Determining appropriate inventory and pricing policies is an important issue in scientific and industrial researches. Here an inventory control model of a decaying item with zero lead time is studied. Two mathematical models under different assumptions are developed. In the first model deterioration rate is time-dependent and demand rate is price sensitive while in the second model deterioration rate is constant and demand rate is time-and price-dependent. Aim of this research is optimizing total cost by deriving decision variables such as dispatch cycle length, order quantity and wholesale price. To optimize the total cost a shipment group dispatching policy is used.

In this article, we consider a three-echelon supply chain including a manufacturer, a vendor and multiple retailers. That is a single-item inventory system which only produces deteriorating items with constant deteriorating rate. Demand in this chain is deterministic and price-sensitive, and lead time for replenishment is considered to be zero. The aim of this article is to determine the selling price, dispatch cycle length and replenishment quantity such that the total profit is maximized. In order to reduce transportation costs we use a kind of shipment group dispatching policy (time-based consolidation policy) in which shipments are consolidated to decrease the total costs. At the end, we present a numerical example to show the applicability of developed model and proposed solution method.