ISYE 3104 Summer 2003
Chapter 12
Homework 7 Solution
Inventory Management
DISCUSSION QUESTIONS:
1. With the advent of low-cost computing, do you see alternatives to the popular
ABC classification?
The advent of low-cost computing should not be seen as obviating the need for the
ABC inventory classification scheme. Although the cost of computing has
decreased considerably, the cost of data acquisition has not decreased in a similar
fashion. Business organizations still have many items for which the cost of data
acquisition for a “perpetual” inventory system is still considerably higher than the
cost of the item.
2. What is the different between the standard EOQ model and the production
inventory model?
The standard EOQ model assumes instantaneous delivery (delivery of the entire lot
is made at one instant of time), whereas the Production Inventory Model assumes
that delivery takes place at a constant rate over time.
3. What are the main reasons that an organization keeps inventory?
Reasons for an organization to maintain inventory include:
 The decoupling function:
 inventory can be used to decouple stages in the production
process within an organization
 inventory can be used to decouple the production process
from instabilities or irregularities in supply of raw materials
or labor
 inventory can be used to decouple the production process
from unstable demand and thus (a) allow production
scheduling to develop a “smoother” schedule, and (b) avoid
shortages or stockouts
 Quantity discounts:
 inventory can be used to enable the organization to purchase
goods in larger lot sizes and take advantage of quantity
discounts
 A hedge against inflation:
 investing in inventory now assures one that the price will not
increase
4. Does the production model or the standard EOQ model yield a higher optimal
order quantity if set up costs and holding costs are the same? Why?
The production inventory model will yield a higher EOQ than the standard model,
other things equal, because the maximum inventory level (and thus the effective
carrying charge) is less.
5. What is meant by “service level”?
In the context of the discussion developed in class, service level refers to the
fraction of operational cycles during which the system will not experience a
stockout – this is known as type-1 service level.
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ISYE 3104 Summer 2003
Homework 7 Solution
There is another notion of service level used in inventory control theory –known as
type-2 service level – that is defined as the fraction of customers to whom the
product or service is delivered when and as promised.
Notice that the safety stock necessary to meet a service level requirement x will
depend on the employed definition of service level. In general, type-1 requirements
are more stringent – and therefore, they require more safety stock for their
satisfaction – than type-2.
6. How would a firm go about determining service level?
Service level is a difficult parameter to determine. Basically, the firm uses its
subjective judgment to balance the cost of additional inventory against the cost of
lost goodwill due to stockouts or shortages.
7. Describe the difference between a fixed-quantity and a fixed-period inventory
system.
In a fixed-quantity inventory system, when the quantity on hand reaches the reorder
point, an order is placed for the specified quantity. In a fixed-period inventory
system, an order is placed at the end of the period. The quantity ordered is that
needed to bring on-hand inventory up to a specified level.
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ISYE 3104 Summer 2003
Homework 7 Solution
END-OF-CHAPTER PROBLEMS
Problem 12.2
He decides that the top 20% of the 10 items, based on a criterion of demand times cost per
unit, should be A items. (In this example, the top 20% constitutes only 58% of the total
inventory value, but in larger samples the value, but in larger samples the value would
probably approach 70% to 80%.) He therefore rates items F3 and G2 as A items. The next
30% of the items are A2, C7, and D1; they represent 23% of the value and are categorized
as B items. The remaining 50% of the items (items B8, E9, H2, I5 and J8) represent 19%
of the value and become C items.
Item
A2
B8
C7
D1
E9
F3
G2
H2
I5
J8
Annual
Demand
3,000
4,000
1,500
6,000
1,000
500
300
600
1,750
2,500
Cost($)
50
12
45
10
20
500
1,500
20
10
5
Demand x Cost
150,000
48,000
67,500
60,000
20,000
250,000
450,000
12,000
17,500
12,500
Classification
B
C
B
B
C
A
A
C
C
C
Problem 12.12
(a) Economic Order Quantity:
2 DS
2  4,000  25
Q =
=
= 149.1 or 149 values
H
0.10  90
Where: D =annual demand, S = setup or order cost, H = holding cost
(b) Average inventory = 74.5 values
(c) Number of orders per year =
4,000
Demand
=
= $26.8 or 27 orders
149
EOQ
(d) Assuming 250 business days per year, the optimal number of business days
between order is given by:
250
1
 9 days
Optimal number of days =
27
4
(e) Total annual inventory cost = Order cost + holding cost
DS QH 4,000  25 149  0.1  90



=
Q
2
149
2
=671.14 + 670.50 = 1,341.64
(f) Reorder point
= demand during lead time
= 16 units/day x 5 days = 80 values
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ISYE 3104 Summer 2003
Homework 7 Solution
Problem 12.14
(a) Total cost = order cost + holding cost =
DS QH

Q
2
1,200  25 25  24

 $1,500
25
2
1,200  25 40  24
Q  40 : 

 $1,230
40
2
1,200  25 50  24
Q  50 : 

 $1,200
50
2
1,200  25 60  24
Q  60 : 

 $1,220
60
2
1,200  25 100  24
Q  100 : 

 $1,500
100
2
For Q  25 : 
For
For
For
For
As expected, small variations in order quantity will not have a significant effect
on total costs.
(b) Economic Order Quantity:
2DS
2  1,200  25
Q

 50 units
H
24
where: D = annual demand, S = setup or order cost, H = holding cost
Problem 12.18
(a) Production Order Quantity, noninstantaneous delivery:
2 DS
2  10,000  40
Q

50 
 d

0.601 

H 1  
p
 500 

= 1217.2 or 1,217 units
where: D = annual demand, S = setup or order cost, H = holding cost, d = daily
demand rate, p = daily production rate
 d
(b) I max  Q1    1,095
p

D 10,000
(c)

 8.22
Q 1,217
I
D
(d) TC  max H  S  328.50  328.80  $657.30
2
Q
Problem 12.20
Under present price of $50.00 per unit, Economic Order Quantity:
2 DS
Q
H
2  1,000  40
Q
 80units
0.25  50
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ISYE 3104 Summer 2003
Homework 7 Solution
where: D = annual demand, S = setup or order cost, H = holding cost, p =
price/unit
Total cost = order cost + holding cost + purchase cost
DS QH


 PD
Q
2
1,000  40 80  0.25  50


 (1,000  50)
80
2
= 500.00 + 500.00 + 50,000 = $51,000
Under the quantity discount price reduction of 3%:
Total cost = order cost + holding cost + purchase cost
DS QH


 PD
Q
2
1,000  40 200  0.25  50  0.97


 (1,000  50  0.97)
200
2
= 200.00 + 1212.50 + 48,500 = $49,912.50
Therefore, the pumps should be ordered in batches of 200 units and the quantity
discount taken.
Problem 12.26
Calculation for EOQ: S = $50, H = 50%, D = 9,600
(a)
Price
$17.00
$16.75
$16.50
EOQ
336.0672
338.5659
341.1211
feasible
not feasible
not feasible
$17.10
$16.85
$16.60
335.0831
337.5598
340.0921
feasible
not feasible
not feasible
Vendor
A
B
(b),(c)
Qty
Price
336 $17.00
500 $16.75
1000 $16.50
Holding
$1,428.00
$2,093.75
$4,125.00
Ordering
$1,428.57
$960.00
$480.00
Costs
Purchase
$163,200.00
$160,800.00
$158,400.00
Total
$166,056.57
$163,853.75
$163,005.00
335
400
800
1200
$1,432.13
$1,685.00
$3,320.00
$4,875.00
$1,432.84
$1,200.00
$600.00
$400.00
$164,160.00
$161,760.00
$159,360.00
$156,000.00
$167,024.97
$164,645.00
$163,280.00
$161,275.00
$17.10
$16.85
$16.60
$16.25
Vendor A
Vendor B
BEST
(d) Other considerations include the perishability of the chemical and whether or not there
is adequate space in the controlled environment to handle 1,200 pounds of the chemical
at one time.
Problem 12.28
(a) Z = 1.88
(b) Safety stock = Z  = 1.88(5) = 9.4 drives
(c) ROP = 50 + 9.4 = 59.4 drives
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ISYE 3104 Summer 2003
Homework 7 Solution
Problem 12.30
Demand during Reorder Period
0
50
100
150
200
Probability
0.1
0.2
0.4
0.2
0.1
1
In this case, we are not given a specific service level, but a stock-out cost. So, our
objective is to select a safety stock level that minimizes the incremental annual
cost of carrying the extra stock and experiencing the expected stock outs. Based
on the above data regarding the demand experienced in a reorder period, the
candidate safety stock levels and the corresponding induced costs are as follows:
Safety Stock
0
50
100
Carrying Cost
0
50 x 10 = 500
100 x 10 = 1,000
Incremental Costs
Stockout Cost
Total Cost
50 x (50 x 0.2 +100 x 0.1) = 1,000
1000
50 x (0.1 x 50) = 250
750
0
1000
The safety stock that minimizes total incremental cost is 50 units. The reorder point
then becomes 100 units + 50 units = 150 units.
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ISYE 3104 Summer 2003
Homework 7 Solution
EXTRA CREDIT
1. What are the types of waste JIT is designed to remove?
JIT is designed to remove all waste—including the waste found in storing, queues,
inspection, adjusting, delays, and defects – actually anything that does not add value
to a product from the customer’s perspective. You can refer to the PwerPoint
presentation on the relevant topic, posted in the course Web page, for more
discussion on this question.
2. What is the difference between a “pull” and a “push” system?
A pull system is a JIT system that moves material only as it is needed. A push
system sends material to the next workstation at the convenience of the sender, not
as it is needed. Thus the inventory level can get very large.
3. What are the types of variability that JIT is expected to help remove?
Variability is removed in a JIT system by systematically identifying and attacking it
wherever it may occur. Variability may be caused by both internal and external
factors such as employees, machines, suppliers, engineering drawing, or customer
capriciousness.
4. What is the impact on JIT of reducing setup costs?
According to the EOQ formula, and the broader inventory control theory, an
effective way to reduce the economic lot sizes is by reducing setup costs. In many
environments, setup cost is highly correlated with setup time; thus, reducing setup
times is a major concern in JIT philosophy.
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