Joint pricing and replenishment policy for deteriorating inventory with declining market

This study deals with a deteriorating inventory model where demand decreases linearly with time and cost of items. Planning horizon is assumed to be finite, the replenishment cycles are constant and shortages are partially back-ordered. The net profit maximizing ordering policy and price are determined for different degree of partial back-ordering. The reduction in revenue resulted from lost sale is expressed in the lost sale shortage penalty in the total cost formulation. A solution method based on nonlinear programming code and the Hessian matrix guarantees global optimality of the solution. A numerical example is provided to illustrate the theory.