Operations and Supply Chain Management The Core

INVENTORY MANAGEMENT chapter 11 373
Relevant Costs in a Three-Price-Break Model exhibit 11.10
Q = 632
WHERE
C = $5
Q = 667
WHERE
C = $4.50
Q = 716
WHERE
C = $3.90 PRICE BREAK 1,000
Holding cost ​ _
(
​ Q 2 ​iC​ ) ​ ​667 ____ ​(0.20)4.50 = $300.15​ ​1,000 _____ ​(0.20)3.90 = $390​
2 2
Ordering cost ​ (
​ D _
Q ​S​ ) ​
Not
feasible
​__________
10,000(20) ​= $299.85​
667
Not
feasible
​__________
10,000(20) ​= $200​
1,000
Holding and ordering cost $600.00 $590
Item cost (DC) 10,000(4.50) 10,000(3.90)
Total cost $45,600 $39,590
and
Solving for the economic order size, we obtain
____
​Q = ​ √
​ ____ 2DS
iC ​
@C = $3.90, Q = 716 Not feasible
@C = $4.50, Q = 667 Feasible, cost = $45,600
Check Q = 1,000, Cost = $39,590 Optimal solution
[11.15]
In Exhibit 11.10, which displays the cost relationship and order quantity range, note that most of
the order quantity–cost relationships lie outside the feasible range and that only a single, continuous
range results. This should be readily apparent because, for example, the first order quantity specifies
buying 632 units at $5.00 per unit. However, if 632 units are ordered, the price is $4.50, not $5.00.
The same holds true for the third order quantity, which specifies an order of 716 units at $3.90 each.
This $3.90 price is not available on orders of less than 1,000 units.
Exhibit 11.10 itemizes the total costs at the economic order quantities and at the price breaks. The
optimal order quantity is shown to be 1,000 units.
•
One practical consideration in price-break problems is that the price reduction from volume
purchases frequently makes it seemingly economical to order amounts larger than
the Q opt . Thus, when applying the model, we must be particularly careful to obtain a valid
estimate of product obsolescence and warehousing costs.
INVENTORY PLANNING AND ACCURACY
Maintaining inventory through counting, placing orders, receiving stock, and so on takes
personnel time and costs money. When there are limits on these resources, the logical
move is to try to use the available resources to control inventory in the best way. In other
words, focus on the most important items in inventory.
In the nineteenth century, Villefredo Pareto, in a study of the distribution of wealth in
Milan, found that 20 percent of the people controlled 80 percent of the wealth. This logic
of the few having the greatest importance and the many having little importance has been
broadened to include many situations and is termed the Pareto principle. This is true in
our everyday lives (most of our decisions are relatively unimportant, but a few shape our
LO11–3 Analyze
inventory using the
Pareto principle.