In the basic EOQ model, we assume that when the order arrives (possibly after a lead time) the entire quantity becomes available immediately. However, this is not typically the case when the company produces its own components, or when there is a constant flow of inventory that is made available to the company (consider, for instance, gas and oil derivatives that arrive through a pipeline an order may take days or even months to be fulfilled, or orders placed to the factory for the production of a new batch). Hence, there are situations where the order is produced and sent to inventory at a certain rate. This is called a production order quantity model with slow production rate. In such a case, the inventory is lower, so are the holding costs. What is the corresponding impact on the EOQ then?

In other words, consider a model with annual demand D, setup cost per order S, holding cost per unit per year h, and assume that orders are arriving at a rate of p units per year, i.e., the annual production rate is p>D. Determine the optimal order quantity.

Hint: In the basic EQO model, the maximum inventory level we could have was Q, since all products were received at once. However, in this case the products are also being consumed by demand as they are being received. What is the maximum inventory level now? Draw the Inventory graph considering two phases; the replenishment phase, which last T_R days, and the selling phase that lasts T_S days, respectively.