A perishable inventory model with variable cycle length having weibull decay and selling price dependent demand

An inventory model is presented for deteriorating items with selling price dependent demand having different cycle lengths through assuming the lifetime commodity is random and follows Weibull distribution. In this inventory model, demand is considered as a function of selling price and cycle length of successive replenishment in a planning period. It is also considered that the cycle length in each cycle reduces by arithmetic progression, and shortages are completely backlogged and allowed with feasible cost consideration. The instantaneous state of inventory and total cost function is derived. The optimal ordering and pricing policies of this model are also obtained. In this work, numerical illustrations and sensitive analysis are utilized to observe the sensitivity of optimal values of the ordering and pricing with respect to deterioration parameters and cost. This model also includes several earlier inventory models as specific cases.