Fuzzy Gaussian mixture optimisation of the newsvendor problem: mixing fuzzy perception and randomness of customer demand

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 feedback 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.

Keywords:

• Inventory control
• judgemental demand
• fuzzy numbers
• GMM
• risk attitude

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

The data that support the findings of this study are available from the corresponding author, Yacine Rekik, upon reasonable request.

Additional information

Funding

F.F. thanks the EMLYON Business School for their hospitality in November 2019 and February 2020, and the great environment, where this work was partially carried out, and acknowledges the support from the Marie Curie/SER Cymru II Cofund Research Fellowship [grant number 663830-SU-008].

Notes on contributors

Farzad Fathizadeh

Farzad Fathizadeh is a quantitative risk analyst, researcher and consultant working with financial institutes. His research focuses on optimal prescription of capital requirements for investment funds while remaining conservative in the sense of being compliant with regulations. Prior to joining industry, he held various visiting and postdoctoral fellowships at world renowned institutes and an academic position. His PhD and research in mathematics focussed on heat kernel expansions for curved geometries.

Jean Savinien

Jean Savinien is an Associate Professor of Data Science at emlyon business school, Lyon, France, and an Associate Professor of Mathematics at the University of Lorraine, Metz, France. He holds a PhD in Mathematics from the Georgia Institute of Technology, Atlanta GA, USA. His current research centres around data science and machine learning, and business applications. He is particularly interested in the analysis of social networks, with sampling methods for filtering large amounts of data, and unsupervised learning methods on graphs and multigraphs to identify exceptional subnetworks of interest.

Yacine Rekik

Yacine Rekik is a Professor of Management Sciences at emlyon business school, France. He gained his Ph. D. degree in Industrial Engineering at Ecole Centrale Paris and an Accreditation to Supervise Research (HDR) from INSA Lyon. Before joining emlyon business school, he occupied a Research Associate position at the Distributed Information & Automation Lab of the University of Cambridge (UK). The purpose of his research project is to develop a set of models that provides qualitative and quantitative insights on the digital transformation of the supply chain. This research covers for instance the benefits of the RFID technology and the contribution of Artificial Intelligence in supply chains. He also works on economical and sustainability considerations in the Inventory Routing Problem.