EOQ revisited: The case of unequal and integral order quantities

The well-known economic order quantity (EOQ) of inventory control is a stationary ordering policy, which can be rigorously verified using dynamic programming techniques. In this paper, an alternative approach based on mathematical programming is used to prove that the EOQ formula is indeed an optimal stationary policy. Additionally, the impact of integer order quantities is investigated and a counterintuitive result is discovered. In particular, the optimal policy when order quantities are required to be integer is not necessarily stationary. This paper introduces an integer nonlinear programming model whose solution yields the optimal integer ordering policy in an EOQ setting over a finite horizon. Due to the inherent difficulties associated with solving integer nonlinear programming problems, a heuristic order policy based on elementary number theory is introduced. The results of a numerical experiment suggest that the proposed policy generates competitive solutions instantaneously using a spreadsheet.