Network Inventory Management: Approximate Optimality in Large-Scale Systems

65 Pages Posted: 12 May 2021

See all articles by Deniz Akturk

Deniz Akturk

University of Chicago - Booth School of Business

Ozan Candogan

University of Chicago - Booth School of Business

Varun Gupta

University of Chicago - Booth School of Business

Date Written: May 10, 2021

Abstract

We consider a discrete time network inventory management problem on a hub-and-spoke network. Each period begins with an initial inventory at each of the nodes in the network, after which the customers (demand) materialize at the nodes. Each customer picks up a unit at the origin node and drops it off at a randomly sampled destination node given by an origin-specific probability distribution. An important task in inventory management of such systems is the periodic physical repositioning of the inventory to avoid stockouts or excess inventory at nodes with unbalanced flows. In our work, we model the above network inventory management problem as an infinite horizon discrete-time discounted Markov Decision Process, and prove the asymptotic optimality of a novel mean-field approximation to the original MDP as the number of spokes becomes large. To compute an approximately optimal policy for the mean-field dynamics, we provide an algorithm whose running time is logarithmic in the desired optimality gap. Lastly, we compare the performance of our mean-field based policy to other policies via synthetic numerical experiments.

Keywords: Inventory Rebalancing, Hub-and-Spoke Networks, Mean-Field Analysis, Deterministic Dynamic Programming

Suggested Citation

Akturk, Tahsin Deniz and Candogan, Ozan and Gupta, Varun, Network Inventory Management: Approximate Optimality in Large-Scale Systems (May 10, 2021). Available at SSRN: https://ssrn.com/abstract=3842817 or http://dx.doi.org/10.2139/ssrn.3842817

Tahsin Deniz Akturk (Contact Author)

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

Ozan Candogan

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

HOME PAGE: http://faculty.chicagobooth.edu/ozan.candogan/

Varun Gupta

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

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