Inventory of damagable items with variable replenishment and stock-dependent demand

Items made of glass, ceramic, etc. break/get damaged during the storage due to the accumulated stress of heaped stock. For the first time, a deterministic inventory model of such a damageable item is developed with variable replenishment rate. Here, replenishment rate is linearly dependent on demand. Demand is assumed to be constant during the early part and towards the end of the scheduling period, and for the rest of the period it is stock dependent in polynomial form. Damage function is taken to be dependent on inventory both linearly and non-linearly. The optimum inventory level is evaluated by the profit maximization principle in integral form. The model is illustrated numerically and some sensitivity analyses are presented in tabular form.