Pricing and inventory control in a competing environment, as separate entities, have attracted much attention from academics and practitioners. However, integrating these decisions in a competitive setting has not been significantly analyzed by academics, but is of great significance to practitioners. In this study, the joint decision on price and inventory control of a deterioration product is investigated in a duopoly setting. We consider two competing supply chains, each consisting of one manufacturer and one retailer. Each manufacturer, as the leader of their supply chain determines the wholesale price to maximize their profit, while the retailer as the follower should determine the retail price and inventory cycle to maximize his or her profit. Using a game theoretic approach, we formulate in-chain, and chain-to-chain competition as a bi-level programming problem, and analyze Stackelberg-Nash equilibrium of the problem. Furthermore, two versions of a nested algorithm are proposed to obtain the equilibrium. Both versions employ a modified threshold-accepting (TA) algorithm to solve the first level of the problem. However, while the first version utilizes the modified TA algorithm to deal with the second level of the problem, the second version applies a differential evolution (DE) approach. Eventually, a numerical study is carried out not only to compare two developed versions of the algorithm, but also to implement the sensitivity analysis of main parameters. Based on numerical experiments, although the accuracy of both versions of algorithm are alike, using TA is more computationally efficient than using DE. Furthermore, despite the permissibility of partial backlogging, it has never occurred in equilibrium points due to in-chain and chain-to-chain competition.
