Economic order quantity

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

LaTeX: I(t) = Q - dt \; for LaTeX:  \; 0 \le t \le T,

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

LaTeX: \min \; (1/2) hdT + K/T,

where LaTeX: h is the holding cost (currency per time units), so LaTeX: (1/2) hdT is the average holding cost, and LaTeX: K is the fixed cost of ordering, so LaTeX: K/T is the average ordering cost. The solution is LaTeX: T^* = (2K/hd)^{1/2}, which yields the Economic Order Quantity (EOQ): LaTeX: Q^* = (2Kd/h)^{1/2}. See the more general production scheduling problem.

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