Joint inventory and constant price decisions for a continuous review system

Purpose – The purpose of this paper is to study joint inventory and pricing strategy for a continuous inventory review system. While dynamic pricing decisions are often studied in the literature along with inventory management, the authors' aim in this study is to obtain a single long‐run optimal price; also to gain insight about how to obtain the optimal price and inventory control variables simultaneously and then the benefits of joint optimization of the inventory and pricing decisions over the sequential optimization policy often followed in practice. Design/methodology/approach – A general ( R;Q ) policy system with fixed cost of ordering is modelled and then the case where unsatisfied demand is lost is studied. General forms of both the additive and multiplicative demand models are used to obtain structural results. Findings – By showing optimality conditions on the price and inventory decision variables, two algorithms on how to obtain optimal decision variables, one for additive and another for multiplicative demand‐price model are provided. Through extensive numerical analyses, the potential profit increases are reported if the price and inventory problem are solved simultaneously instead of sequentially. In addition, the sensitivities of optimal decision variables to system parameters are revealed. Practical implications – Although there are several studies in the literature investigating emergency price change models, they use arbitrary exogenous prices menus. However, the value of a price change can be better appreciated if the long‐run price is optimal for the system. Originality/value – Very few researchers have investigated constant price and inventory optimization, and while there are several past studies demonstrating the benefits of dynamic pricing over a static one, there still are not many findings on the benefit of joint price and inventory optimization.