Pricing and inventory decisions of oligopoly retailers with partial backlogging: a game theoretic approach

Pricing and inventory strategies are two important decisions of a retailer which directly affect her/his profitability. They are even more prominent when the considered product undergoes deterioration. In this paper, the problem of joint pricing and inventory control is investigated in a competitive environment. In particular, we consider a number of competing retailers who sell substitutable deteriorating items to a common market. In addition, shortage is allowed and partially backlogged at the retailers. Each retailer aims to maximize their profit determining their price and inventory policies. At first, the profit function of the retailers is derived. Then, the existence of Nash Equilibrium solution is shown. Next, a solution procedure is developed to obtain the equilibrium quantities of price and replenishment policy. Furthermore, a numerical study is carried out to analyze the effect of the main parameters on the equilibrium solution. Numerical results show that the increase of competition intensity would decrease the summation of the retailers' profits, while it would increase the total satisfied demands. Moreover, in contrast to the monopoly models, changing the deterioration rate at a retailer does not significantly impact his/her selling price.