An inventory system of non-instantaneous deteriorating items with backlogging and time discounting

In this paper, an economic order quantity inventory model is analysed, considering the effect of inflation on a multivariate demand function and inventory control for non-instantaneous deteriorating items. The demand rate is a linear function of price and decreases negative exponentially with time. Shortages are allowed and partially backlogged. The objective is to find the optimal selling price, the optimal replenishment cycles and the optimal lot size simultaneously such that the present value of total profit in a finite time horizon is maximised. An algorithm has been presented to find the replenishment number and then the optimal solution for the proposed model. Finally, numerical examples are used to illustrate the theoretical results and the sensitivity analysis with respect to major parameters on the optimal solutions is also performed.