Robustness of Online Inventory Balancing Algorithm to Inventory Shocks

28 Pages Posted: 2 Mar 2021 Last revised: 5 Mar 2024

See all articles by Yiding Feng

Yiding Feng

University of Chicago Booth School of Business

Rad Niazadeh

University of Chicago - Booth School of Business

Amin Saberi

Stanford University - Department of Management Science & Engineering

Date Written: March 1, 2021

Abstract

In classic adversarial online resource allocation problems, such as matching, AdWords, or assortment planning, customers (demand) arrive in an online fashion, while the products (supply) are given offline with a fixed initial inventory. To achieve acceptable revenue guarantees given the uncertainty in future customer arrivals, the decision maker must balance consumption across different products. Motivated by this simple intuition, the famous policy -- "inventory balancing" (IB)} -- is introduced and studied in the literature and proved to be optimal or near-optimal competitive in almost all the classic settings. However, an important feature that these classic models do not capture is inventory shocks on the supply side, which could play a significant role in many real-world applications and can possibly cause the revenue performance of the IB algorithm to degrade.

We introduce and study a new variant of online assortment planning with inventory shocks. Our model considers both exogenous shocks (e.g., due to purchase return from another channel, misalignment between inventory management and sale) that are adversarial, and endogenous shocks (following a simple restocking strategy with a lead time). For the objective of maximizing total revenue, we show that the original IB no longer achieves the optimal competitive ratio in this new model. In contrast, we design a new family of algorithms, which we call "batched inventory balancing (BIB)", which generalizes the original IB against inventory shocks. We develop a novel randomized primal-dual method to bound the competitive ratio of our BIB algorithm against any feasible policy. We show that with the proper choice of a certain parameter, this competitive ratio is asymptotically optimal and converges to (1-1/e), as the initial inventories converge to infinity. We then show how to characterize BIB's competitive ratio in its general form. We use a refined analysis that reduces the dual construction to a combinatorial problem referred to as the ``interval assignment problem''. Our solution to this problem is algorithmic and might be of independent interest.

Keywords: Online algorithms, Inventory Balancing, Assortment Planning, Robustness in Operations

Suggested Citation

Feng, Yiding and Niazadeh, Rad and Saberi, Amin, Robustness of Online Inventory Balancing Algorithm to Inventory Shocks (March 1, 2021). Available at SSRN: https://ssrn.com/abstract=3795056 or http://dx.doi.org/10.2139/ssrn.3795056

Yiding Feng

University of Chicago Booth School of Business ( email )

Chicago
United States

Rad Niazadeh (Contact Author)

University of Chicago - Booth School of Business ( email )

5807 S Woodlawn Ave
Chicago, IL 60637

HOME PAGE: http://https://faculty.chicagobooth.edu/rad-niazadeh

Amin Saberi

Stanford University - Department of Management Science & Engineering ( email )

473 Via Ortega
Stanford, CA 94305-9025
United States

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