ECONOMIC ORDER QUANTITY

Economic order quantity (EOQ) - This is the level of inventory to order that minimizes the sum of holding and ordering costs. The inventory function , I(t), is the following periodic sawtooth function, where T = time between orders, and Q = ordering quantity:

I(t)= Q - dt   for   0 <= t <= T, where d is the rate of demand (inventory units per time units), and I(t) = I(t-T) for t > T. The inventory becomes zero at T = Q/d, which requires a new order of Q units. The model is thus:

min ½ hdT + K/T, where h = holding cost (currency per time units), so ½ hdT is the average holding cost, and K = fixed cost of ordering, so K/T is the average ordering cost. The solution is T* = (2K/hd)^½, which yields the Economic Order Quantity (EOQ): Q* = (2Kd/h)^½.   See the more general production scheduling problem .