An improved compact formulation for the assortment optimization problem with small consideration sets

Roberto Roberti, Domenico Salvagnin and Matteo Fischetti

Journal of the Operational Research Society, 2025, vol. 76, issue 10, 2060-2070

Abstract: We investigate the assortment optimization problem with small consideration sets, where customers belong to classes and choose according to the k-product non-parametric ranking-based choice model – i.e., each customer’s preference list contains at most k products, and customers purchase the most preferred product among the ones offered in the assortment. This problem is known to be NP-hard even when k is equal to 2. The best approximation method from the literature has a performance guarantee of 2(1−1k)k−1(1k) and can find, empirically, assortments that are 0.3-0.5% within optimality when k equals 4 and there are 100 products and 10 000 customer classes. By building upon a compact Mixed-Integer Linear Programming model proposed, in the literature, for the full non-parametric ranking-based choice model, we propose an improved compact model that features a very tight continuous relaxation and can be easily solved with a general-purpose solver. An extensive set of computational experiments shows that our improved formulation can find provably optimal assortments of instances with up to 200 products, 100 000 customers classes, and k equal to 5, in a few minutes of runtime.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/01605682.2025.2451738 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:tjorxx:v:76:y:2025:i:10:p:2060-2070

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/tjor20

DOI: 10.1080/01605682.2025.2451738

Access Statistics for this article

Journal of the Operational Research Society is currently edited by Tom Archibald

More articles in Journal of the Operational Research Society from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().