A Model for Integrated Inventory and Assortment Planning

Martínez-de-Albéniz, V and Kunnumkal, S (2022) A Model for Integrated Inventory and Assortment Planning. Management Science, 68 (7). pp. 5049-5067. ISSN 0025-1909

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Integrating inventory and assortment planning decisions is a challenging task that requires comparing the value of demand expansion through broader choice for consumers with the value of higher in-stock availability. We develop a stockout-based substitution model for trading off these values in a setting with inventory replenishment, a feature missing in the literature. Using the closed form solution for the single-product case, we develop an accurate approximation for the multiproduct case. This approximated formulation allows us to optimize inventory decisions by solving a fractional integer program with a fixed point equation constraint. When products have equal margins, we solve the integer program exactly by bisection over a one-dimensional parameter. In contrast, when products have different margins, we propose a fractional relaxation that we can also solve by bisection and that results in near-optimal solutions. Overall, our approach provides solutions within 0.1% of the optimal policy and finds the optimal solution in 80% of the random instances we generate.

This paper was accepted by David Simchi-Levi, optimization.

Item Type: Article
Subjects: Operations Management
Date Deposited: 04 Sep 2023 16:38
Last Modified: 04 Sep 2023 16:38
URI: https://eprints.exchange.isb.edu/id/eprint/2056

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