An economic order quantity model with a quadratic demand, time-proportional deterioration and shortages in all cycles

We develop here an economic order quantity (EOQ) model over a finite time-horizon for a deteriorating item with a quadratic, time-dependent demand, allowing shortages in inventory. The rate of deterioration is taken to be time-proportional and it is assumed that shortage occurs in every cycle. The time-horizon is divided into a finite number of equal replenishment cycles. The reorder number, the interval between two successive reorders and the shortage intervals are all determined in an optimal manner so as to minimize the average system cost. The results are illustrated with the help of a numerical example. Sensitivity of the optimal solution is also studied with respect to changes in different parameter values.