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_{0} then the cost of placing all N orders is:
OC = C_{0}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_{n} of this value:
The third component of total costs is simply the purchase cost of all the items, or . PC = pD = Assuming that C_{0}, D, C_{n} and p are constant, what is the optimal order size q?