Online Demand Fulfillment Problem with Initial Inventory Placement: A Regret Analysis

38 Pages Posted: 28 Dec 2023 Last revised: 26 Apr 2024

See all articles by Alessandro Arlotto

Alessandro Arlotto

Duke University - Decision Sciences

Irem Nur Keskin

Duke University - Decision Sciences

Yehua Wei

Decision Sciences Area, Fuqua School of Business, Duke University

Date Written: December 16, 2023

Abstract

We investigate a joint inventory placement and online fulfillment problem. At the beginning, the inventory of a single item is distributed to different warehouses. Then, at each period, an order arrives from one of the demand regions, and the decision maker makes an irrevocable decision on whether to accept or reject the order. In our model, we propose the minimum-inventory regret, a notion that includes both the selection of initial inventories and the performance of the selected fulfillment policy. We consider two state-of-the-art fulfillment policies: probabilistic fulfillment and score-based fulfillment. We prove that probabilistic fulfillment has a minimum-inventory regret that scales with the square root of the time horizon. On the other hand, we show that the score-based fulfillment policy has a minimum-inventory regret bound that is independent of the time horizon and polynomial with respect to the number of warehouses and demand regions. Our results have the following implication: the score-based fulfillment policy, when paired with offline inventory placement, outperforms probabilistic fulfillment with any inventory placement, and the performance gap increases with the time horizon.

Keywords: Online Fulfillment, inventory placement, resolving policies, minimum-inventory regret

Suggested Citation

Arlotto, Alessandro and Keskin, Irem Nur and Wei, Yehua, Online Demand Fulfillment Problem with Initial Inventory Placement: A Regret Analysis (December 16, 2023). Available at SSRN: https://ssrn.com/abstract=4666493 or http://dx.doi.org/10.2139/ssrn.4666493

Alessandro Arlotto

Duke University - Decision Sciences ( email )

Durham, NC 27708-0120
United States

HOME PAGE: http://people.duke.edu/~aa249/

Irem Nur Keskin (Contact Author)

Duke University - Decision Sciences ( email )

Durham, NC 27708-0120
United States

Yehua Wei

Decision Sciences Area, Fuqua School of Business, Duke University ( email )

100 Fuqua Drive
Durham, NC 27708-0204
United States

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