ECONOMIC ORDER QUANTITY |
EOQ.xls |

Open the file EOQ.xls

**SITUATION 1: **Over the course of a
year, a large retail store orders 4500 units of a product at a
unit cost of $250. Consumer demand for the product is uniform
over the year. The retail store does not acquire all 4500 units
at the beginning of the year. Regular size orders are placed
throughout the year. Each time an order is placed, there is a
fixed ordering cost of $75. If the size of the regular order ( or
lot) is Q then there will be orders placed at a cost of $75 per order. Each new
order is delivered when the inventory reaches zero. Carrying
costs per unit for the inventory on hand is assumed to be 5% of
the unit cost of the product. If Q is the size of a regular order
then we will assume that an average of Q/2 units are held in
inventory at an associated carrying cost of (.05)(250). The total annual cost
is made up of three parts:

**base cost + ordering cost + holding cost****.****
**In this situation, total cost as a function of the size of
the regular order is: . The retailer's objective is to minimize total cost.
She wants to know the optimal size of the order that will achieve
this objective. Since base cost of $1,125,000 is a constant we
can focus on the ordering cost plus the holding cost as a
function of Q:

Given this ordering and holding cost function, we can compare
the cost of just a few large orders with more frequent but
smaller orders. If the size of the order is 1,500 units then the
ordering cost would be only $225. The annual carrying costs would
be $9,375 for a sum of $9600. If the size of the order is 150
units then the cost of thirty purchase orders would be $2250 but
the carrying costs would drop to $937.50 for a sum of $3,187.50.
The second ordering strategy results in a significantly lower
total for ordering plus holding.

The graph above suggests that the optimal value of Q occurs
somewhere between 200 and 300. A precise theoretical minimum
value of 232.38 can be verified using *Solver* or with
calculus. The theoretical number of orders would be 19.365 which,
of course, is impossible. If the company places 19 or 20 orders
then the total cost will be within one or two dollars of the
theoretical lowest cost.

Copyright © Joseph F. Aieta, Babson
College 1997