Single-Item, Multi-Period Problems

1 Continuous-Review Reorder Point-Order Quantity Model 

Following our framework, in order to completely describe the (Q, R) inventory system, we must first describe demand. Let us begin with the case where demand is known with certainty. Let us also consider the case where demand occurs at a constant rate for the foreseeable future, meaning that we consider the extreme multi-period case of perpetual, stationary demand 

With these pieces in place, we can build a model of the annual cost of managing inventory. First, we consider the annual cost of ordering goods. In this constant-demand setting, our sole decision variable is, as it was in the newsvendor model, the order quantity Q. Since each order costs A /order, and an average of D/Q orders would be placed annually, the expected annual cost of ordering is OC = A D/Q. 

With these pieces in place, we can express the total annual cost of the constant-demand EOQ model as 

To find the optimal value of Q, we take the derivative of this expression, set 

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