×

Technical note – pricing and prioritization in a duopoly with self-selecting, heterogeneous, time-sensitive customers under low utilization. (English) Zbl 1455.90051

Summary: Time is often used as a differentiating factor in several service operations contexts by service providers (SPs) who prioritize their customers. We use a three-stage game to investigate the competition between two SPs providing service with relatively low utilization to impatient and patient customers. In the first stage, the SPs decide whether to offer single service in which customers are seen on a first-come-first-serve basis or differentiated service with prioritization. In the second stage, they set their prices. In the third stage, customers self-select and make their purchase decisions. We use a novel approach to model customers’ self-selection through an optimization problem with appropriate individual rationality (IR) and incentive compatibility (IC) conditions. In the pricing subgame, we focus on scenarios in which all customers get a positive net utility from using the service. We analyze the following three kinds of service delivery by the SPs, and we characterize different types of equilibrium associated with them: (i) \(\mathscr{S} \mathscr{S}\) in which both SPs provide single service, (ii) \( \mathscr{S} \mathscr{D}\) in which one SP provides single service and the other SP provides differentiated service, and (iii) \( \mathscr{D} \mathscr{D}\) in which both of them provide differentiated service. We then use these results to determine the overall equilibrium. We derive conditions (on customer heterogeneity and the fraction of impatient customers) for \(\mathscr{S} \mathscr{S}\), \( \mathscr{S} \mathscr{D}\), or \( \mathscr{D} \mathscr{D}\) to result in the overall equilibrium.
The online appendix is available at https://doi.org/10.1287/opre.2020.1983.

MSC:

90B22 Queues and service in operations research
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Afeche P (2013) Incentive-compatible revenue management in queueing systems: optimal strategic delay. Manufacturing Service Oper. Management 15(3):423-443.Link, Google Scholar
[2] Afeche P, Mendelson H (2004) Pricing and priority auctions in queueing systems with a generalized delay cost structure. Management Sci. 50(7):869-882.Link, Google Scholar · Zbl 1232.90134
[3] Afeche P, Baron O, Kerner Y (2013) Pricing time-sensitive services based on realized performance. Manufacturing Service Oper. Management 15(3):492-506.Link, Google Scholar
[4] Ahlin C, Ahlin PD (2013) Product differentiation under congestion: Hotelling was right. Econom. Inquiry 51(3):1750-1763.Crossref, Google Scholar
[5] Allon G, Federgruen A (2009) Competition in service industries with segmented markets. Management Sci. 55(4):619-634.Link, Google Scholar · Zbl 1232.90262
[6] Anand KS, Pac MF, Veeraraghavan S (2011) Quality-speed conundrum: Trade-offs in customer-intensive services. Management Sci. 57(1):40-56.Link, Google Scholar · Zbl 1214.90031
[7] Armony M, Haviv M (2003) Price and delay competition between two service providers. Eur. J. Oper. Res. 147(1):32-50.Crossref, Google Scholar · Zbl 1011.90017
[8] Boyaci T, Ray S (2003) Product differentiation and capacity cost interaction in time and price sensitive markets. Manufacturing Service Oper. Management 5(1):18-36.Link, Google Scholar
[9] Chen H, Wan YW (2003) Price competition of make-to-order firms. IIE Trans. 35(9):817-832.Crossref, Google Scholar
[10] Dobson G, Sainathan A (2011) On the impact of analyzing customer information and prioritizing in a service system. Decision Support Systems 51(4):875-883.Crossref, Google Scholar
[11] Gavirneni S, Kulkarni VG (2016) Self-selecting priority queues with burr distributed waiting costs. Production Oper. Management 25(6):979-992.Crossref, Google Scholar
[12] Gibbens R, Mason R, Steinberg R (2000) Internet service classes under competition. IEEE J. Selected Areas Comm. 18(12):2490-2498.Crossref, Google Scholar
[13] Hassin R, Haviv M (1997) Equilibrium threshold strategies: The case of queues with priorities. Oper. Res. 45(6):966-973.Link, Google Scholar · Zbl 0895.90093
[14] Hassin R, Haviv M (2003) To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems (Kluwer Academic Publishers, Boston).Crossref, Google Scholar · Zbl 1064.60002
[15] Hassin R, Haviv M (2006) Who should be given priority in a queue? Oper. Res. Lett. 34(2):191-198.Crossref, Google Scholar
[16] Hsu VN, Xu SH, Jukic B (2009) Optimal scheduling and incentive compatible pricing for a service system with quality of service guarantees. Manufacturing Service Oper. Management 11(3):375-396.Link, Google Scholar
[17] Katta A, Sethuraman J (2005) Pricing strategies and service differentiation in queues-a profit maximization perspective. Technical Report TR-2005-04, CORC, Columbia University, New York.Google Scholar
[18] Knowledge@Wharton (2013) Skipped out on your restaurant reservation? That will be \(200, please. Time (June 8) http://business.time.com/2013/06/08/skipped-out-on-your-restaurant-reservation-that-will-be-200-please/.Google Schola\)
[19] Lederer PJ, Li L (1997) Pricing, production, scheduling, and delivery-time competition. Oper. Res. 45(3):407-420.Link, Google Scholar · Zbl 0890.90020
[20] Li L, Lee YS (1994) Pricing and delivery-time performance in a competitive environment. Management Sci. 40(3):633-646.Link, Google Scholar · Zbl 0805.90031
[21] Li L, Jiang L, Liu L (2012) Service and price competition when customers are naive. Production Oper. Management 21(4):747-760.Crossref, Google Scholar
[22] Luski I (1976) On partial equilibrium in a queuing system with two servers. Rev. Econom. Stud. 43(3):519-525.Crossref, Google Scholar · Zbl 0343.90019
[23] Markovich M (2014) Pay up and show up: Local restaurant charges for reservations. KOMO News (September 9) http://www.komonews.com/news/local/Pay-up-and-show-up-Seattle-restaurant-charges-for-making-reservations-274556091.html.Google Scholar
[24] Mendelson H, Whang S (1990) Optimal incentive-compatible priority pricing for the M/M/1 queue. Oper. Res. 38(5):870-883.Link, Google Scholar · Zbl 0723.90023
[25] Pangburn MS, Stavrulaki E (2008) Capacity and price setting for dispersed, time-sensitive customer segments. Eur. J. Oper. Res. 184(3):1100-1121.Crossref, Google Scholar · Zbl 1141.90016
[26] Rao S, Peterson ER (1998) Optimal pricing of priority services. Oper. Res. 46(1):46-56.Link, Google Scholar · Zbl 0987.90023
[27] Sainathan A (2018) Customer differentiation with shipping as an ancillary service? Free service, prioritization, and strategic delay. Decision Sci. 49(4):690-727.Crossref, Google Scholar
[28] So KC, Song JS (1998) Price, delivery time guarantees, and capacity selection. Eur. J. Oper. Res. 111(1):28-49.Crossref, Google Scholar · Zbl 0948.90081
[29] Van Mieghem JA (2000) Price and service discrimination in queuing systems: Incentive compatibility of gcμ scheduling. Management Sci. 46(9):1249-1267.Link, Google Scholar · Zbl 1232.90157
[30] Wallop H (2010) £350 to queue jump at a theme park. Telegraph (June 12) http://www.telegraph.co.uk/finance/newsbysector/retailandconsumer/7821388/350-to-queue-jump-at-a-theme-park.html.Google Scholar
[31] Wieczner J (2013) Pros and cons of concierge medicine. Wall Street Journal (November 10) http://www.wsj.com/articles/SB10001424052702303471004579165470633112630.Google Scholar
[32] Zhang Z,
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.