Abstract: This paper aims to investigate the inventory policy for non-instantaneously deteriorating items. A generalized inventory replenishment model is formulated by maximizing the average profit of the system. In the model, it is assumed that the demand rate is influenced by the instantaneous inventory level with different influence coefficients in the deterioration period and non-deterioration period, the deterioration rate in the deterioration period and the holding cost are time-varying, shortage is allowed and the unmet demand is partially backlogged in the shortage period. The sufficient condition for the existence of the unique optimal solution to the model is presented. Finally, some numerical examples and the sensitivity analyses on the main parameters are given using the Newton's method. The results indicate that, to prolong the non-deterioration period of items will be helpful to the increase of the system's average profit. The increase of the demand in the deterioration period is more beneficial to the increase of the system's average profit than that in the non-deterioration period. For deteriorating items with high deterioration rate, the influence of the disposal cost of the deterioration items on the optimal policy and the average profit is significant. Besides, the model formulated in this paper is generalized, so it has a wide range of application.

Key words: non-instantaneously deteriorating item, stock dependent demand rate, time-varying holding cost, partially backlogging