A note on inventory replenishment policies for deteriorating items in an exponentially declining market

In determining the replenishment policy for an inventory system, some researchers advocated that the iterative method of Newton could be applied to the derivative of the total cost function in order to get the optimal solution. But, this approach suffers some drawbacks. In this paper we first show the inventory carrying cost is in proportion to the cost of deteriorated items, then offer a formulated approximated solution. Our formula solution is accurate enough to be taken as an optimal solution. Sensitivity analysis shows that our solution is stable. Finally, we give some numerical examples to show the applicability of our solution.