Inventory of damagable items with variable replenishment rate, stock-dependent demand and some units in hand

Items made of glass, ceramics, etc., break/get damaged during the storage due to the accumulated stress of headed stock. For the first time, a deterministic inventory model of such a damagable item is developed with variable replenishment when both demand and damage rates are stock-dependent in polynomial form. Here replenishment rate for the first cycle is partly instantaneous and partly varies with demand. For the next cycle, the variable replenishment is augmented when the inventory level falls to Q(o), the instantaneous replenishment amount for the first cycle. After this, the cycle repeats itself. The amount, Q(o) is also here varied and the optimum Q(o) and Q (inventory level) are evaluated following the profit maximization principle in integral form. The model is illustrated numerically and sensitivity analyses are presented.