1. business and industrial
2. manufacturing

Chapter
12
Inventory Management
DISCUSSION QUESTIONS
1. The short answer is that higher inventories do not provide an advantage in any of the nine
competitive priority categories. The important point is that firms must have the “right
amount” of inventory to meet their competitive priorities.
The only relevant costs considered in this chapter are ordering costs, holding costs,
and stockout costs. In the economic order quantity (EOQ) model, costs of placing
replenishment orders tradeoff against the costs of holding inventory. Under the
assumptions of the EOQ, average inventory is one-half of the order quantity. The number
of orders placed per year varies inversely with order quantity. When we consider
stockout costs, an additional inventory (safety stock), is held to trade-off costs of poor
customer service or costs for expediting shipments from unreliable suppliers.
In the lean systems chapter, we see order quantities (lot sizes) that are much smaller
than the “ideal” suggested by the EOQ model. As a result, lean systems average
inventory is also much lower. Are there some other relevant costs of holding inventory
that we have not considered in the EOQ model? If there are, a firm that ignores these
costs will make the wrong inventory decisions. These wrong decisions will make the firm
less competitive.
Let’s examine the relationships between inventory and the nine competitive priorities
discussed in the operations strategy chapter. We compare competitors H and L. They are
similar in all respects except H maintains much higher inventory than does L.
1) Low-cost operations. Costs include materials, scrap, labor, and equipment capacity
that are wasted when products are defective. When a process drifts out of control,
competitor H’s large lot sizes tend to result in large quantities of defectives. The EOQ
does not consider the cost of defectives, and erroneously assumes that setup costs are
constant. Small lots cause frequent setups, but the cost per setup decreases due to the
learning curve. Competitor L will enjoy competitive advantages with lower setup,
materials, labor, equipment, and inventory holding costs.
2) Top quality. Superior features, durability, safety, and convenience result from
improved designs. High inventories force competitor H to choose between scrapping
obsolete designs or delaying introduction of product improvements until the old
inventory is consumed. In either case, L gains a competitive advantage.
3) Consistent quality. Consistency in conforming to design specifications requires
consistency in supplied materials, setups, and processes. Small lots made frequently
tend to increase consistency. Again, advantage goes to L.
4) Delivery speed. Large lots take longer to produce than small lots. A customer will
wait less time for competitor L to set up and produce orders made in small batches.
Inventory Management • CHAPTER 12 • 307
5) On-time delivery. Contrary to expectations, large inventories do not equate to ontime delivery. It’s more like, lots of inventory equals lots of chaos. Big lots make big
scheduling problems. Big lots get dropped, mishandled, and pilfered. Most lean
companies experience dramatic improvement in on-time delivery.
6) Development speed. This response is similar to that given for high-performance
design. Low inventories result in getting new designs to the market more quickly.
7) Customization. Lean companies usually don’t claim an advantage in customization.
However, large inventories provide no advantage with regard to customization either.
It remains unlikely that a customized product will be found in inventory, no matter
how large.
8) Variety. Mass customizers compete on service or product variety. They will keep
products at raw material or component levels until a customer orders a specific
configuration. Inventories are at as low a level as possible.
9) Volume flexibility. Lean (low inventory) companies tend to produce the same
quantity of every product every day, but they claim considerable volume flexibility
from month to month. On the other hand, a large finished goods inventory can be
used to absorb volume fluctuations.
In summary, a case can be made that several competitive priorities are not
considered in the EOQ model. It is sometimes difficult to place a dollar value on
these competitive advantages, but the advantages invariably go to the low-inventory,
small lot-size firm. So if the EQO is too large, what is the “ideal” lot size? According
to the lean philosophy, the “ideal” lot size is one.
2. Reducing cycle inventories has an effect on practically every functional area. Although
responses will vary, and sometimes be quite insightful, the following list contains some
standard answers:
Marketing—Reducing cycle inventories implies that there is less inventory on hand,
which could increase stockouts if the inventories are not managed properly.
Finance—Smaller-cycle inventories implies that there is less capital tied up in
inventory, thereby reducing the pressure for short-term operating capital and allowing for
alternative investment options.
Operations—Reducing cycle inventories implies that order quantities are to be
reduced. Order times and costs must be reduced to facilitate that move. Smaller order
quantities enable a shift toward a lean system and enhance a uniform flow of materials
through the production process.
3. Organizations will never get to the point where inventories are unneeded. Inventories
provide many functions and should be managed, not eliminated. It is impossible to
eliminate uncertainties in the provision of products or services. In addition, unless
materials can be transported instantaneously, there will always be pipeline inventories.
Cycle inventories will exist unless we universally get to the point where production of
single units is feasible.
308 • PART 3 • Managing Value Chains
PROBLEMS
1. A part
a. Average cycle inventory
=Q 2
= 1000 2 = 500 units
= (500 units) ($50+$60)
= $55,000
Value of cycle inventory
b. Pipeline inventory
Value of the pipeline inventory
= dL
[(3800 units/year)/(50wks/yr)](6 weeks)
= 456 units
= (456 units)($50+$30)
= $36,480
2. Prince Electronics
a. Value of each DC’s pipeline inventory
= (75 units/wk)(2 wk)($350/unit)
= $52,500
b. Total inventory
= cycle + safety + pipeline
= 5[(400/2) + (2*75) + (2*75)]
= 2,500 units
3. Lockwood Industries
First we rank the items from top to bottom on the basis of their dollar usage. Then we
partition them into classes. The analysis was done using OM Explorer Tutor12.2—ABC
Analysis.
Part # Description
4
7
5
2
6
8
3
1
Total
Qty Used/Year
44,000
70,000
900
120,000
350
200
100
1,200
Value Dollar Usage
$1.00
$44,000
$0.30
$21,000
$4.50
$4,050
$0.03
$3,600
$0.90
$315
$1.50
$300
$0.45
$45
$0.01
$12
$73,322
Pct of Total
60.0%
28.6%
5.5%
4.9%
0.4%
0.4%
0.1%
0.0%
Cumulative % Cumulative %
of Dollar Value
of Items Class
60.0%
12.5%
A
88.7%
25.0%
A
94.2%
37.5%
B
99.1%
50.0%
B
99.5%
62.5%
C
99.9%
75.0%
C
100.0%
87.5%
C
100.0%
100.0%
C
Inventory Management • CHAPTER 12 • 309
The dollar usage percentages don’t exactly match the predictions of ABC analysis. For
example, Class A items account for 88.7% of the total, rather than 80%. Nonetheless, the
important finding is that ABC analysis did find the “significant few.” For the items
sampled, particularly close control is needed for items 4 and 7.
4. Terminator Inc.
a. Average cycle inventory
Value of cycle inventory
=Q 2
= 250/2
= 125 units
= (125 units)($450)
= $56,250
⎧ ( 4, 000 units yr ) ⎫
= dL = ⎨
⎬ ( 3 wk )
50
wk
yr
⎩
⎭
= 240 units
Value of pipeline inventory = (240 units)($150 + $300/2)
= $72,000
b. Pipeline inventory
5. Stock-Rite Inc.
Computing the annual usage value for each item and rank ordering them highest to
lowest, we get:
Item
D205
U404
Annual Value ($)
9,690
6,075
Cumulative Value ($)
9,690
15,765
A104
L205
3,220
3,035
18,985
22,020
L104
S104
X205
X104
2,005
1,604
1,603
1,500
24,025
25,629
27,232
28,732
A: 55%
B: 22%
C: 23%
310 • PART 3 • Managing Value Chains
One classification might be to group the top two items (i.e., 25% of the items) in A class
accounting for 55% of the total value. The next two items would be classified as B and
the last four as C.
The dollar usage percentages don’t exactly match the predictions of ABC analysis.
For example, Class A items account for only 55% of the total, rather than 80%.
Nonetheless, the important finding is that ABC analysis did find the “significant few.”
For the items sampled, particularly close inventory management is needed for items
D205 and U404.
6. Yellow Press, Inc.
a. Economic order quantity
D = 2500 rolls
Price = $800 roll
H = 15% ( $800 ) = $120 roll-year
S = $50
EOQ =
2 DS
2 ( 2500 rolls year )( $50 )
=
= 2083.33 = 45.64 or 46 rolls
$120 roll-year
H
b. Time between orders
Q
46
=
= 0.0184 year, or every 4.6 days
D 2500
if there are 250 working days in a year
7. Babble Inc.
a. d = 400 tapes/month
D = 4800 tapes/year
H = $0.12
S = $12.50
2 DS
2 ( 4,800 )( $12.50 )
EOQ =
=
= 1, 000, 000 = 1000 tapes
H
$0.12
b. Time between orders
Q 1, 000
=
= 0.2083 years or 2.5 months
D 4,800
8. Dot Com
a. EOQ =
2 ( 32, 000 )( $10 )
2 DS
=
= 400 books
H
$4
b. Optimal number of orders/year
c. Optimal interval between orders
d. Demand during lead time = dL
= (32,000)/400 = 80 orders
= 300/80 = 3.75 days
= (5 days)(32,000/300) = 533 books
Inventory Management • CHAPTER 12 • 311
e. Reorder point = dL + safety stock
f. Inventory position = OH + SR – BO
= 533 + 0 = 533 books
= 533 + 400 – 0 = 933 books
9. Leaky Pipe Inc.
a. EOQ =
b.
c.
d.
e.
f.
2 ( 30, 000 )( $10 )
2 DS
=
= 775 units
H
$1
Optimal number of orders
Optimal interval between orders
Demand during lead time = dL
Reorder point = dL + safety stock
Inventory position = OH + SR – BO
= (30,000)/(775) = 38.7 or 39
= (300)/(39) = 7.69 days
= (4 days)(30,000/300) = 400 units
= 400 + 0 = 400 units
= 400 +775 – 0 = 1175 units
10. Sam’s Cat Hotel
a. Economic order quantity
d = 90 week
D = 4, 680
S = $54
Price = $11.70
H = 27% ( $11.70 ) = $3.159
2 ( 4, 680 )( 54 )
2 DS
=
= 160, 000 = 400 bags
H
3.159
Time between orders, in weeks
Q 400
=
= 0.08547 years = 4.44 weeks
D 4680
EOQ =
b. Reorder point, R
R = demand during protection interval + safety stock
Demand during protection interval = dL = 90 * 3 = 270 bags
Safety stock = zσ L
When the desired cycle-service level is 80%, z = 084
. .
σ L = σ t L = 15 3 = 26 = 25.98 or 26
Safety stock = 0.84 * 26 = 21.82 or about 22 bags
R = 270 + 22 = 292
c. Initial inventory position = OH + SR – BO = 320 + 0 – 0
320 – 10 = 310.
Because inventory position remains above 292, it is not yet time to place an order.
312 • PART 3 • Managing Value Chains
d. Annual holding cost
Q
500
(27% )($11.70)
H=
2
2
= $789.75
Annual ordering cost
D
4, 680
S=
$54
Q
500
= $505.44
At the EOQ, these two costs are equal. When Q = 500 , the annual holding cost is
larger than the ordering cost, therefore Q is too large. Total costs are $789.75 +
$505.44 = $1,295.19.
e. Annual holding cost
Q
400
(27% )($11.70)
H=
2
2
= $631.80
Annual ordering cost
D
4, 680
S=
$54
Q
400
= $631.80
Total costs at EOQ: = $1,263.60, which is $31.59 less than when order quantity is
500 bags.
11. Sam’s Cat Hotel, revisited
a. If the demand is only 60 bags per week, the correct EOQ is:
D = (60 units/wk)(52 wk/yr) = 3,120 bags
EOQ =
2 ( 3,120 )( 54 )
2 DS
=
= 326.6 or 327 bags
H
3.159
If the demand is incorrectly estimated at 90 bags, the EOQ would be incorrectly
calculated (from problem 10) as 400 bags:
The total cost, working with the actual demand, is:
Q
D
C= H+ S
2
Q
C327 =
327
3,120
3.159 +
54
2
327
C327 = $516.50 + $515.23
C327 = $1, 031.73
400
3,120
3.159 +
54
2
400
= $631.80 + $421.20
C400 =
C400
C400 = $1, 053
We can see clearly now that the cost penalty of Sam’s difficulty in foreseeing demand
for kitty litter is $21.27 ($1,053.00 – $1,031.73).
Inventory Management • CHAPTER 12 • 313
b. If S = $6, and D = 60 × 52 = 3120 , the correct EOQ is:
EOQ =
2 ( 3,120 )( 6 )
2 DS
=
= 108.9 or 109 bags
H
3.159
The total cost, working with the actual ordering cost, is
Q
D
H+ S
Q
2
109
3,120
=
3.159 +
6
2
109
= $172.17 + $171.74
C=
C109
C109
C109 = $343.91
327
3,120
3.159 +
6
2
327
= $516.50 + $57.25
C327 =
C327
C327 = $573.74
If the reduced ordering cost continues to be unseen, the cost penalty for not updating
the EOQ is (573.74 – 343.91) = $229.83.
12. A Q system (also known as a reorder point system)
gizmos
d = 300
week
σ t = 15 gizmos
a. Standard deviation of demand during the protection interval:
σ L = σt L
σ L = 15 9 = 45 gizmos
b. Average demand during the protection interval:
gizmos
(9 weeks) = 2700 gizmos
dL = 300
week
c. Reorder point
R = demand during protection interval + safety stock – backorders
Safety stock = zσ L
When the desired cycle-service level is 99%, z = 2.33.
Safety stock = 2.33 * 45 = 104.85 or 105 gizmos
R = 2,700 + 105 – 0 = 2,805
13. Petromax Enterprises
a. EOQ =
2 ( 50, 000 )( 35 )
2 DS
=
= 1,323 units
H
2
314 • PART 3 • Managing Value Chains
(
)
b. Safety stock = Zσ L = Z σ t L = (1.29 )(125 )
Reorder point
( 3 ) = 279.29 or 280 units
= average lead time demand + safety stock
= (3)(50,000/50) + 278
= 3,278 units
14. A perpetual system (also known as a continuous review system). Find the safety stock
reduction when lead time is reduced from five weeks to one week, given:
Standard deviation of demand during the (five-week) protection interval is 85 dohickies.
Desired cycle service level is 99% (therefore z = 2.33).
Safety stock required for five-week protection interval
Safety stock = zσ L = 2.33(85) = 198 dohickies
Safety stock required for one-week protection interval
σ L = σ t L = 85 dohickies
85
= 38 dohickies
5
Safety stock = zσ t = 2.33(38) = 88.54 or 89 dohickies
σt =
15. A two-bin system.
“The two-bin system is really a Q system, with the normal level in the second bin being
the reorder point R.”
Find cycle-service level, given:
L = 2 weeks
d = 53 whatchamacallits week
σ t = 5 whatchamacallits
R = 120 whatchamacallits
Safety stock = R – dL = 120 – (53*2) = 14 whatchamacallits
Safety stock = zσ L = 14 whatchamacallits
σ L = σ t L = 5 2 = 7.07 or 7 whatchamacallits
z(7) = 14
z=2
When z = 2, the cycle-service level is 97.72%.
16. Nationwide Auto Parts
a. Protection interval (PI)
= P + L = 6 +3 = 9 weeks
Average demand during PI = 9 (100) = 900 units
Standard deviation during PI = 9 • (20) = 60 units
b. Target inventory = d(P+L)+zσP+L
= 900 + (1.96)(60) = 1,018
c. Order quantity
= Target inventory – IP
= 1,018 – 350 = 668 units presuming no SR or BO
Inventory Management • CHAPTER 12 • 315
17. A P system (also known as a periodic review system). Find cycle-service level, given:
L = 2 weeks
P = 1 week
d(P + L) = 218 gadgets
σ P + L = 40 gadgets
T = 300 gadgets
T = Average demand during protection interval + Safety stock
T = 218 + z(40) = 300
z = (300 – 218)/40 = 2.05
When z = 2.05, cycle-service level is 97.98 or 98%.
18. A Successful Product
Annual Demand, D = (200)(50) = 10,000 units, H = ((0.20)(12.50)) = 2.50
a. Optimal ordering quantity =
(
b. Safety stock = Zσ L = Z σ t L
2 (10, 000 )( 50 )
2 DS
=
= 633 units
H
2.5
)
= (2.33)(16) (4) = 74.56 or 75 units
c. Safety stock will now be
% reduction in safety stock
d. Safety stock will be
% reduction in safety stock
= (2.33)(16) (2) = 52.72 or 53 units
= (75 – 53)/75 = 29.33%
= (2.33)(8) (4) = 37.28 or 38 units
= (75 – 38)/75 = 49.33%
19. Sam’s Cat Hotel with a P system
a. Referring to Problem 10, the EOQ is 400 bags. When the demand rate is 15 per day,
the average time between orders is (400/15) = 26.67 or about 27 days. The lead time
is 3 weeks × 6 days per week = 18 days. If the review period is set equal to the EOQs
average time between orders (27 days), then the protection interval (P + L) = (27 +
18) = 45 days.
For an 80% cycle-service level
z = 084
.
σ P+ L = σ t P + L
.
45 = 4108
.
σ P + L = 6124
Safety stock = zσ P + L = 0.84(41.08) = 34.51 or 35 bags
T = Average demand during the protection interval + Safety stock
T = (15*45) + 35 = 710
b. In Problem 10, the Q system required a safety stock of 22 bags to achieve an 80%
cycle-service level. Therefore, the P system requires a safety stock that is larger by
(35 – 22) 13 bags.
c. From Problem 10, inventory position, IP = 310.
The amount to reorder is T – IP = 710 – 310 = 400.
316 • PART 3 • Managing Value Chains
20.
Continuous review system.
a. Economic order quantity.
EOQ =
2 ( 2, 000 )( 40 )
2 DS
=
= 894.4 or 894 units
H
2
Time between orders (TBO) = Q/D = 894/20,000 = 0.0447 years = 2.32 weeks
b. Weekly demand = 20,000/52 = 385 units
For a 95% cycle-service level, z = 1.645
. (100) 2 = 232.6 or 233 units
Safety stock = zσ L = zσ t L = 1645
Now solve for R, as
R = dL + Safety stock = 385(2) + 233 = 1003 units
c. i. Annual holding cost of cycle inventory
Q
894
H=
( 2 ) = $894.00
2
2
ii. Annual ordering cost
D
20,000
S=
$40 = $894.85
Q
894
d. With the 15-unit withdrawal, IP drops from 1,040 to 1,025 units. Because this level is
above the reorder point (1,025 > 1,003), a new order is not placed.
21. Periodic review system
a. From Problem 20,
EOQ =
2 ( 20, 000 )( 40 )
2 DS
=
= 894.4 or 894 units
H
2
Number of orders per year = D Q = 20,000/894 = 22.4 orders per year.
EOQ
894
=
= 0.0447 years × 52 weeks year = 2.3244 weeks
D
20,000
P is rounded to two weeks.
P=
b. For a 95% cycle-service level, z = 1.645. Therefore
Safety stock = zσ P + L
σ P+ L = σ t P + L
σ P + L = 100 2 + 2 = 200 units
Safety stock = 1.645(200) = 329 units,
T = Average demand during the protection interval + Safety stock
T = (385 * 4) + 329 = 1,869 units
c. In Problem 20, with a Q system the safety stock is 233 units. Therefore, (329 – 233) =
96 more units of safety stock are needed.
Inventory Management • CHAPTER 12 • 317
22. Continuous review system
a. Economic order quantity
2 DS
2(64)(52)(50)
EOQ =
=
= 160 units
H
13
b. Safety stock. When cycle-service level is 88%, z = 1.175.
σ L = σ t L = 12 2 = 17 units
Safety stock = zσ L = 1.175(17) = 20 units
c. Reorder point
R = dL + Safety stock
= 64(2) + 20
= 148 units
d. If Q = 200 and R = 180, average inventory investment is higher than necessary to
achieve an 88% cycle-service level. The larger order quantity increases average cycle
stock by 20 units, and the higher reorder point increases safety stock by 32 units.
23. Periodic review system
a. From problem 22, EOQ = 160
EOQ
160
P=
=
= 2. 5 weeks
d
64 week
P is rounded to three weeks.
b. For an 88% cycle-service level, z = 1.175. Therefore
Safety stock = zσ P + L
σ P+ L = σ t P + L
. or 27 units
σ P + L = 12 3 + 2 = 268
Safety stock = 1.175(27) = 32 units
T = average demand during the protection interval + Safety stock
T = (64 * 5) + 32 = 352 units
24. Wood County Hospital
a. D = (1000 boxes/wk)(52 wk/yr) = 52,000 boxes
H = (0.l5)($35/box)=$5.25/box
EOQ =
2 ( 52, 000 )( $15 )
2 DS
=
= 545.1 or 545 boxes
H
$5.25
318 • PART 3 • Managing Value Chains
Q
D
H+ S
2
Q
900
52, 000
=
$5.25 +
$15.00 = $3, 229.16
2
900
545
52, 000
=
$5.25 +
$15.00 = $2,861.82
2
545
C=
C900
C545
The savings would be $3,229.16 – $2,861.82 = $367.34.
b. When the cycle-service level is 97%, z = 1.88. Therefore,
σ L = σt L
σ L = 100 2 = 141.4, or 141 boxes
Safety stock = zσ L = 1.88(141) = 265.08, or 265 boxes
R = dL + Safety stock = 1000(2) + 265 = 2,265 boxes
c. In a periodic review system, find target inventory T, given:
P = 2 weeks
L = 2 weeks
Safety stock = zσ P + L
σ P+ L = σ t P + L
σ P + L = 100 2 + 2 = 200 units
Safety stock = 1.88(200) = 376 units
T = Average demand during the protection interval + Safety stock
T = 1000(2 + 2) + 376
T = 4376 units
The screen shot below is taken from OM Explorer Solver—Inventory Systems.
Notice that the total cost for the Q system is much less than that of the P system. The
.
reason is that the optimal value of P was not used here. The optimal value is P = 055
weeks.
Inventory Management • CHAPTER 12 • 319
Results
Solver Inventory Systems
Continuous Review (Q) System
z
Periodic Review (P) System
1.88 Time Between Reviews (P)
2.00 Weeks
; Enter manually
Safety Stock
Reorder Point
Annual Cost
266 Standard Deviation of Demand
During Protection Interval
2266
Safety Stock
$4,258.32
Average Demand During
Protection Interval
Target Inventory Level (T)
Annual Cost
25.
Golf specialty wholesaler
a. Periodic Review System
2 DS
2(2000)(40)
EOQ =
=
= 17888
. or about 179 1-irons
H
5
P=
EOQ 179
=
= 0.0895 years = 4.475 or 4.0 weeks
D
2000
When cycle-service level is 90%, z = 1.28.
Weekly demand is (2,000 units/yr)/(50 wk/yr) = 40 units/wk
L = 4 weeks
T = d ( P + L ) + zσ P + L P + L
= 40 ( 8 ) + 1.29 ( 3) 8 = 320 + 10.94
= 331
b. Continuous review system
dL = 40 × 4 = 160
SS = zσ L = (1.29)(3) 4 = 7.68 or 8
R = 160 + 8 = 168
200
376
4000
4376
$7,614.00
320 • PART 3 • Managing Value Chains
26. Office Supply Shop
The screen shot below is taken from OM Explorer Solver – Demand During Protection
Interval Simulator. It shows the results of 500 trials.
Demand During Protection Interval Distribution
Bin
Back to Inputs
Upper Bound
17
29
41
53
65
77
89
101
113
125
Demand
Frequency
11
23
35
47
59
71
83
95
107
More
Total
83
114
151
57
63
14
16
2
0
0
500
Average Demand During Protection Interval
Cumulative
Percentage
35
16.6%
39.4%
69.6%
81.0%
93.6%
96.4%
99.6%
100.0%
100.0%
100.0%
Demand During Protection Interval
151
120%
140
Frequency
100
96.4%
93.6%
114
120
99.6%
100.0%
100.0%
100.0%
81.0%
80
60
80%
69.6%
83
57
39.4%
100%
60%
63
40%
40
20
16.6%
14
20%
16
2
0
0
95
107
More
0
11
23
35
47
59
71
83
Cumulative Percentage
160
0%
Demand
Frequency
Cumulative Percentage
a. Given the simulation, the value of R must yield a service level that meets or exceeds
the desired value of 95%. That value of R is 71 pens, which will yield a cycle service
level of 96.4%.
b. The average demand during the protection interval is 35 pens. Since the reorder point
is 71, the safety stock must be 71 – 35 = 36 pens. The high level of safety stock is
necessary because of the high variance in the demand during protection interval
distribution and the high variance in lead time.
Inventory Management • CHAPTER 12 • 321
27. Grocery store.
a.
The target level (T) should be 150 tubes of Happy Breath Toothpaste. This result
comes from OM Explorer Solver – Demand During Protection Interval Simulator.
Demand During Protection Interval Distribution
Bin
Back to Inputs
Upper Bound
60
80
100
120
140
160
180
200
220
240
Demand
Frequency
50
70
90
110
130
150
170
190
210
More
Total
2
14
71
110
115
113
57
18
0
0
500
Average Demand During Protection Interval
Cumulative
Percentage
132
0.4%
3.2%
17.4%
39.4%
62.4%
85.0%
96.4%
100.0%
100.0%
100.0%
Demand During Protection Interval
120%
120
110
115
113
100.0%
100.0%
80%
80
71
62.4%
60%
57
60
39.4%
40%
40
14
20
0
100%
85.0%
100
Frequency
96.4%
100.0%
2
3.2%
50
70
0.4%
18
17.4%
90
110
130
150
170
190
20%
0
0
210
More
Cumulative Percentage
140
0%
Demand
Frequency
b.
28.
Cumulative Percentage
Using OM Explorer once again, the cycle-service level for T = 150 would be
97.8%. Eliminating the variance in supply lead times will significantly increase the
cycle service level of the inventory.
Floral shop
a.
The EOQ for the continuous review system would be as follows.
Q=
2(2550)($30)
= 391
$1
The demand during protection interval distribution is shown below.
322 • PART 3 • Managing Value Chains
Demand During Protection Interval Distribution
Bin
Back to Inputs
Upper Bound
76
112
148
184
220
256
292
328
364
400
Demand
Frequency
58
94
130
166
202
238
274
310
346
More
Total
135
159
95
67
34
10
0
0
0
0
500
Average Demand During Protection Interval
Cumulative
Percentage
109
27.0%
58.8%
77.8%
91.2%
98.0%
100.0%
100.0%
100.0%
100.0%
100.0%
Demand During Protection Interval
Frequency
140
120%
159
160
100.0%
98.0%
135
100.0%
100.0%
100.0%
100.0%
91.2%
77.8%
120
80%
95
100
58.8%
60%
80
67
60
40
100%
40%
27.0%
34
10
20
0
58
94
130
166
202
238
20%
0
0
0
0
274
310
346
More
Cumulative Percentage
180
0%
Demand
Frequency
Cumulative Percentage
To attain at least a 90% cycle service level, the florist needs to set the reorder point at
166 baskets.
Inventory Management • CHAPTER 12 • 323
b. As the output from OM Explorer Solver – Q-System Simulator shows, the average
cost per day is $274.74.
Probability of Weekly Demand
Probabilty of Lower Range
Demand
Probability
0.40
0.00
0.30
0.40
0.15
0.70
0.10
0.85
0.05
0.95
1.00
Random Numbers
RN I
Demand
0.6586
0.4101
0.8676
0.2831
0.4569
0.8689
0.1591
0.9864
0.4978
0.0223
0.5906
0.8835
0.1373
0.0001
0.7819
0.9917
0.5232
0.7593
0.3090
0.5006
0.4173
0.8148
0.2962
0.3003
0.3560
0.9473
0.7621
0.4240
0.9240
0.3494
0.9098
0.0235
0.2316
0.6310
0.8768
0.8892
0.4683
0.3062
0.3298
0.1754
0.2214
0.8985
0.8108
0.7581
0.7205
0.1673
0.7142
0.8320
0.9648
0.5548
RN II Lead
Time
0.8794
0.2609
0.5330
0.8584
0.8724
0.9560
0.2470
0.9519
0.8590
0.7551
0.2691
0.4734
0.4465
0.4061
0.4404
0.8927
0.2572
0.2128
0.8100
0.6821
0.5249
0.4963
0.2767
0.1054
0.7946
0.9374
0.0953
0.2803
0.2087
0.8918
0.0755
0.3544
0.1659
0.8530
0.9013
0.4419
0.6197
0.4341
0.9087
0.7790
0.3099
0.4848
0.2892
0.4780
0.4660
0.4669
0.3310
0.0554
0.1822
0.1393
Probability of Lead Time
Demand
(Units)
40
50
60
70
80
Probabilty
of Lead
Time
0.30
0.40
0.20
0.10
0.00
1.00
Lower
Range
Lead Time
Probability (Periods)
0.00
1
0.30
2
0.70
3
0.90
4
1.00
5
Holding Cost ($/unit/period) $
Order Cost ($/order)
$
Stockout Cost ($/unit)
$
Order Size
Reorder Point
Beginning Inventory
1.0
30
10
391
166
300
Simulation of 50 Weeks
Beginning
Inventory
Week
1
300
2
250
3
200
4
130
5
481
6
431
7
361
8
321
9
241
10
191
11
151
12
101
13
422
14
382
15
342
16
282
17
202
18
543
19
483
20
443
21
393
22
343
23
283
24
243
25
203
26
163
27
93
28
424
29
374
30
304
31
264
32
194
33
154
34
505
35
455
36
385
37
315
38
265
39
225
40
185
41
145
42
105
43
426
44
366
45
306
46
246
47
206
48
146
49
477
50
397
Averages 296.94
Simulated
Demand
50
50
70
40
50
70
40
80
50
40
50
70
40
40
60
80
50
60
40
50
50
60
40
40
40
70
60
50
70
40
70
40
40
50
70
70
50
40
40
40
40
70
60
60
60
40
60
60
80
50
53.80
Ending
Inventory
250
200
130
90
431
361
321
241
191
151
101
31
382
342
282
202
152
483
443
393
343
283
243
203
163
93
33
374
304
264
194
154
114
455
385
315
265
225
185
145
105
35
366
306
246
206
146
86
397
347
243.14
Stockout
Units
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.00
Place
Order?
No
No
Yes
No
No
No
No
No
No
Yes
No
No
No
No
No
No
Yes
No
No
No
No
No
No
No
Yes
No
No
No
No
No
No
Yes
No
No
No
No
No
No
No
Yes
No
No
No
No
No
No
Yes
No
No
No
Simulated
Lead Time
2
3
1
3
2
3
2
2.29
Days to
Receive
Order
2
1
0
3
2
1
0
1
0
3
2
1
0
2
1
0
3
2
1
0
2
1
0
-
Holding
Cost
$
275
$
225
$
165
$
110
$
456
$
396
$
341
$
281
$
216
$
171
$
126
$
66
$
402
$
362
$
312
$
242
$
177
$
513
$
463
$
418
$
368
$
313
$
263
$
223
$
183
$
128
$
63
$
399
$
339
$
284
$
229
$
174
$
134
$
480
$
420
$
350
$
290
$
245
$
205
$
165
$
125
$
70
$
396
$
336
$
276
$
226
$
176
$
116
$
437
$
372
$270.04
Ordering
Cost
30
30
30
30
30
30
30
$4.20
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
Stockout
Cost
$0.00
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
Total Cost
$
275
$
225
$
195
$
110
$
456
$
396
$
341
$
281
$
216
$
201
$
126
$
66
$
402
$
362
$
312
$
242
$
207
$
513
$
463
$
418
$
368
$
313
$
263
$
223
$
213
$
128
$
63
$
399
$
339
$
284
$
229
$
204
$
134
$
480
$
420
$
350
$
290
$
245
$
205
$
195
$
125
$
70
$
396
$
336
$
276
$
226
$
206
$
116
$
437
$
372
$274.24
324 • PART 3 • Managing Value Chains
29. The simulation results with Q = 40 and R = 15 are:
Day
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
a.
b.
Beginning
Inventory
19
14
11
7
46
36
27
20
16
14
7
4
38
28
28
23
13
9
TOTAL
Open
Orders
Received
—
—
—
40
—
—
—
—
—
—
—
40
—
—
—
—
—
—
Daily
Demand
5
3
4
1
10
9
7
4
2
7
3
6
10
0
5
10
4
7
Ending
Inventory
14
11
7
46
36
27
20
16
14
7
4
38
28
28
23
13
9
2
343
Inventory
Position
14
51
47
46
36
27
20
16
14
47
44
38
28
28
23
13
49
42
The average ending inventory is:
343
= 19.05 or 19 units
18
No stockouts occurred during any of the three cycles.
Amount
Ordered
40
—
—
—
—
—
—
—
40
—
—
—
—
—
—
40
—
—
Inventory Management • CHAPTER 12 • 325
EXPERIENTIAL LEARNING: SWIFT ELECTRONIC SUPPLY, INC.
This in-class exercise allows students to test an inventory system of their design
against a new demand set. On the day of the simulation, students should come with
sufficient copies of Table 12.6.
It is best to precede the simulation with a brief overview of the simulation process
and the calculation of costs. The instructor may decide to require students to bring a
computer to class and use a spreadsheet of their design to accomplish the manual tasks
embodied in Table 12.6.
Once everyone understands the simulation procedure, the instructor uses the “actual”
demands in TN1, one at a time, and proceeding at a pace such that students have a chance to
decide whether or not to order that period, how much to order, and calculate relevant costs.
The instructor can stop at any point, using TN2 to benchmark students’ results against any of
the four provided systems in this manual. A good idea is to stop at the halfway point in the
simulation and ask students what their total costs are. The variance is often quite high. The
same benchmarking comparisons can be done at the end of the simulation. The instructor can
use the students’ results to discuss differences in the systems tried, the importance of using
safety stocks, and the value of perfect information. One of the provided systems in this
manual utilizes the Wagner-Whitin (WW) approach, which is optimal for perfect forecasts.
The variance in student results will be greater if this exercise is used as a prelude to a
discussion of formal inventory systems (such as the Q-system or P-system). Alternatively,
the exercise can be used after a presentation of the formal systems to give students a
practicum for the theory.
TN3 shows the cost structure and system parameters for the EOQ-system, Q-system
and P-system. All the relevant case information and derived data are on the left side of the
sheet, and key computed parameters for three systems are presented on the right side of the
sheet. There are some other points that need to be addressed about TN3 through TN7:
•
•
•
“Average Demand/day” and “Standard Deviation” come from a statistical
analysis of the historical demand data in Table 12.4.
All the ordering quantities are rounded up as integers. Consequently, the
associated costs might differ a little from what they actually are.
The review time in the EOQ-system is actually up to the student. In TN4 we
have used the EOQ divided by average daily demand.
326 • PART 3 • Managing Value Chains
TN4 through TN6 show the application of the provided systems for the demand data
in TN1. TN7 shows the results from WW system. In all of our reported results, inventory
levels at the start of the day are used to make inventory decisions. This is consistent with the
daily purchasing routine at Swift.
Economic Order Quantity (EOQ) System
Under this system, students order the EOQ each and every review period, which
using the case data would be 3 days, without any forecasts of future demand or consideration
of demand variability. TN4 shows the performance of this system. Students may elect to use
varying review periods. If so, their results will differ from TN4.
Q-system
This system assumes that inventory levels are checked on a daily basis and compared
to a “Reorder Point (RP).” If actual inventory level goes below the RP, an order of EOQ is
placed; if above, no order will be placed. In the provided results, the RP is calculated by
adding safety stock to average demand during the two-day lead time. The safety stock is
designed to meet the 95 percent cycle service level. TN5 shows the results of the Q-system.
P-system
The inventory level is reviewed every three days, which is determined by dividing
EOQ by average demand. The target inventory level is composed of two parts: “average
demand during the protection interval,” which is the review period plus the lead time, and the
“safety stock.” Every review period (three days in the provided results), an order is placed to
bring the inventory position up to the target inventory level. TN6 shows the performance of
the P-system.
Wager-Whitin (WW) System
The WW system is based on dynamic programming and assumes all demands are
known with certainty. Consequently, it provides an absolute lower bound on the solution
found by the students. The WW system assumes that stockouts are to be avoided. It is
interesting to show the difference in total costs between the
WW solution and another
system because it demonstrates the cost of uncertainty. The solution using the WW system is
shown in TN7. Also note that the lot sizes are shown in the day in which they must arrive.
Actual release dates would be two days earlier. This implies that the first order for 1733
would have been placed in day 0, one day before the actual start of the simulation.
Inventory Management • CHAPTER 12 • 327
TN 1. Actual Data for Simulation
328 • PART 3 • Managing Value Chains
TN 2. Total Costs for Four Systems
Day
Demand
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
870
901
960
702
1068
975
977
662
1147
1085
1041
890
1001
960
863
794
1109
948
1040
1008
961
828
764
933
960
988
1028
967
918
965
1068
996
1123
855
1035
1085
824
941
883
828
993
1008
852
725
667
1015
1167
878
824
863
1085
1067
930
1021
828
724
987
737
750
765
EOQ System
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
241.50
383.50
471.70
724.80
736.80
824.25
1,062.85
1,068.35
1,152.70
1,382.80
2,260.80
2,352.50
2,594.15
2,848.15
2,941.20
3,194.55
3,278.55
3,367.35
3,604.15
4,148.15
4,236.30
4,483.05
4,491.60
4,589.70
4,839.80
4,840.50
4,926.00
5,163.15
5,513.15
5,601.10
5,835.65
6,445.65
6,525.70
6,763.00
7,341.00
7,422.95
7,663.70
7,915.70
8,007.75
8,258.40
8,259.40
8,346.20
8,590.40
8,598.35
8,709.15
8,969.20
8,970.90
9,064.90
9,317.70
9,327.35
9,418.95
9,657.20
9,987.20
10,072.35
10,316.10
10,323.65
10,418.05
10,675.60
10,695.65
10,813.65
Q-System
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
241.50
383.50
671.70
724.80
860.70
1,147.85
1,186.15
1,327.55
1,611.60
1,641.40
1,755.35
2,024.80
2,044.20
2,151.80
2,416.25
2,441.00
2,746.50
2,804.60
2,946.90
3,238.80
3,282.65
3,421.30
3,721.75
3,775.55
3,917.55
4,210.15
4,251.35
4,380.40
4,663.55
4,698.45
4,816.15
5,084.05
5,095.80
5,401.00
5,454.45
5,589.85
5,884.05
5,931.20
6,070.40
6,368.20
6,416.35
6,550.30
6,841.65
6,896.75
7,054.70
7,361.90
7,410.75
7,551.90
7,851.85
7,908.65
8,047.40
8,332.80
8,371.70
8,495.75
8,778.40
8,824.85
8,958.15
9,254.60
9,313.55
9,470.45
P-System
$
241.50
$
383.50
$
548.95
$
879.30
$
956.25
$ 1,109.05
$ 1,413.00
$ 1,483.85
$ 1,648.35
$ 1,958.60
$ 2,016.80
$ 2,175.20
$ 2,483.55
$ 2,543.90
$ 2,707.70
$ 3,031.80
$ 3,100.45
$ 3,252.55
$ 3,552.65
$ 3,602.35
$ 3,758.85
$ 4,073.95
$ 4,150.85
$ 4,320.95
$ 4,643.05
$ 4,715.75
$ 4,869.90
$ 5,175.70
$ 5,235.60
$ 5,396.40
$ 5,703.80
$ 5,761.40
$ 5,910.40
$ 6,216.65
$ 6,271.15
$ 6,420.10
$ 6,727.85
$ 6,788.55
$ 6,952.30
$ 7,274.65
$ 7,347.35
$ 7,502.25
$ 7,814.55
$ 7,890.60
$ 8,075.95
$ 8,410.55
$ 8,486.80
$ 8,639.50
$ 8,951.00
$ 9,019.35
$ 9,176.90
$ 9,481.10
$ 9,538.80
$ 9,696.20
$ 10,012.20
$ 10,092.00
$ 10,261.40
$ 10,593.95
$ 10,689.00
$ 10,868.20
WW Solution
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
41.50
324.60
359.70
359.70
690.40
772.35
805.45
805.45
1,059.70
1,059.70
1,354.25
1,404.30
1,404.30
1,687.15
1,726.85
1,726.85
2,026.25
2,078.25
2,078.25
2,367.70
2,409.10
2,409.10
2,703.75
2,751.75
2,751.75
3,051.50
3,099.85
3,099.85
3,401.50
3,454.90
3,454.90
3,753.80
3,796.55
3,796.55
4,092.00
4,133.20
4,133.20
4,418.75
4,460.15
4,460.15
4,753.15
4,795.75
4,795.75
5,079.85
5,130.60
5,130.60
5,458.85
5,543.20
5,586.35
5,586.35
5,886.20
5,932.70
5,932.70
6,210.30
6,246.50
6,246.50
6,559.10
6,634.85
6,673.10
6,673.10
Inventory Management • CHAPTER 12 • 329
TN 3. Cost Structure and System Parameters
In-case information
Cost of DRAM/piece
Ordering cost/lot (S)
Stockout cost/piece per day
Holding Cost (% of Cost of DRAM per day)
Beginning balance
The cycle inventory service level
Lead tme (Days)
Data referred
Z value at 95% confidence interval
Average Demand/day
Standard Deviation
Holding Cost/day
EOQ
$
$
$
$
10.00
200.00
2.00
0.50%
1700
95%
2
1.645
927
126
0.05
2724
EOQ System
Average time between orders
Order Amount
Review time in EOQ system
3
2724
3
Q system
Average demand during lead time
Safety stock
Reorder Point for Q system
1854
294
2148
P system
Average demand during the protection interval
Safety stock
Review Period
Targeted Inventory Level
4635
464
3
5099
330 • PART 3 • Managing Value Chains
TN 4. EOQ System
Day
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Demand
870
901
960
702
1068
975
977
662
1147
1085
1041
890
1001
960
863
794
1109
948
1040
1008
961
828
764
933
960
988
1028
967
918
965
1068
996
1123
855
1035
1085
824
941
883
828
993
1008
852
725
667
1015
1167
878
824
863
1085
1067
930
1021
828
724
987
737
750
765
Order
quantity
2724
2724
2724
2724
2724
2724
2724
2724
2724
2724
2724
2724
2724
2724
2724
2724
2724
2724
2724
2724
Average
EOQ
2724
Beginning
Inventory
1700
830
2724
1764
1062
2724
1749
772
2834
1687
602
2724
1834
833
2724
1861
1067
2724
1776
736
2724
1763
935
2895
1962
1002
2738
1710
743
2724
1759
691
2724
1601
746
2724
1639
815
2724
1841
1013
2744
1736
884
2883
2216
1201
2758
1880
1056
2917
1832
765
2724
1703
875
2875
1888
1151
3125
Ending
Actual Ending
Inventory with
Inventory
Back orders
830
-71
1764
1062
-6
1749
772
110
1687
602
-439
1834
833
-127
1861
1067
-42
1776
736
-272
1763
935
171
1962
1002
14
1710
743
-175
1759
691
-305
1601
746
-289
1639
815
-126
1841
1013
20
1736
884
159
2216
1201
34
1880
1056
193
1832
765
-165
1703
875
151
1888
1151
401
2360
830
0
1764
1062
0
1749
772
110
1687
602
0
1834
833
0
1861
1067
0
1776
736
0
1763
935
171
1962
1002
14
1710
743
0
1759
691
0
1601
746
0
1639
815
0
1841
1013
20
1736
884
159
2216
1201
34
1880
1056
193
1832
765
0
1703
875
151
1888
1151
401
2360
Holding
Cost
Stockout Cost
Daily total
Cost
Order Cost
$ 41.50
$
$ 88.20
$ 53.10
$
$ 87.45
$ 38.60
$ 5.50
$ 84.35
$ 30.10
$
$ 91.70
$ 41.65
$
$ 93.05
$ 53.35
$
$ 88.80
$ 36.80
$
$ 88.15
$ 46.75
$ 8.55
$ 98.10
$ 50.10
$ 0.70
$ 85.50
$ 37.15
$
$ 87.95
$ 34.55
$
$ 80.05
$ 37.30
$
$ 81.95
$ 40.75
$
$ 92.05
$ 50.65
$ 1.00
$ 86.80
$ 44.20
$ 7.95
$ 110.80
$ 60.05
$ 1.70
$ 94.00
$ 52.80
$ 9.65
$ 91.60
$ 38.25
$
$ 85.15
$ 43.75
$ 7.55
$ 94.40
$ 57.55
$ 20.05
$ 118.00
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
142.00
12.00
878.00
254.00
84.00
544.00
350.00
610.00
578.00
252.00
330.00
-
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
-
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
241.50
142.00
88.20
253.10
12.00
87.45
238.60
5.50
84.35
230.10
878.00
91.70
241.65
254.00
93.05
253.35
84.00
88.80
236.80
544.00
88.15
246.75
8.55
98.10
250.10
0.70
85.50
237.15
350.00
87.95
234.55
610.00
80.05
237.30
578.00
81.95
240.75
252.00
92.05
250.65
1.00
86.80
244.20
7.95
110.80
260.05
1.70
94.00
252.80
9.65
91.60
238.25
330.00
85.15
243.75
7.55
94.40
257.55
20.05
118.00
927 $ 46.33
$
67.23
$
66.67
$
180.23
Accumulative
Costs from Last
Day
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
241.50
383.50
471.70
724.80
736.80
824.25
1,062.85
1,068.35
1,152.70
1,382.80
2,260.80
2,352.50
2,594.15
2,848.15
2,941.20
3,194.55
3,278.55
3,367.35
3,604.15
4,148.15
4,236.30
4,483.05
4,491.60
4,589.70
4,839.80
4,840.50
4,926.00
5,163.15
5,513.15
5,601.10
5,835.65
6,445.65
6,525.70
6,763.00
7,341.00
7,422.95
7,663.70
7,915.70
8,007.75
8,258.40
8,259.40
8,346.20
8,590.40
8,598.35
8,709.15
8,969.20
8,970.90
9,064.90
9,317.70
9,327.35
9,418.95
9,657.20
9,987.20
10,072.35
10,316.10
10,323.65
10,418.05
10,675.60
10,695.65
Accumulative
Cost to Date
$
241.50
$
383.50
$
471.70
$
724.80
$
736.80
$
824.25
$ 1,062.85
$ 1,068.35
$ 1,152.70
$ 1,382.80
$ 2,260.80
$ 2,352.50
$ 2,594.15
$ 2,848.15
$ 2,941.20
$ 3,194.55
$ 3,278.55
$ 3,367.35
$ 3,604.15
$ 4,148.15
$ 4,236.30
$ 4,483.05
$ 4,491.60
$ 4,589.70
$ 4,839.80
$ 4,840.50
$ 4,926.00
$ 5,163.15
$ 5,513.15
$ 5,601.10
$ 5,835.65
$ 6,445.65
$ 6,525.70
$ 6,763.00
$ 7,341.00
$ 7,422.95
$ 7,663.70
$ 7,915.70
$ 8,007.75
$ 8,258.40
$ 8,259.40
$ 8,346.20
$ 8,590.40
$ 8,598.35
$ 8,709.15
$ 8,969.20
$ 8,970.90
$ 9,064.90
$ 9,317.70
$ 9,327.35
$ 9,418.95
$ 9,657.20
$ 9,987.20
$ 10,072.35
$ 10,316.10
$ 10,323.65
$ 10,418.05
$ 10,675.60
$ 10,695.65
$ 10,813.65
Inventory Management • CHAPTER 12 • 331
TN 5. Q-System
Day
Beginning
Inventory
Demand
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
1700
830
2724
1764
3786
2718
1743
3490
2828
1681
3320
2279
1389
3112
2152
1289
3219
2110
3886
2846
1838
3601
2773
2009
3800
2840
1852
3548
2581
1663
3422
2354
1358
2959
2104
3793
2708
1884
3667
2784
1956
3687
2679
1827
3826
3159
2144
3701
2823
1999
3860
2775
1708
3502
2481
1653
3653
2666
1929
3903
870
901
960
702
1068
975
977
662
1147
1085
1041
890
1001
960
863
794
1109
948
1040
1008
961
828
764
933
960
988
1028
967
918
965
1068
996
1123
855
1035
1085
824
941
883
828
993
1008
852
725
667
1015
1167
878
824
863
1085
1067
930
1021
828
724
987
737
750
765
Average
Reorder Point for Q System
Order Quantity
Ending
Inventory
with Back
Orders
830
-71
1764
1062
2718
1743
766
2828
1681
596
2279
1389
388
2152
1289
495
2110
1162
2846
1838
877
2773
2009
1076
2840
1852
824
2581
1663
698
2354
1358
235
2104
1069
2708
1884
943
2784
1956
963
2679
1827
1102
3159
2144
977
2823
1999
1136
2775
1708
778
2481
1653
929
2666
1929
1179
3138
2148
2724
Actual
Ending
Inventory
Inventory
Position
Order
Quantity
830
0
1764
1062
2718
1743
766
2828
1681
596
2279
1389
388
2152
1289
495
2110
1162
2846
1838
877
2773
2009
1076
2840
1852
824
2581
1663
698
2354
1358
235
2104
1069
2708
1884
943
2784
1956
963
2679
1827
1102
3159
2144
977
2823
1999
1136
2775
1708
778
2481
1653
929
2666
1929
1179
3138
830
2724
1764
3786
2718
1743
3490
2828
1681
3320
2279
1389
3112
2152
1289
3219
2110
3886
2846
1838
3601
2773
2009
3800
2840
1852
3548
2581
1663
3422
2354
1358
2959
2104
3793
2708
1884
3667
2784
1956
3687
2679
1827
3826
3159
2144
3701
2823
1999
3860
2775
1708
3502
2481
1653
3653
2666
1929
3903
3138
2724
0
2724
0
0
2724
0
0
2724
0
0
2724
0
0
2724
0
2724
0
0
2724
0
0
2724
0
0
2724
0
0
2724
0
0
2724
0
2724
0
0
2724
0
0
2724
0
0
2724
0
0
2724
0
0
2724
0
0
2724
0
0
2724
0
0
2724
0
0
1709.48
2662.88
953.40
Holding Cost
Stockout Cost Ordering Cost
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$ 142.00
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
-
41.50
88.20
53.10
135.90
87.15
38.30
141.40
84.05
29.80
113.95
69.45
19.40
107.60
64.45
24.75
105.50
58.10
142.30
91.90
43.85
138.65
100.45
53.80
142.00
92.60
41.20
129.05
83.15
34.90
117.70
67.90
11.75
105.20
53.45
135.40
94.20
47.15
139.20
97.80
48.15
133.95
91.35
55.10
157.95
107.20
48.85
141.15
99.95
56.80
138.75
85.40
38.90
124.05
82.65
46.45
133.30
96.45
58.95
156.90
85.47
2.37
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
70.00
Daily Total
Cost
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
241.50
142.00
288.20
53.10
135.90
287.15
38.30
141.40
284.05
29.80
113.95
269.45
19.40
107.60
264.45
24.75
305.50
58.10
142.30
291.90
43.85
138.65
300.45
53.80
142.00
292.60
41.20
129.05
283.15
34.90
117.70
267.90
11.75
305.20
53.45
135.40
294.20
47.15
139.20
297.80
48.15
133.95
291.35
55.10
157.95
307.20
48.85
141.15
299.95
56.80
138.75
285.40
38.90
124.05
282.65
46.45
133.30
296.45
58.95
156.90
157.84
Accumulative
Costs from Last
Day
Accumulative
Cost to Date
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
241.50
383.50
671.70
724.80
860.70
1,147.85
1,186.15
1,327.55
1,611.60
1,641.40
1,755.35
2,024.80
2,044.20
2,151.80
2,416.25
2,441.00
2,746.50
2,804.60
2,946.90
3,238.80
3,282.65
3,421.30
3,721.75
3,775.55
3,917.55
4,210.15
4,251.35
4,380.40
4,663.55
4,698.45
4,816.15
5,084.05
5,095.80
5,401.00
5,454.45
5,589.85
5,884.05
5,931.20
6,070.40
6,368.20
6,416.35
6,550.30
6,841.65
6,896.75
7,054.70
7,361.90
7,410.75
7,551.90
7,851.85
7,908.65
8,047.40
8,332.80
8,371.70
8,495.75
8,778.40
8,824.85
8,958.15
9,254.60
9,313.55
241.50
383.50
671.70
724.80
860.70
1,147.85
1,186.15
1,327.55
1,611.60
1,641.40
1,755.35
2,024.80
2,044.20
2,151.80
2,416.25
2,441.00
2,746.50
2,804.60
2,946.90
3,238.80
3,282.65
3,421.30
3,721.75
3,775.55
3,917.55
4,210.15
4,251.35
4,380.40
4,663.55
4,698.45
4,816.15
5,084.05
5,095.80
5,401.00
5,454.45
5,589.85
5,884.05
5,931.20
6,070.40
6,368.20
6,416.35
6,550.30
6,841.65
6,896.75
7,054.70
7,361.90
7,410.75
7,551.90
7,851.85
7,908.65
8,047.40
8,332.80
8,371.70
8,495.75
8,778.40
8,824.85
8,958.15
9,254.60
9,313.55
9,470.45
332 • PART 3 • Managing Value Chains
TN 6. P-System
Day
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Average
Target
Inventory
Level
Beginning
Inventory
Demand
1700
830
4269
3309
2607
4031
3056
2079
4437
3290
2205
4058
3168
2167
4139
3276
2482
3990
3042
2002
4091
3130
2302
4335
3402
2442
4111
3083
2116
4181
3216
2148
4103
2980
2125
4064
2979
2155
4158
3275
2447
4106
3098
2246
4374
3707
2692
3932
3054
2230
4236
3151
2084
4169
3148
2320
4375
3388
2651
4349
870
901
960
702
1068
975
977
662
1147
1085
1041
890
1001
960
863
794
1109
948
1040
1008
961
828
764
933
960
988
1028
967
918
965
1068
996
1123
855
1035
1085
824
941
883
828
993
1008
852
725
667
1015
1167
878
824
863
1085
1067
930
1021
828
724
987
737
750
765
Ending
Inventory
with Back
orders
830
-71
3309
2607
1539
3056
2079
1417
3290
2205
1164
3168
2167
1207
3276
2482
1373
3042
2002
994
3130
2302
1538
3402
2442
1454
3083
2116
1198
3216
2148
1152
2980
2125
1090
2979
2155
1214
3275
2447
1454
3098
2246
1521
3707
2692
1525
3054
2230
1367
3151
2084
1154
3148
2320
1596
3388
2651
1901
3584
Actual Ending
Inventory
830
0
3309
2607
1539
3056
2079
1417
3290
2205
1164
3168
2167
1207
3276
2482
1373
3042
2002
994
3130
2302
1538
3402
2442
1454
3083
2116
1198
3216
2148
1152
2980
2125
1090
2979
2155
1214
3275
2447
1454
3098
2246
1521
3707
2692
1525
3054
2230
1367
3151
2084
1154
3148
2320
1596
3388
2651
1901
3584
2219
Inventory
Position
Order
quantity
830
4269
4269
3309
2607
2492
4031
3056
2079
3020
4437
3290
2205
2894
4058
3168
2167
2932
4139
3276
2482
2617
3990
3042
2002
3097
4091
3130
2302
2797
4335
3402
2442
2657
4111
3083
2116
2983
4181
3216
2148
2951
4103
2980
2125
2974
4064
2979
2155
2944
4158
3275
2447
2652
4106
3098
2246
2853
4374
3707
2692
2407
3932
3054
2230
2869
4236
3151
2084
3015
4169
3148
2320
2779
4375
3388
2651
2448
4349
3584
3196.441 2882.5
5099
Holding Cost
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
41.50
165.45
130.35
76.95
152.80
103.95
70.85
164.50
110.25
58.20
158.40
108.35
60.35
163.80
124.10
68.65
152.10
100.10
49.70
156.50
115.10
76.90
170.10
122.10
72.70
154.15
105.80
59.90
160.80
107.40
57.60
149.00
106.25
54.50
148.95
107.75
60.70
163.75
122.35
72.70
154.90
112.30
76.05
185.35
134.60
76.25
152.70
111.50
68.35
157.55
104.20
57.70
157.40
116.00
79.80
169.40
132.55
95.05
179.20
110.97
Stockout
Cost
$
$ 142.00
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
2.41
Ordering
Cost
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
200.00
66.67
Daily total
Cost
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
241.50
142.00
165.45
330.35
76.95
152.80
303.95
70.85
164.50
310.25
58.20
158.40
308.35
60.35
163.80
324.10
68.65
152.10
300.10
49.70
156.50
315.10
76.90
170.10
322.10
72.70
154.15
305.80
59.90
160.80
307.40
57.60
149.00
306.25
54.50
148.95
307.75
60.70
163.75
322.35
72.70
154.90
312.30
76.05
185.35
334.60
76.25
152.70
311.50
68.35
157.55
304.20
57.70
157.40
316.00
79.80
169.40
332.55
95.05
179.20
181.17
Accumulative
Costs from Last
Day
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
241.50
383.50
548.95
879.30
956.25
1,109.05
1,413.00
1,483.85
1,648.35
1,958.60
2,016.80
2,175.20
2,483.55
2,543.90
2,707.70
3,031.80
3,100.45
3,252.55
3,552.65
3,602.35
3,758.85
4,073.95
4,150.85
4,320.95
4,643.05
4,715.75
4,869.90
5,175.70
5,235.60
5,396.40
5,703.80
5,761.40
5,910.40
6,216.65
6,271.15
6,420.10
6,727.85
6,788.55
6,952.30
7,274.65
7,347.35
7,502.25
7,814.55
7,890.60
8,075.95
8,410.55
8,486.80
8,639.50
8,951.00
9,019.35
9,176.90
9,481.10
9,538.80
9,696.20
10,012.20
10,092.00
10,261.40
10,593.95
10,689.00
Accumulative
Cost to Date
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
241.50
383.50
548.95
879.30
956.25
1,109.05
1,413.00
1,483.85
1,648.35
1,958.60
2,016.80
2,175.20
2,483.55
2,543.90
2,707.70
3,031.80
3,100.45
3,252.55
3,552.65
3,602.35
3,758.85
4,073.95
4,150.85
4,320.95
4,643.05
4,715.75
4,869.90
5,175.70
5,235.60
5,396.40
5,703.80
5,761.40
5,910.40
6,216.65
6,271.15
6,420.10
6,727.85
6,788.55
6,952.30
7,274.65
7,347.35
7,502.25
7,814.55
7,890.60
8,075.95
8,410.55
8,486.80
8,639.50
8,951.00
9,019.35
9,176.90
9,481.10
9,538.80
9,696.20
10,012.20
10,092.00
10,261.40
10,593.95
10,689.00
10,868.20
Inventory Management • CHAPTER 12 • 333
TN 7. Wagner-Whitin (WW) Solution
Period
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Average
Demand
Lot Size
870
901
960
702
1068
975
977
662
1147
1085
1041
890
1001
960
863
794
1109
948
1040
1008
961
828
764
933
960
988
1028
967
918
965
1068
996
1123
855
1035
1085
824
941
883
828
993
1008
852
725
667
1015
1167
878
824
863
1085
1067
930
1021
828
724
987
737
750
765
0
1733
0
0
3682
0
0
0
2232
0
2932
0
0
2617
0
0
3097
0
0
2797
0
0
2657
0
0
2983
0
0
2951
0
0
2974
0
0
2944
0
0
2652
0
0
2853
0
0
2407
0
0
3732
0
0
0
3082
0
0
2573
0
0
3239
0
0
0
902.3
Minimum Total Cost
6673.10
End Inventory
1700
830
1662
702
0
2614
1639
662
0
1085
0
1891
1001
0
1657
794
0
1988
1040
0
1789
828
0
1893
960
0
1995
967
0
2033
1068
0
1978
855
0
1909
824
0
1711
828
0
1860
852
0
1682
1015
0
2565
1687
863
0
1997
930
0
1552
724
0
2252
1515
765
0
973.9
End Backorder
Cum. Cost
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
41.5
324.6
359.7
359.7
690.4
772.35
805.45
805.45
1059.7
1059.7
1354.25
1404.3
1404.3
1687.15
1726.85
1726.85
2026.25
2078.25
2078.25
2367.7
2409.1
2409.1
2703.75
2751.75
2751.75
3051.5
3099.85
3099.85
3401.5
3454.9
3454.9
3753.8
3796.55
3796.55
4092
4133.2
4133.2
4418.75
4460.149
4460.149
4753.149
4795.75
4795.75
5079.85
5130.6
5130.6
5458.85
5543.2
5586.35
5586.35
5886.2
5932.7
5932.7
6210.3
6246.5
6246.5
6559.1
6634.85
6673.1
6673.1
334 • PART 3 • Managing Value Chains
CASE: PARTS EMPORIUM *
A. Synopsis
This case describes the problems facing Sue McCaskey, the new materials manager of a
wholesale distributor of auto parts. She seeks ways to cut the bloated inventories while
improving customer service. Back orders with excessive lost sales are all too frequent.
Inventories were much higher than expected when the new facility was built, even though
sales have not increased. Summary data on inventory statistics, such as inventory turns,
are not available. McCaskey decides to begin with a sample of two products to uncover
the nature of the problems—the EG151 exhaust gasket and the DB032 drive belt.
B. Purpose
The purpose of this case is to allow the student to put together a plan, using either a
continuous review system (Q system) or a periodic review system (P system), for two
inventory items. Enough information is available to determine the EOQ and R for a
continuous review system (or P and T for a periodic review system). Because stockouts
are costly relative to inventory holding costs, a 95% cycle-service level is recommended.
Inventory holding costs are 21% of the value of each item (expressed at cost). The
ordering costs ($20 for exhaust gaskets and $10 for drive belts) should not be increased
to include charges for making customer deliveries. These charges are independent of the
inventory replenishment at the warehouse and are reflected in the pricing policy.
C. Analysis
We now find appropriate policies for a Q system, beginning with the exhaust gasket. Shown
here are the calculations of the EOQ and R, followed by a cost comparison between this
continuous review system and the one now being used. The difference is what can be realized
by a better inventory control system. Reducing lost sales due to back orders is surely the
biggest benefit.
1. EG151 Exhaust Gasket
a. New plan
Begin by estimating annual demand and the variability in the demand during the
lead time for this first item. Working with the weekly demands for the first 21
weeks of this year and assuming 52 business weeks per year, we find the EOQ as
follows:
Weekly demand average = 102 gaskets/week
Annual demand (D) = 102(52) = 5304 gaskets
Holding cost = $1.85 per gasket per year (or 0.21 × 0.68 × $12.99)
Ordering cost = $20 per order
EOQ = 2 ( 5,304 )( $20 ) $1.85 = 339 gaskets
Turning to R, the Normal Distribution appendix shows that a 95% cycle-service
level corresponds to a z = 1.645. We then find
*
This case was prepared by Dr. Rob Bregman, University of Houston, as a basis for classroom discussion.
Inventory Management • CHAPTER 12 • 335
Standard deviation in weekly demand (σ t ) = 2.86 gaskets, where t = 1σ
Standard deviation in demand during lead time (σ L ) = 2.86
2=4
R = Average demand during the lead time + Safety stock
= 2(102) + 1.645(4) = 210.6, or 211 gaskets
b. Cost comparison
After developing their plan, students can compare its annual cost with what would
be experienced with current policies.
Cost Category
Ordering cost
Holding cost (cycle inventory)
TOTAL
Current Plan
$707
139
$846
Proposed Plan
$313
314
$627
The total of these two costs for the gasket is reduced by 26 percent (from $846 to
$627) per year. The safety stock with the proposed plan may be higher than the
current plan, if the reason for the excess back orders is that no safety stock is now
being held (inaccurate inventory records or a faulty replenishment system are other
explanations). The extra cost of this safety stock is minimal, however. Only four
gaskets are being held as safety stock, and their annual holding cost is just another
$1.85(4) = $7.40.
Surely the lost sales due to back orders are substantial with the current plan
and will be much less with the proposed plan. One symptom of such losses is that
11 units are on back order in week 21. A lost sale costs a minimum of $4.16 per
gasket (0.32. × $12.99). If 10 percent of annual sales were lost with the current
policy, this cost would be $4.16(0.10)(5304) = $2,206 per year. Such a loss would
be much reduced with the 95% cycle-service level implemented with the
proposed plan.
2. DB032 Drive Belt
a. New plan
The following demand estimates are based on weeks 13 through 21. Weeks 11
and 12 are excluded from the analysis because the new product’s start-up makes
them unrepresentative. We find the EOQ as follows:
Weekly demand average = 52 belts/week
Annual demand (D) = 52(52) = 2704 belts
Holding cost $0.97 per belt per year (or 0.21 × 0.52 × $8.89)
Ordering cost $10 per order
EOQ = 2 ( 2, 704 )( $10 ) $0.97 = 236 gaskets
Turning now to R, where z remains at 1.645, we find:
Standard deviation in weekly demand (σ t ) = 1.76 belts, where t = 1
Standard deviation in demand during lead time (σ L ) = 1.76 3 = 3 belts
R = Average demand during the lead time + Safety stock
= 3(52) + 1.645(3) = 160.9, or 161 belts
336 • PART 3 • Managing Value Chains
b. Cost comparison
After developing their plan, students again can compare the cost for the belts with
what would be experienced with current policies.
Cost Category
Ordering cost
Holding cost (cycle inventory)
TOTAL
Current Plan
$ 27
485
$512
Proposed Plan
$115
114
$229
With the belt, the total of these two costs is reduced by 55 percent. The safety
stock with the proposed plan may be higher with the proposed system, as with the
gaskets, but added cost for safety stock is only $0.97(3) = $2.91.
The big cost once again is the lost sales due to back orders with the current plan.
A lost sale costs a minimum of $4.27 per belt (0.48 × $8.89). If 10 percent of annual
sales were lost, the cost with the current policy would be $4.27(0.10)(2704) = $1,155.
Such a loss would be much less with the 95% cycle-service level implemented with
the proposed plan.
D. Recommendations
For the gasket, the recommendation is to implement a continuous review system with
Q = 339 and R = 211. For the belt, the recommendation is to implement a continuous
review system with Q = 236 and R = 161.
E. Teaching Strategy
This case can be used as a “cold-call” case or as a short case prepared in advance of the
class meeting. If used without prior student preparation, it works best as a team
assignment. Each team can have a different assignment (P or Q system, gasket or belt).
When used as a cold-call case and time is a concern, the instructor should provide the
mean and standard deviation of the weekly demand for the two products.
Begin with a general discussion of how to do the analysis and then work through the
analysis. If done with teams, give each time to follow through. After the teams develop
their policies, have them make the cost comparison. It brings back the fundamental
notions of cycle inventory and ordering costs that were introduced in this Inventory
Management chapter. The discussion at the end can broaden into other issues, such as
applying the notion of inventory levers and the use of systems other than a Q system to
control inventories.
If time permits, the instructor can have the class hand-simulate their policies, using
the actual demand data in the first 21 weeks of this year for the gaskets and the last 9
weeks of this year for the belts. Use a form to record the simulation, either as a handout
or transparency. The starting conditions on back orders, scheduled receipts, and on-hand
inventory can be what is mentioned in the case for week 21. Simulating the new system is
similar to what is to be done in Advanced Problem 29 in the chapter.