Stock dependent demand inventorymodel for instanteneous deteriorating item with time dependent back logging rate

This paper investigates stock dependent demand model having instantaneous deterioration, linear time dependent holding cost and linear time dependent partial backlogging rate. In real life situation, deterioration of some items such as fruits, vegetables, meat, fish, and so on start immediately the item arrives the inventory and the backlogging rate cannot always be complete because it is not every customer will be patient enough to wait for arrival of item during the stockout period. The inventory policy is to determine the optimal replenishment policy in order to maximize the profit function. The inventory system was represented by a system of differential equations and also appropriate methods for solving differential equations were used to obtain the solutions to the inventory system. We determined the necessary and sufficient condition for optimality, after which we provided numerical example. We also conducted sensitivity analysis to demonstrate the application of the model. The results of the model show that the various changes on the input parameters have a great impact on the optimal replenishment policy