Congestion-Based Lead-Time Quotation for Heterogenous Customers with Convex-Concave Delay Costs: Optimality of a Cost-Balancing Policy Based on Convex Hull Functions

Authors:
Mustafa Akan;Barı ş Ata;Tava Olsen
Affiliations:
Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213;Kellogg School of Management, Northwestern University, Evanston, Illinois 60208;The University of Auckland Business School, University of Auckland, Auckland 1142, New Zealand
Venue:
Operations Research
Year:
2012

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Abstract

We consider a congestible system serving multiple classes of customers who differ in their delay sensitivity and valuation of service or product. Customers are endowed with convex-concave delay cost functions. A system manager offers a menu of lead times and corresponding prices to arriving customers, who then choose the lead-time--price pair that maximizes their net utility value minus disutility of delay and price. We investigate how such menus should be chosen dynamically depending on the system backlog to maximize welfare. We formulate a novel fluid model of the problem and show that the cost-balancing policy based on the convex hulls of the delay cost functions is socially optimal if the system manager can tell customer types apart. If types are indistinguishable to the system manager, the cost-balancing policy is also incentive compatible under social optimization. Finally, we show through a simulation study that the cost-balancing policy does well in the context of the original stochastic problem by testing it against various natural benchmarks.