Fuzzy Gaussian mixture optimization of the newsvendor problem: mixing online reviews and judgemental demand data

TL;DR

This paper introduces a fuzzy Gaussian mixture model for the newsvendor problem that combines probabilistic and fuzzy demand data, allowing for more flexible and realistic demand modeling influenced by online reviews and expert opinions.

Contribution

It develops a novel fuzzy GMM framework that integrates fuzzy and probabilistic demand inputs, extending traditional models to better capture demand uncertainty and decision maker risk attitudes.

Findings

Fuzzy GMM can be reformulated as a classical newsvendor problem with a combined density function.

The model accommodates multiple demand modalities and subjective risk preferences.

It provides a tractable approach to incorporate fuzzy and probabilistic demand information.

Abstract

Motivated by the increasing exposition of decision makers to both statistical and judgemental based sources of demand information, we develop in this paper a fuzzy Gaussian Mixture Model (GMM) for the newsvendor permitting to mix probabilistic inputs with a subjective weight modelled as a fuzzy number. The developed framework can model for instance situations where sales are impacted by customers sensitive to online review feedbacks or expert opinions. It can also model situations where a marketing campaign leads to different stochastic alternatives for the demand with a fuzzy weight. Thanks to a tractable mathematical application of the fuzzy machinery on the newsvendor problem, we derived the optimal ordering strategy taking into account both probabilistic and fuzzy components of the demand. We show that the fuzzy GMM can be rewritten as a classical newsvendor problem with an associated density function involving these stochastic and fuzzy components of the demand. The developed model enables to relax the single modality of the demand distribution usually used in the newsvendor literature and to encode the risk attitude of the decision maker.