Structural properties of an inventory system with deterioration and trended demand

An order-level inventory model for deteriorating items is developed under the conditions of exponential decay, instantaneous replenishment and linear time-dependent demand rate with a positive trend. A number of structural properties of the inventory system is proved analytically. The exact formulae for the optimal average cost and the lot size are derived without carrying out any approximation over the constant deterioration rate. A numerical example is taken to illustrate the procedure of finding the optimal lot size, the average cost and the cycle period. A sensitivity analysis is carried out to demonstrate the effects of changing parameter values on the optimal solution of the system.