Order Now, Pickup in 30 Minutes: Managing Queues with Static Delivery Guarantees

Forthcoming, Operations Research

46 Pages Posted: 9 Apr 2020 Last revised: 28 Oct 2021

See all articles by Mehdi H. Farahani

Mehdi H. Farahani

Massachusetts Institute of Technology

Milind Dawande

University of Texas at Dallas - Department of Information Systems & Operations Management

Ganesh Janakiraman

University of Texas at Dallas - Naveen Jindal School of Management

Date Written: March 19, 2020

Abstract

We study the problem of managing queues in online food-ordering services where customers, who place orders online and pick up at the store, are offered a common quote time, i.e., the promised pick-up time minus the time the order is placed. The objective is to minimize the long-run average expected earliness and tardiness cost incurred by the customers. We introduce the family of static threshold policies for managing such queues. A static threshold policy is one that starts serving the first customer in the queue as soon as the server is free and the time remaining until the promised pick-up time of that customer falls below a fixed threshold. In important technical contributions for establishing the attractiveness of the optimal static threshold policy, we develop three sets of lower bounds on the optimal cost. The first set of lower bounds exploits structural properties of two special static threshold policies, while the second set utilizes the idea of a clairvoyant optimal policy by considering a decision maker who has either full or partial knowledge of the outcomes of future uncertainties. To obtain our third set of lower bounds, we develop bounds on the optimal earliness and tardiness costs by establishing lower and upper bounds on the steady-state waiting time under an optimal policy. The optimal static threshold policy is asymptotically optimal in several cases, including the heavy traffic and the light traffic regimes. We also develop a dynamic threshold policy in which the threshold depends on the queue length. Finally, through a comprehensive numerical study, we demonstrate the excellent performance of both the static and the dynamic threshold policies.

Keywords: queueing, earliness and tardiness costs, quote time, clairvoyant bounds, asymptotic optimality

Suggested Citation

Farahani, Mehdi H. and Dawande, Milind and Janakiraman, Ganesh, Order Now, Pickup in 30 Minutes: Managing Queues with Static Delivery Guarantees (March 19, 2020). Forthcoming, Operations Research, Available at SSRN: https://ssrn.com/abstract=3557605 or http://dx.doi.org/10.2139/ssrn.3557605

Mehdi H. Farahani (Contact Author)

Massachusetts Institute of Technology ( email )

1 Amherst Street, E40-365
Cambridge, MA 02142
United States

Milind Dawande

University of Texas at Dallas - Department of Information Systems & Operations Management ( email )

P.O. Box 830688
Richardson, TX 75083-0688
United States

Ganesh Janakiraman

University of Texas at Dallas - Naveen Jindal School of Management ( email )

P.O. Box 830688
Richardson, TX 75083-0688
United States

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