Optimal economic order quantity for announced price increases in infinite horizon

In this paper we consider an infinite horizon economic order quantity (EOQ) model with single announced price increase, with an option of placing a special order just before the price increase takes effect. We extend earlier work where it is assumed that the special order is an integral multiple of the new EOQ quantity. In the process, we show that when the assumption of integrality is not valid, the earlier approach of minimizing the cost difference over a finite horizon is no longer valid and establish the periodicity of cost difference function. Next, we show that the Cesaro limit of the function exists and utilize that to derive the optimal special-order quantity. We find that the optimal special-ordering policy is of (s,S) type.