An optimal replenishment policy for EOQ models with time-varying demand and shortages

Abstract

While considering time dependent demand rate, most of the researchers developed their inventory models considering time dependent linear demand rate. Some models have been developed also by considering time dependent quadratic demand because by considering quadratic demand increasing, decreasing or constant all types of situations can be explained and hence it is more realistic than that of linear demand rate. But in the present paper, we have developed an EOQ model to describe an optimal replenishment policy with shortages and general time-varying demand instead of time dependent linear or time dependent quadratic demand. The successive replenishment cycle lengths are assumed to be reduced in arithmetic progression. The model is extended to the no shortage case also. The model is solved analytically to obtain the optimal solution of the problem. It is then illustrated with the help of numerical examples. The sensitivity analysis of the optimal solution towards changes in the values of different system parameters is also studied.