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

Operations Research, 60(6), 1505-1519. https://doi.org/10.1287/opre.1120.1117

The University of Auckland Business School Research Paper Series

Posted: 27 Oct 2021

See all articles by Mustafa Akan

Mustafa Akan

Carnegie Mellon University, David A. Tepper School of Business, Students

Baris Ata

Northwestern University - Kellogg School of Management

Tava Lennon Olsen

University of Auckland Business School

Date Written: 2012

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. Full paper available at https://doi.org/10.1287/opre.1120.1117

Suggested Citation

Akan, Mustafa and Ata, Baris and Lennon Olsen, Tava, Congestion-Based Lead-Time Quotation for Heterogenous Customers with Convex-Concave Delay Costs: Optimality of a Cost-Balancing Policy Based on Convex Hull Functions (2012). Operations Research, 60(6), 1505-1519. https://doi.org/10.1287/opre.1120.1117 , The University of Auckland Business School Research Paper Series, Available at SSRN: https://ssrn.com/abstract=3947477

Mustafa Akan (Contact Author)

Carnegie Mellon University, David A. Tepper School of Business, Students ( email )

Pittsburgh, PA
United States

Baris Ata

Northwestern University - Kellogg School of Management ( email )

2001 Sheridan Road
Evanston, IL 60208
United States

Tava Lennon Olsen

University of Auckland Business School ( email )

12 Grafton Rd
Private Bag 92019
Auckland, 1010
New Zealand

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