قیمتگذاری تعادلی در یک زنجیره تأمین سهسطحی.

Purpose: Proper pricing of products or services can have a significant impact on corporate earnings. Therefore, this study aims to address the optimization of price and production quantity to maximize the total profit using game theory in the coffee supply chain (composed of suppliers, retailers and customers) in Isfahan city. Design/methodology/approach: The applied model focuses on competition among members of the chain in probabilistic space. It is based on discrete selection models in which the impact of inventory costs and routing is analyzed on the pricing model simultaneously. In this model, competition between coffee importers (because coffee is not produced in the country) is studied in the probable space. Due to complexity in computation, it could not solve problems with a large number of customers. Therefore, the approximation of the binomial distribution by the normal distribution is used, an approximate model is proposed. Finally, the equilibrium point is determined by solving a system of nonlinear equations using the Newton method. Findings: The maximum profit in non-cooperative game conditions is achievable based on the appropriate demand function. Finally, the equilibrium price was calculated. Findings indicated that the computational time of the approximate model did not change with increasing the number of customers, and the model can determine the optimal price and production quantity. The model results implied that the time of solving the approximate model used did not change with the increasing number of customers, and the model was able to determine the optimal quantity and price. Practical implications - In the present study, the equilibrium behaviour of suppliers, retailers and customers in a two-tier supply chain of the coffee supply and distribution industry was investigated in Isfahan city. A price competition model was proposed, and ten active companies were studied in the Isfahan market. Moreover, the computational speed diagram indicated that the computational time in the original function increased with increasing the number of customers, but this time in the approximation function did not react to the increase in the number of customers and remained constant. Social implications: In the proposed model of the present study, competition among coffee suppliers was investigated in a probabilistic environment in which retailers acted as intermediaries and had no effect on pricing. Holding and shortage costs were also taken into account. Also, routing costs were approximated using the proposed Himovich model. Then, a pricing model was proposed. The proposed model could not solve problems with a large number of customers due to complexity in computation. Originality/value: The advantage of the proposed model over basic models is in considering the inventory costs, which has not been considered yet in price competition models based on discrete selection models. Another significant feature of the price competition problem is the type of demand function. In this paper, to study a competitive model, a stochastic demand function was developed based on the logit model. The advantage of the introduced demand function is that it considers shortage and inventory holding costs in a one-period model. Also, in the game theory studies, usually with the increasing number of customers, the model is computationally complicated and less effective to solve real-world problems. For this reason, in this study, the normal distribution approximation was used instead of the binomial distribution. [ABSTRACT FROM AUTHOR]