An optimal inventory replenishment policy for a deteriorating item with time-quadratic demand and time-dependent partial backlogging with shortages in all cycles

The paper deals with an optimal inventory replenishment policy for a deteriorating item considering time-quadratic demand and time-dependent partial backlogging which depends on the length of the waiting time for the next replenishment over a finite time horizon and variable replenishment cycle. The model is solved analytically to obtain the optimal solution of the problem. It is then illustrated with the help of numerical examples.