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
Famous quotes containing the words total, cost and/or function:
“The total and universal want of manners, both in males and females, is ... remarkable ... that polish which removes the coarser and rougher parts of our nature is unknown and undreamed of.”
—Frances Trollope (1780–1863)
“Now that is the wisdom of a man, in every instance of his labor, to hitch his wagon to a star, and see his chore done by the gods themselves. That is the way we are strong, by borrowing the might of the elements. The forces of steam, gravity, galvanism, light, magnets, wind, fire, serve us day by day and cost us nothing.”
—Ralph Waldo Emerson (1803–1882)
“It is the function of vice to keep virtue within reasonable bounds.”
—Samuel Butler (1835–1902)