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CHAPTER 12
DISCUSSION QUESTIONS
1.
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.
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.
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.
Costs that are associated with ordering and maintaining inventory include:

Initial purchase cost of the item

Holding cost (insurance, space, heat, light, security, warehouse personnel, etc.)

Obsolescence or deterioration cost (particularly important in perishable goods or in a product
that is undergoing rapid technological evolution)

Ordering or setup cost (cost of forms, clerical processing, etc., or cost of machine setup)
5.
The more important assumptions of the basic EOQ model are:

Demand is known and constant over time.

The lead time, that is, the time between the placement of the order and the receipt of the
goods, is known and constant.

The receipt of the inventory is instantaneous; i.e., the goods arrive in a single batch, at one
instant in time.
Chapter 12: Inventory Management
1



Quantity discounts are not possible.
The only variable costs are the cost of setting up or placing an order and the cost of holding or
storing inventory over time.
If orders are placed at the right time, stockouts or shortages can be completely avoided.
6.
The EOQ is relatively insensitive to small changes in demand or setup or carrying costs. If, for
example, demand increases by 10%, EOQ will increase by approximately 5%.
9.
A decrease in setup time decreases the cost per order, encourages more and smaller orders, and thus
decreases the EOQ.
12.
If per unit holding costs increase with increasing inventory, total inventory cost will increase; EOQ
will decrease.
14.
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.
END-OF-CHAPTER PROBLEMS
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 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
12.3
12.4
2
Annual Demand
3,000
4,000
1,500
6,000
1,000
500
300
600
1,750
2,500
Cost ($)
50
12
45
10
20
500
1,500
20
10
5
Item
Annual Demand Cost ($)
E102
800
4.00
D23
1,200
8.00
D27
700
3.00
R02
1,000
2.00
R19
200
8.00
S107
500
6.00
S123
1,200
1.00
U11
800
7.00
U23
1,500
1.00
V75
1,500
4.00
700  20  35
7,000  010
.  700
2450  60  40.83
7,000  0.35  2,450
Demand  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
Demand  Cost Classification
3,200
C
9,600
A
2,100
C
2,000
C
1,600
C
3,000
C
1,200
C
5,600
B
1,500
C
6,000
B
35 A items per day
41 B items per day
27%
16%
33%
17%
Instructor’s Solutions Manual t/a Operations Management
7,000  0.55  3850
,
3850  120  32
12.5
EOQ 
2100062.50
 500 units
0.50
12.6
EOQ 
28,00045
 600 units
2
12.7
300 
35 C items per day
108 items
28,00045
720,000
 90,000 
H
H
720,000
H
 $8
90,000
12.8 (a)
Economic Order Quantity (Holding cost = $5 per year):
2 DS
2  400  40

 80 units
H
5
Q
(b)
where: D = period demand, S = setup or order cost, H = holding cost
Economic Order Quantity (Holding cost = $6 per year):
2 DS
2  400  40

 73 units
H
6
Q
where: D = period demand, S = setup or order cost, H = holding cost
12.9 (a)
Economic Order Quantity:
Q
(b)
(c)
(d)
2 DS
2  1,500  150

 100 units
H
45
where: D = period demand, S = setup or order cost, H = holding cost
QH 100  45
Holding cost 

 $2,250.00
2
2
DS 1500  150
Order cost 

 $2,250.00
Q
100
Reorder point:
1,500
Reorder point = demand during lead time 
units day  6 days  30 units
300
,
units
12.10 Reorder point = demand during lead time  100 units day  21 days  2100
12.11 Reorder point = demand during lead time  500 units day  14 days  7,000 units
12.12 (a)
Economic Order Quantity:
Q
(b)
2 DS
2  4,000  25

 1491
. or 149 valves
H
010
.  90
where: D = period demand, S = setup or order cost, H = holding cost
Average inventory  74.5 valves
Chapter 12: Inventory Management
3
(c)
(d)
Demand 4,000

 26.8 or 27 orders
EOQ
149
Assuming 250 business days per year, the optimal number of business days between orders is
given by:
Number of orders per year 
Optimal number of days 
(e)
Total annual inventory cost  Order cost  holding cost

(f)
12.13 (a)
(c)
(d)
DS QH 4,000  25 149  01
.  90



Q
2
149
2
 67114
.  670.50  $1,34164
.
Note: Order and carrying costs are not equal due to rounding of the EOQ to a whole number.
Reorder point = demand during lead time  16 units day  5 days  80 valves
Economic Order Quantity:
Q
(b)
2 DS
2  5,000  30

 77.46 or 78 units
H
50
where: D = period demand, S = setup or order cost, H = holding cost
78
Average inventory 
 39 units
2
Demand 5,000
Number of orders per year 

 641
. or 64 orders
EOQ
78
Assuming 250 business days per year, the optimal number of business days between orders is
given by:
Optimal number of days 
(e)
250
 3.91 days
64
Total cost  order cost  holding cost

(f)
250
1
 9 days
27
4
DS QH 5,000  30 78  50



Q
2
78
2
 1,923.02  1,950  $3,873.08
Note: Order and carrying costs are not equal due to rounding of the EOQ to a whole number.
If an EOQ of 77.46 is used, the order and carrying costs calculate to $1,936.49 for a total cost
of $3,872.98.
Reorder point:
Reorder point = demand during lead time 
5,000 units
 10 days  200 units
250 days
This is not to say that we reorder when there are 200 units on hand (as there never are). The
ROP indicates that orders are placed several cycles prior to their actual demand.
12.14 (a)
Economic Order Quantity:
Q
2 DS
2  1,200  25

 50 units
H
24
where: D = period demand, S = setup or order cost, H = holding cost
4
Instructor’s Solutions Manual t/a Operations Management
(b)
Total cost = order cost + holding cost 
DS QH

Q
2
1,200  25 25  24

 $1,500
25
2
1,200  25 40  24

 $1,230
Q  40 : 
40
2
1,200  25 50  24

 $1,200
Q  50 : 
50
2
1,200  25 60  24

 $1,220
Q  60 : 
60
2
1,200  25 100  24

 $1,500
Q  100 : 
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.
12.15 (a)
Total cost = order cost + holding cost 
DS QH

Q
2
For Q  50 :
600  60 50  20

 720  500  $1,220
50
2
(b)
Economic Order Quantity:
Q
2 DS
2  600  60

 60 units
H
20
where: D = period demand, S = setup or order cost, H = holding cost
For Q  60 :
600  60 60  20

 600  600  $1,200
60
2
(c)
Reorder point:
Reorder point = demand during lead time 
600 units
 10 days  24 units
250 days
12.16 Economic Order Quantity, noninstantaneous delivery:
Q
2 DS
H [1  ( d / p )

2  10000  200
 50 
1.00 1 
 200 
 2309 .4 units
where: D = period demand, S = setup or order cost, H = holding cost, d = daily demand rate, p = daily
production rate
12.17 Economic Order Quantity, noninstantaneous delivery:
Q
Chapter 12: Inventory Management
2 DS
H [1  ( d / p )

2  8000  100
 40 
0.80 1 
 150 
 1651 .4 units
5
where: D = period demand, S = setup or order cost, H = holding cost, d = daily demand rate, p = daily
production rate
12.18 (a)
Economic Order Quantity, noninstantaneous delivery:
Q
(b)
(c)
(d)
2 DS
H [1  ( d / p )

2  10000  40
 50 
0.60 1 
 500 
 1217 .2 units
where: D = period demand, S = setup or order cost, H = holding cost, d = daily demand rate,
p = daily production rate
  d 
  50 
I
 Q 1      1217 .2 1  
  1095 .5 units
max
  500 
  p 
D 10,000

 8.22
Q 1,217
I
D
T. C.  max H  S  328.50  328.80  657.30
2
Q
12.19 Economic Order Quantity:
Q
2 DS
H
where: D = period demand, S = setup or order cost, H = holding cost, P  price/unit
(a)
Economic Order Quantity, standard price:
Q
2  2,000  10
 200 units
1
Total cost  order cost  holding cost  purchase cost

(b)
DS QH
2,000  10 200  1

 PD 

 2,000  1  100  100  2,000  $2,200
Q
2
200
2
Quantity Discount:
Total cost  order cost  holding cost  purchase cost

DS QH
2,000  10 2,000  1

 PD 

 2,000  0.75
Q
2
2,000
2
 10  1,000  1,500  $2,510
Note: No, EOQ with 200 units and a total cost of $2,200 is better.
12.20 Under present price of $50.00 per unit, Economic Order Quantity:
Q
2 DS
H
Q
2  1,000  40
 80 units
0.25  50
where: D = period demand, S = setup or order cost, H = holding cost, P  price/unit
6
Instructor’s Solutions Manual t/a Operations Management
Total cost  order cost  holding cost  purchase cost

DS QH
1,000  40 80  0.25  50

 PD 

 1,000  50
Q
2
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
1,000  40 200  0.25  50  0.97

 PD 

 1,000  50  0.97
Q
2
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.
12.21 Under present price of $7.00 per unit, Economic Order Quantity:
Q
2 DS
H
Q
2  6,000  20
 4781
. or 478 units
015
. 7
where: D = period demand, S = setup or order cost, H = holding cost, P  price/unit
Total cost  order cost  holding cost  purchase cost

DS QH
6,000  20 478  015
. 7

 PD 

  7  6,000
Q
2
478
2
 25105
.  250.95  42,000  $42,502.00
Note: Order and carrying costs are not equal due to rounding of the EOQ to a whole number.
Under the quantity discount price of $6.65 per unit:
Total cost  order cost  holding cost  purchase cost

DS QH
6,000  20 3,000  015
.  6.65

 PD 

 6,000  6.65
Q
2
3,000
2
 40.00  1,496.25  39,900  $41,436.25
Therefore, the new policy, with a total cost of $41,436.25, is preferable.
12.22 Economic Order Quantity:
Q
2 DS
H
where: D = period demand, S = setup or order cost, H = holding cost, P  price/unit
(a)
Economic Order Quantity, standard price:
Q
Chapter 12: Inventory Management
2  45  10
 30 units
0.05  20
7
Total cost  order cost  holding cost  purchase cost

DS QH
45  10 30  0.05  20

 PD 

  45  20 
Q
2
30
2
 15  15  900  $930
(b)
Quantity Discount, 75 units or more. Economic Order Quantity, discount over 75 units:
Q
2  45  10
 3119
. or 31 units
0.05  18.50
Because EOQ = 31 and a discount is given only on orders of 75 or more, we must calculate
the total cost using a 75-unit order quantity:
Total cost  order cost  holding cost  purchase cost

DS QH
45  10 75  0.05  18.50

 PD 

  45  18.50 
Q
2
75
2
 6  34.69  832.50  $873.19
(c)
Quantity Discount, 100 units or more; Economic Order Quantity, discount over 100 units:
Q
2  45  10
 3381
. or 34 units
0.05  15.75
EOQ = 34 and a discount is given only on orders of 100 or more, thus we must calculate the
total cost using a 100-unit order quantity. Calculate total cost using 100 as order quantity:
Total cost  order cost  holding cost  purchase cost

DS QH
45  10 100  0.05  15.75

 PD 

  45  15.75
Q
2
100
2
 4.5  39.38  708.75  $752.63
Based purely upon cost, the decision should be made to order in quantities of 100, for a total
cost of $752.63.
It should be noted, however, that an order quantity of 100 implies that an order will be
placed roughly every two years. When orders are placed that infrequently, obsolescence may
become a problem.
12.23 Economic Order Quantity:
Q
2 DS
H
where: D = period demand, S = setup or order cost, H = holding cost, P  price/unit
(a)
Order quantity 9 sheets or less, unit price = $18.00
Q
8
2  100  45
 50 units
0.20  18
Instructor’s Solutions Manual t/a Operations Management
Total cost  order cost  holding cost  purchase cost

DS QH
100  45 50  0.20  18

 PD 

 18  100 
Q
2
50
2
 90  90  1800
,
 $1,980 see note at end of problem re. actual price
(b)
Order quantity 10 to 50 sheets: unit price = $17.50
Q
2  100  45
 50.7 units or 51 units
0.20  17.50
Total cost  order cost  holding cost  purchase cost
DS QH
100  45 51  0.20  17.50

 PD 

 17.50  100 
Q
2
51
2
 88.23  89.25  1750.00  1927.48

(c)
Note: Order and carrying costs are not equal due to rounding the EOQ to a whole number. See
note at end of problem regarding price.
Order quantity more than 50 sheets: unit price = $17.25
Q
2  100  45
 511
. units or 51 units
0.20  17.25
Total cost  order cost  holding cost  purchase cost

DS QH
100  45 51  0.20  17.25

 PD 

 17.25  100 
Q
2
51
2
 88.24  87.98  1,725.00  $1,90122
.
Therefore, order 51 units.
Note: Order and carrying costs are not equal due to rounding of the EOQ to a whole
number.
Important Note: Calculations of total cost under (a) and (b) are actually inappropriate
because the original assumptions as to lot size would not be satisfied by the calculated EOQs.
12.24 D  700  12 , H  5 , S  50
Allen
1–499
500–999
1000+
$16.00
$15.50
$15.00
Baker
1–399
400–799
800+
$16.10
$15.60
$15.10
Q
2 DS
28,40050

 409.88  410
H
5
Vendor: Allen
at 410, TC 
Chapter 12: Inventory Management
410
8,400
5 
50   8,40016  $136,449.36
2
410
9
at 500, TC 
500
8,400
5 
50   8,40015.5  $132,290
2
500
at 1000, TC 
1,000
8,400
5 
50  8,40015  $128,920 BEST
2
1,000
Vendor: Baker
410
8,400
5 
50   8,40015.60   $133,089.39
2
410
800
8,400
5 
50   8,4001510
at 800, TC 
.   $129,365
2
800
at 410, TC 
10
Instructor’s Solutions Manual t/a Operations Management
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