The Total Cost Function
The single-item EOQ formula finds the minimum point of the following cost function:
Total Cost = purchase cost + ordering cost + holding cost
- Purchase cost: This is the variable cost of goods: purchase unit price × annual demand quantity. This is P×D
- Ordering cost: This is the cost of placing orders: each order has a fixed cost S, and we need to order D/Q times per year. This is S × D/Q
- Holding cost: the average quantity in stock (between fully replenished and empty) is Q/2, so this cost is H × Q/2
.
To determine the minimum point of the total cost curve, partially differentiate the total cost with respect to Q (assume all other variables are constant) and set to 0:
Solving for Q gives Q* (the optimal order quantity):
Therefore: .
Q* is independent of P; it is a function of only S, D, H.
Read more about this topic: Economic Order Quantity
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