A comparative study of optimal replenishment policy for a retailer in declining market

The aim of this article is to provide an analytical solution to a retailer whether to adopt positive stock on hand or stockless inventory policy. Mathematical models are developed for both the policies for a product with price and time sensitive demand to maximise the profit functions. Here, unlike the conventional inventory models with pricing strategy, which were restricted to pre-specified replenishment or pricing cycle times and hence fixed number of price changes over the finite time horizon, we allow the number of price changes to be a decision variable for both policies. Within a fixed planning horizon, existence and uniqueness of optimal solutions are verified. A solution procedure is presented to determine optimal inventory policy and corresponding optimal prices, optimal number of pricing cycles, optimal lot size and optimal profit simultaneously. Numerical examples are provided to illustrate the development of the models.