Spreadsheet Models for Managers

This reading is especially relevant for Session 11Economic Order Quantity

o understand why the Economic Order Quantity is given by the formula in the session notes, we have to understand why the minimum value of C_t, total cost, occurs when the two contributing terms are equal. Remember that the total cost per unit has two components — the cost of ordering and the cost of carrying inventory.

This total cost per unit, of course, isn't really the total cost, despite our use of the word "total." This total cost ignores the cost of the unit itself. But since we're assuming that this element of cost is independent of Q, the task of finding the optimal value of Q reduces to the task of minimizing the sum of the two terms above.

where

D is annual demand (units)
Q is quantity per order
C₀ is cost per order
C_c is carrying Cost of inventory (dollars per unit per year)

To find out why this strange coincidence occurs, you usually need to use Calculus, but we can give a pretty good argument without it. Let's work a simpler problem first. We will find the value of Q that minimizes the expression

This looks a lot like (1) except we've replaced DC₀ by a and C_c/2 by b. In the end, we'll undo the replacement and get the result we're actually looking for.

Let's suppose that the value of Q that minimizes C_T is Q₀. Then at the minimum, C_T is C_T0 given by:

A tiny little distance away from Q₀, Q₀ + dQ, the cost of carrying inventory is given by

Now if we get really close to the minimum, C_T0= C_Td. Equating the right sides of (3) and (4):

Move the b terms to the right side and the a terms to the left:

Now simplify algebraically:

Now since we're extremely close to Q₀, we can ignore the dQ term:

Remember now what a and b are:

So