Greedy-like algorithms for dynamic assortment planning under multinomial logit preferences

Aouad, A, Levi, R and Segev, D (2018) Greedy-like algorithms for dynamic assortment planning under multinomial logit preferences. Operations Research, 66 (5). pp. 1321-1345. ISSN 0030-364X OPEN ACCESS

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 been extensively studied in recent literature, notably the static assortment planning problem. Nevertheless, to our knowledge, the general formulation is not known to admit efficient algorithms with analytical performance guarantees before this work, and most of its computational aspects are still wide open. In this paper, we devise what is, to our knowledge, the first provably good approximation algorithm for dynamic assortment planning under the MNL model. We derive 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 an average revenue gain of 4% to 12% in computational experiments. 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

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Item Type: Article
Subject Areas: Management Science and Operations
Additional Information: © 2018 INFORMS
Subjects: I > Inventory control
A > Ancillary printing and publishing industries
A > Algorithms
A > Approximations
Date Deposited: 30 May 2019 10:49
Last Modified: 14 Jul 2019 15:41
URI: http://lbsresearch.london.edu/id/eprint/1086
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