A major component of the costs of many large firms is the cost associated with ordering and holding inventory. If the yearly demand for the good is D and the size of each order placed is q then the number of orders N in each year is:
N=D/Q
If the cost of placing each order is C_{o }then the cost of placing all N orders is:
OC = C_{o}N
The second component is the carrying or handling cost of an inventory. Under the assumption that the average number of items in stock is q / 2 and with cost of each item set at p , the value of this average number of items is p (q / 2) . The carrying in this situation is the proportion C of this value:
CC = C_{n}p (q/2)
The third component of total costs is simply the purchase cost of all the items, or PC = pD. Assuming that C_{o}, D, C_{n} and p are constant, what is the optimal order size q?