Location-pricing problem in a two-echelon supply chain: A behavioral game-theoretic approach

The location-pricing problem is a relatively new class of problems in operations research that aims to solve both the pricing and facility location problems simultaneously. Unlike the classical facility location problem, where the demand of customers is known, in the location-pricing problem, the demand is a function of price. Other factors can also influence the final price of products, including production, transportation and inventory costs, competition and agents' behavior, which make the location-pricing problem complex. To this end, this paper proposes a bi-level mixed integer nonlinear programming model for the location-pricing problem in a two-echelon supply chain with players who make decisions based on their social preferences in a competitive market. The social preferences of players are a topic of great importance in the field of behavioral game theory. If the supply chain players care about the profits of other competitors in their utility functions, the simplifying assumption of pure selfishness must be corrected. It is predicted that considering social preferences for supply chain members can lead to better outcomes and payoffs. This paper proposes a single-to-multiple Stackelberg-Nash game in which a focal company serves as the leader, responsible for the location, capacity allocation, pricing, and production/distribution planning of manufacturers. Additionally, there are two competing retailers, as followers who base their pricing strategies on social preferences in order to gain a larger market share. The competition between the retailers determines the demands of customers. The effects of various parameters are then examined using a sensitivity analysis, and some economic and managerial insights are provided. The findings indicate that when both retailers exhibit status-seeking behavior in the market, average market demand increases as a result of lower retail and wholesale prices, resulting in an increase in the profit margins of the supply chain and agents compared to a model with self-interested players.