Trade and bank credit in a non-cooperative chain with a price-sensitive demand

ABSTRACT

The purpose of this article is to examine the impact of the working capital in the borrowing decision of a retailer. The proposed analysis is based on a model with a retailer, a supplier and a bank in a non-cooperative game with price-sensitive demand. The retailer, the supplier and the bank (if concerned) determine, respectively, the ordering quantity, the wholesale price and the interest rate. A Stackelberg game-theoretic approach is employed where the retailer is a follower and either the supplier or the bank is the leader. Some structural properties are first derived from the mathematical models. Then, some numerical simulations show that: (i) a trade credit guarantees the same profits for the retailer and the supplier as in the case where the retailer has sufficient cash holdings, (ii) there exist some situations where the retailer has a better profit with a borrow than with sufficient cash holdings, and (iii) borrowing decision depends on both retailer's and supplier's discount rate and the retailer's cash holdings.

Keywords:

• Trade credit
• bank credit
• supply chain finance
• inventory
• game theory

Acknowledgments

This work was funded by the research project RCSM, Risk, Credit Chain & Supply Chain Management (FUI 15 of the French government) and by the research project FILEAS-FOG (ANR-17-CE10-0001-01). An initial version was presented to the French speaking conference CIGI in Montreal (2015).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Agence Nationale de la Recherche [FILEAS-FOG (ANR-17-CE10-0001-01)] and Fonds Unique Interministériel [FUI 15, Project RCSM].

Notes on contributors

Vincent Hovelaque

Vincent Hovelaque (https://www.igr.univ-rennes1.fr/enseignant/hovelaque/, ORCID 0000-0002-2492-1758) is a Full Professor at IGR-IAE of Rennes (University of Rennes 1) and Deputy Director of the CREM, UMR CNRS 6211. His current research focuses on stakeholders coordination in supply chain, sustainable location and supply chain finance. It has notably published papers dealing with supply chain finance, carbon issues in both problems of inventory management and location. His research contributions have been published in several articles in academic journals and collective books.

Jean-Laurent Viviani

Jean-Laurent Viviani (https://www.igr.univ-rennes1.fr/enseignant/viviani/, ORCID 0000-0001-5331-9451) is a Full Professor at IGR-IAE of Rennes (University of Rennes 1) and member of the CREM, UMR CNRS 6211. His current research focuses on finance and CSR, banking risks, corporate finance and supply chain finance. He is interested in the applications of the decision in ambiguity and real option models to green finance and company investing and financing. His research contributions have been published in several articles in academic journals and collective books.

Mohamed Ait Mansour

Mohamed Ait Mansour got his Doctorate from University of Rennes 1 at the CREM, UMR CNRS 6211. He spent 1 year as a Post-Doc in JMSB (University of Concordia) at Montreal-Canada. He is presently a Senior Statistical Analyst and Operation Research Engineer in INTGRAL. His research is focusing on the competition and cooperation among supply chain members. Specifically, applying game theory and stochastic modelling in analysing problems in areas of supply chain finance, as well as optimisation of supply chain members payoff and consumer welfare.