Operations and Supply Chain Management The Core

382 OPERATIONS AND SUPPLY CHAIN MANAGEMENT
The steel producer has a minimum order quantity of 1,000 sheets, and offers a sliding price scale
based on the quantity in each order, as follows:
ORDER QUANTITY
UNIT PRICE
1,000–9,999 $2.35
10,000–29,999 $2.20
30,000 or more $2.15
The purchasing department estimates that it costs $300 to process each order, and SMI has
an inventory carrying cost equal to 15 percent of the value of inventory.
Based on this information, use the price-break model to determine an optimal order quantity.
Solution
The first step is to take the information in the problem and assign it to the proper notation in the
model.
D = 200,000 units (annual demand )
​
S = $300 to place and process each ​
order ​
I ​ ​
= 15 percent of the item cost ​
​
C = Cost per unit, based on the order quantity Q, as shown in the table above
Next, solve the economic order size at each price point starting with the lowest unit price.
Stop when you reach a feasible Q.
_______________
2 ∗ 200,000 ∗ 300
​Q​ $2.15 ​ = ​ √
​ _______________ ​ = 19,290 (infeasible)​
0.15 ∗ 2.15
The EOQ at $2.15 is not feasible for that price point. The best quantity to order at that price
point is therefore the minimum feasible quantity of 30,000.
_______________
2 ∗ 200,000 ∗ 300
​Q​ $2.20 ​ = ​ √
​ _______________ ​ = 19,069 (feasible)​
0.15 ∗ 2.20
The EOQ at $2.20 is feasible, therefore the best quantity to order at that price point is the
EOQ of 19,069. Since we found a feasible EOQ at this price point, we do not need to consider
any higher price points. The two ordering policies to consider are: Order 30,000 sheets each
time at $2.15 apiece, or order 19,069 sheets each time at $2.20 each. The question is whether
the purchase price savings at the $2.15 price point will offset the higher holding costs that
would result from the higher ordering quantity. To answer this question, compute the total cost
of each option.
T ​C​ Q=30,000 ​ = 200,000 ∗ $2.15 + ​ _______ 200,000 ​ ($300) + ​ ______ 30,000
​ (0.15)($2.15) ≈ $436,837
30,000 2
​
T ​C​ Q=19,069 ​ = 200,000 ∗ $2.20 + ​ _______ 200,000
​
19,069
​ ($300) + ​ ______ ​ (0.15)($2.20) ≈ $446,293
19,069 2
The lowest total annual cost comes when ordering 30,000 units at $2.15, so that would be the best
ordering policy. Are you surprised that the 5-cent difference in unit price would make such a difference
in total cost? When dealing in large volumes, even tiny price changes can have a significant
impact on the big picture.