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Promised Delivery Time and Capacity Games in Time-Based Competition


  • Weixin Shang

    () (School of Management, Fudan University, Shanghai 200433, China)

  • Liming Liu

    () (Faculty of Business, Hong Kong Polytechnic University, Hong Kong, China)


We investigate firms' competitive behaviors in industries where customers are sensitive to both promised delivery time (PDT) and quality of service (QoS) measured by the on-time delivery rate. To study the competition in PDT at the marketing level, we construct an oligopoly game with an external QoS requirement. We show that there exists a unique Nash equilibrium, and the equilibrium QoS exhibits a switching surface structure with respect to capacities. To study the competition in capacity at the strategic level, we construct a two-stage game in which the firms compete in terms of their capacities in stage 1 and in terms of PDT in stage 2. We show the existence of two different types of pure strategy equilibria and characterize them. This study provides the following insights: an index of time-based competitive advantage (ITCA) and the first-mover advantage determine the positions of the firms in time-based competition; either the well-known prisoner's dilemma or off-equilibrium behaviors due to different preferences for equilibria (when multiple equilibria exist) may lead the firms to overinvest in capacity, but no one may gain a competitive advantage; a uniform improvement in internal efficiency (i.e., a uniform capacity cost reduction) may harm everyone; quality differentiation (i.e., going beyond the QoS benchmark) plays a dual role in time-based competition, either helping a firm with a larger ITCA to compete more effectively, or helping a firm possibly with a smaller ITCA to preempt competitors and protect its market advantage. This paper was accepted by Paul H. Zipkin, operations and supply chain management.

Suggested Citation

  • Weixin Shang & Liming Liu, 2011. "Promised Delivery Time and Capacity Games in Time-Based Competition," Management Science, INFORMS, vol. 57(3), pages 599-610, March.
  • Handle: RePEc:inm:ormnsc:v:57:y:2011:i:3:p:599-610

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    References listed on IDEAS

    1. Izak Duenyas & Wallace J. Hopp, 1995. "Quoting Customer Lead Times," Management Science, INFORMS, vol. 41(1), pages 43-57, January.
    2. Slotnick, Susan A. & Sobel, Matthew J., 2005. "Manufacturing lead-time rules: Customer retention versus tardiness costs," European Journal of Operational Research, Elsevier, vol. 163(3), pages 825-856, June.
    3. Kut C. So, 2000. "Price and Time Competition for Service Delivery," Manufacturing & Service Operations Management, INFORMS, vol. 2(4), pages 392-409, April.
    4. Olivier Armantier & Oliver Richard, 2008. "Domestic airline alliances and consumer welfare," RAND Journal of Economics, RAND Corporation, vol. 39(3), pages 875-904.
    5. Lode Li & Yew Sing Lee, 1994. "Pricing and Delivery-Time Performance in a Competitive Environment," Management Science, INFORMS, vol. 40(5), pages 633-646, May.
    6. Berry, Steven T, 1992. "Estimation of a Model of Entry in the Airline Industry," Econometrica, Econometric Society, vol. 60(4), pages 889-917, July.
    7. Liming Liu & Mahmut Parlar & Stuart X. Zhu, 2007. "Pricing and Lead Time Decisions in Decentralized Supply Chains," Management Science, INFORMS, vol. 53(5), pages 713-725, May.
    8. Suman Basuroy & Dung Nguyen, 1998. "Multinomial Logit Market Share Models: Equilibrium Characteristics and Strategic Implications," Management Science, INFORMS, vol. 44(10), pages 1396-1408, October.
    9. Tamer Boyaci & Saibal Ray, 2003. "Product Differentiation and Capacity Cost Interaction in Time and Price Sensitive Markets," Manufacturing & Service Operations Management, INFORMS, vol. 5(1), pages 18-36, May.
    10. Teck H. Ho & Yu-Sheng Zheng, 2004. "Setting Customer Expectation in Service Delivery: An Integrated Marketing-Operations Perspective," Management Science, INFORMS, vol. 50(4), pages 479-488, April.
    11. Lode Li, 1992. "The Role of Inventory in Delivery-Time Competition," Management Science, INFORMS, vol. 38(2), pages 182-197, February.
    12. Steven T. Berry, 1994. "Estimating Discrete-Choice Models of Product Differentiation," RAND Journal of Economics, The RAND Corporation, vol. 25(2), pages 242-262, Summer.
    13. Candace Arai Yano, 1987. "Setting Planned Leadtimes in Serial Production Systems with Tardiness Costs," Management Science, INFORMS, vol. 33(1), pages 95-106, January.
    14. So, Kut C. & Song, Jing-Sheng, 1998. "Price, delivery time guarantees and capacity selection," European Journal of Operational Research, Elsevier, vol. 111(1), pages 28-49, November.
    15. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
    16. 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.
    17. 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.
    18. Piyush Kumar & Manohar U. Kalwani & Maqbool Dada, 1997. "The Impact of Waiting Time Guarantees on Customers' Waiting Experiences," Marketing Science, INFORMS, vol. 16(4), pages 295-314.
    19. GĂ©rard P. Cachon & Fuqiang Zhang, 2007. "Obtaining Fast Service in a Queueing System via Performance-Based Allocation of Demand," Management Science, INFORMS, vol. 53(3), pages 408-420, March.
    20. Lawrence M. Wein, 1991. "Due-Date Setting and Priority Sequencing in a Multiclass M/G/1 Queue," Management Science, INFORMS, vol. 37(7), pages 834-850, July.
    21. Ehud Kalai & Morton I. Kamien & Michael Rubinovitch, 1992. "Optimal Service Speeds in a Competitive Environment," Management Science, INFORMS, vol. 38(8), pages 1154-1163, August.
    22. Jing-Sheng Song & Candace A. Yano & Panupol Lerssrisuriya, 2000. "Contract Assembly: Dealing with Combined Supply Lead Time and Demand Quantity Uncertainty," Manufacturing & Service Operations Management, INFORMS, vol. 2(3), pages 287-296, July.
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    Cited by:

    1. Zhu, Stuart X., 2015. "Integration of capacity, pricing, and lead-time decisions in a decentralized supply chain," International Journal of Production Economics, Elsevier, vol. 164(C), pages 14-23.
    2. Li, Gang & Huang, Feng Feng & Cheng, T.C.E. & Zheng, Quan & Ji, Ping, 2014. "Make-or-buy service capacity decision in a supply chain providing after-sales service," European Journal of Operational Research, Elsevier, vol. 239(2), pages 377-388.
    3. 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.
    4. repec:eee:transb:v:104:y:2017:i:c:p:317-336 is not listed on IDEAS
    5. repec:osi:bulimm:v:17:y:2017:p:265-280 is not listed on IDEAS
    6. repec:spr:annopr:v:241:y:2016:i:1:d:10.1007_s10479-012-1085-6 is not listed on IDEAS


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