A Model for Integrated Inventory and Assortment Planning

Victor Martínez- de-Albéniz () and Sumit Kunnumkal ()
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Victor Martínez- de-Albéniz: IESE Business School, University of Navarra, 08034 Barcelona, Spain
Sumit Kunnumkal: Indian School of Business, Gachibowli, Hyderabad, India

Management Science, 2022, vol. 68, issue 7, 5049-5067

Abstract: 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.

Keywords: stockout-based substitution; choice models; Markov chain; integer programming (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:68:y:2022:i:7:p:5049-5067

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