Inventory model with a one-time opportunity to order extra items

Abstract

We study the inventory model with a one-time opportunity to order extra items of a lower purchasing cost. Davis and Gaither had investigated this problem and published in the journal Management Science. There are some improvements that can be achieved. The purpose of this paper is fourfold: Firstly, we point out the well-defined problem in the construction of the inventory model such that we extend from one year plan horizon to several years plan horizon. Secondly, we offer easy methods to derive the objective function. Thirdly, we provide lower bounds to simplify the computation for determining the extra replenishment quantity. Fourthly, we show that there are some questionable numerical results in the examples and prove that the multiplier factor is proportional to the monthly return rate.