Learning in infinite-horizon inventory competition with total demand observations

Ashkan Zeinalzadeh, Aydin Alptekinoglu, Gurdal Arslan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider single-period and infinite-horizon inventory competition between two firms that replenish their inventories as in the well-known newsvendor model. Normally customers have a preference for shopping in one firm or the other. A fixed percentage of them who encounter a stockout in the firm of their first choice, though, visits the other firm. This substitution behavior makes the firm's replenishment decisions strategically related. Our main contribution is to introduce a simple learning algorithm to inventory competition. The learning algorithm requires each firm (a) to have the knowledge of its own critical fractile, which the firm can calculate using the values of its own per unit revenue, order cost, and holding cost; and (b) to observe its own total demand realizations. They do not necessarily know their true demand distributions. The firms need not even have any information about each other, beyond the implicit information encoded in their own total demand realizations affected by their competitors' inventory decisions. In fact, the firms need not even be aware that they are engaged in inventory competition. We prove that the inventory decisions generated by the learning algorithm converge, with probability one, to certain threshold values that constitute an equilibrium in pure Markov strategies for an infinite-horizon discounted-reward inventory competition game.

Original languageEnglish (US)
Title of host publication2012 American Control Conference, ACC 2012
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1382-1387
Number of pages6
ISBN (Print)9781457710957
DOIs
StatePublished - 2012
Event2012 American Control Conference, ACC 2012 - Montreal, QC, Canada
Duration: Jun 27 2012Jun 29 2012

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619

Other

Other2012 American Control Conference, ACC 2012
CountryCanada
CityMontreal, QC
Period6/27/126/29/12

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

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    Zeinalzadeh, A., Alptekinoglu, A., & Arslan, G. (2012). Learning in infinite-horizon inventory competition with total demand observations. In 2012 American Control Conference, ACC 2012 (pp. 1382-1387). [6315678] (Proceedings of the American Control Conference). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/acc.2012.6315678