland Dilemma: Two-Part Tariffs for a Mickey Mouse Monopoly," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 85(1), pages 77-96.
    7. Rey, Patrick & Tirole, Jean, 1986. "The Logic of Vertical Restraints," American Economic Review, American Economic Association, vol. 76(5), pages 921-939, December.
    8. Colin E. Bell & Shaler Stidham, Jr., 1983. "Individual versus Social Optimization in the Allocation of Customers to Alternative Servers," Management Science, INFORMS, vol. 29(7), pages 831-839, July.
    9. W. J. Hurley & E. R. Petersen, 1994. "Nonlinear Tariffs and Freight Network Equilibrium," Transportation Science, INFORMS, vol. 28(3), pages 236-245, August.
    10. K. R. Balachandran, 1972. "Purchasing Priorities in Queues," Management Science, INFORMS, vol. 18(5-Part-1), pages 319-326, January.
    11. Knudsen, Niels Chr, 1972. "Individual and Social Optimization in a Multiserver Queue with a General Cost-Benefit Structure," Econometrica, Econometric Society, vol. 40(3), pages 515-528, May.
    12. Balachandran, K R & Schaefer, Mark E, 1979. "Class Dominance Characteristics at a Service Facility," Econometrica, Econometric Society, vol. 47(2), pages 515-519, March.
    13. Avraham Beja & Esther Sid, 1975. "Optimal Priority Assignment with Heterogeneous Waiting Costs," Operations Research, INFORMS, vol. 23(1), pages 107-117, February.
    14. Robert J. Dolan, 1978. "Incentive Mechanisms for Priority Queuing Problems," Bell Journal of Economics, The RAND Corporation, vol. 9(2), pages 421-436, Autumn.
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    Cited by:

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    3. Ying Xu & Alan Scheller-Wolf & Katia Sycara, 2015. "The Benefit of Introducing Variability in Single-Server Queues with Application to Quality-Based Service Domains," Operations Research, INFORMS, vol. 63(1), pages 233-246, February.
    4. Erica L. Plambeck, 2004. "Optimal Leadtime Differentiation via Diffusion Approximations," Operations Research, INFORMS, vol. 52(2), pages 213-228, April.
    5. Petersen, E. R. & Taylor, A. J., 2001. "An investment planning model for a new North-Central railway in Brazil," Transportation Research Part A: Policy and Practice, Elsevier, vol. 35(9), pages 847-862, November.
    6. Rajat Talak & D. Manjunath & Alexandre Proutiere, 2019. "Strategic arrivals to queues offering priority service," Queueing Systems: Theory and Applications, Springer, vol. 92(1), pages 103-130, June.
    7. Zhongju Zhang & Debabrata Dey & Yong Tan, 2007. "Pricing Communication Services with Delay Guarantee," INFORMS Journal on Computing, INFORMS, vol. 19(2), pages 248-260, May.
    8. Vernon N. Hsu & Susan H. Xu & Boris Jukic, 2009. "Optimal Scheduling and Incentive Compatible Pricing for a Service System with Quality of Service Guarantees," Manufacturing & Service Operations Management, INFORMS, vol. 11(3), pages 375-396, May.
    9. Xiaojun Liang & Yinghui Tang, 2019. "The improvement upon the reliability of the k-out-of-n:F system with the repair rates differentiation policy," Operational Research, Springer, vol. 19(2), pages 479-500, June.
    10. Philipp Afèche, 2013. "Incentive-Compatible Revenue Management in Queueing Systems: Optimal Strategic Delay," Manufacturing & Service Operations Management, INFORMS, vol. 15(3), pages 423-443, July.
    11. Zhang, Jian & Nault, Barrie R. & Tu, Yiliu, 2015. "A dynamic pricing strategy for a 3PL provider with heterogeneous customers," International Journal of Production Economics, Elsevier, vol. 169(C), pages 31-43.
    12. Yasushi Masuda & Seungjin Whang, 2006. "On the Optimality of Fixed-up-to Tariff for Telecommunications Service," Information Systems Research, INFORMS, vol. 17(3), pages 247-253, September.
    13. Albert Y. Ha, 2001. "Optimal Pricing That Coordinates Queues with Customer-Chosen Service Requirements," Management Science, INFORMS, vol. 47(7), pages 915-930, July.
    14. Philipp Afèche & Opher Baron & Joseph Milner & Ricky Roet-Green, 2019. "Pricing and Prioritizing Time-Sensitive Customers with Heterogeneous Demand Rates," Operations Research, INFORMS, vol. 67(4), pages 1184-1208, July.
    15. Nilay Tan{i}k Argon & Serhan Ziya, 2009. "Priority Assignment Under Imperfect Information on Customer Type Identities," Manufacturing & Service Operations Management, INFORMS, vol. 11(4), pages 674-693, June.
    16. Zhang, Zhongju & Dey, Debabrata & Tan, Yong, 2008. "Price and QoS competition in data communication services," European Journal of Operational Research, Elsevier, vol. 187(3), pages 871-886, June.
    17. Jan A. Van Mieghem, 2000. "Price and Service Discrimination in Queuing Systems: Incentive Compatibility of Gc\mu Scheduling," Management Science, INFORMS, vol. 46(9), pages 1249-1267, September.
    18. Liu, Jian & Chen, Jian & Bo, Rui & Meng, Fanlin & Xu, Yong & Li, Peng, 2023. "Increases or discounts: Price strategies based on customers’ patience times," European Journal of Operational Research, Elsevier, vol. 305(2), pages 722-737.

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