This applet looks at economic ordering quantity, or EOQ.[br][br]For each order there is a cost of setting up an order. That cost is inversely proportional to the order size, so it is minimized by having few orders, but of large size. [br] [br]Based on order size, there is also a cost of holding inventory. That cost is proportional to the order size, so it is minimized by having many small orders.[br][br]We are interested in minimizing the total cost from these two factors.

For our simplified model the holding cost computed as the cost of holding one unit is storage for a year times the average number of units we will be holding, or half an order's worth of units.[br][br]If H is the cost of holding one unit for a year, and Q is the number of units per order, then our annual holding cost is Q(H/2).[br][br]We also assume that the cost of making the orders is simply the number of orders [br]If D is the annual demand, Q is the size of an order, and S is the cost of processing an order, then the cost of processing orders is S(D/Q).[br][br]The total cost is Q(H/2)+S(D/Q)

We want to find a Q that minimizes total cost. In calculus terms, we want the derivative of total cost with respect to Q to be zero.[br][br]If you remember the formulas for differentiation from calculus that derivative is [br](H/2)-SD/Q^2.[br][br]Solving for Q, this happens when [math]Q=\sqrt{\frac{2SD}{H}}[/math].[br](You should play with the sliders in the applet and verify that this happens for all choices of values.[br][br]By coincidence this also happens when the Cost of ordering equals the cost of holding.