An EPQ model for non-instantaneous deteriorating item with time dependent holding cost and exponential demand rate

We consider the problem of a vendor that supplies an item to the buyer, which is a function of non‐instantaneous deterioration. It is an integrated production inventory model of non‐instantaneous deteriorating item in which demand rate is exponential and production rate is a function of demand rate. The holding cost varies with time. Partially deteriorated items are allowed to sale with a discount rate from original one, and the units which are completely deteriorated, are superfluous. Shortages are not allowed. The optimal cycle time is derived and the result is applied to numerical problems. A solution procedure is presented to determine an optimal replenishment cycle such that the total cost is maximised. Numerical example is cited to illustrate the results and its significant features. Finally, to study the effect of changes of demand parameters, deterioration, price discount and holding cost, on supplier a sensitivity analysis is presented numerically.