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Greedy-Like Algorithms for Dynamic Assortment Planning Under Multinomial Logit Preferences

54 Pages Posted: 5 Sep 2015 Last revised: 24 Oct 2016

Ali Aouad

Massachusetts Institute of Technology (MIT) - Operations Research Center

Retsef Levi

MIT Sloan School of Management - Operations Research Center

Danny Segev

University of Haifa - Department of Statistics

Date Written: September 3, 2015

Abstract

We study the joint assortment planning and inventory management problem, where stock-out events elicit dynamic substitution effects, described by the Multinomial Logit (MNL) choice model. Special cases of this setting have extensively been studied in recent literature, notably the static assortment planning problem. Nevertheless, the general formulation is not known to admit efficient algorithms with analytical performance guarantees prior to this work, and most of its computational aspects are still wide open.

In this paper, we devise the first provably-good approximation algorithm for dynamic assortment planning under the MNL model, attaining a constant-factor guarantee for a broad class of demand distributions, that satisfy the increasing failure rate property. Our algorithm relies on a combination of greedy procedures, where stocking decisions are restricted to specific classes of products, and the objective function takes modified forms. We demonstrate that our approach substantially outperforms state-of-the-art heuristic methods in terms of performance and speed, leading to a revenue gain of 6% to 10% on synthetic instances. In the course of establishing our main result, we develop new algorithmic ideas that may be of independent interest. These include weaker notions of submodularity and monotonicity, shown sufficient to obtain constant-factor worst-case guarantees, despite using noisy estimates of the objective function.

Keywords: assortment planning, dynamic substitution, approximation algorithms, submodularity.

Suggested Citation

Aouad, Ali and Levi, Retsef and Segev, Danny, Greedy-Like Algorithms for Dynamic Assortment Planning Under Multinomial Logit Preferences (September 3, 2015). Available at SSRN: https://ssrn.com/abstract=2655759 or http://dx.doi.org/10.2139/ssrn.2655759

Ali Aouad

Massachusetts Institute of Technology (MIT) - Operations Research Center ( email )

77 Massachusetts Avenue
Bldg. E 40-149
Cambridge, MA 02139
United States

Retsef Levi

MIT Sloan School of Management - Operations Research Center ( email )

100 Main Street
E62-416
Cambridge, MA 02142
United States

Danny Segev (Contact Author)

University of Haifa - Department of Statistics ( email )

Haifa 31905
Israel

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