Supply Chain Management: Indian Institute of Management Lucknow
Supply Chain Management: Indian Institute of Management Lucknow
Supply Chain Management: Indian Institute of Management Lucknow
1/20/2016
On
On--hand inventory
Q2
P
Q1
Q3
P
P
Time
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Figure 11.9
3
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1/20/2016
Car Showrooms
Backordering is allowed
Furniture Shops
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Inventory level
Order quantity
= Q (maximum
inventory
level)
Average
inventory on
hand
Q - So
2
Zero
inventory
So
T1
Q* =
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T2
2DS (H + Cbo)
H*C
H*
Cbo
Time
So =
2DSH
Cbo*(H + Cbo)
7
Q* =
2DS (H + Cbo)
H*C
H*
Cbo
So =
= 1837.1
= 612.4
2DSH
Cbo*(H + Cbo)
Multi-Echelon Inventories
Control the entire channel inventory levels, not just a
single echelon.
Warehouse
echelon
Warehouse
lead-time, LTw
S
Supplier
da
e
l
l
i
a
t
Re e, LT R
tim
R1
R2
d 1 , s d1
d 2 , sd 2
Warehouse
R3
d 3 , sd 3
Retailer
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10
11
Warehouse
1
2
3
Current
stock
level,
units
400
350
0
Forecasted
demand,
units
2,300
1,400
900
4,600
Forecast
error (std.
dev.), units
100
55
20
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12
Total
requirements
a
2,428
1,470
926
4,824
= 2,300 + 1.28(100)
13
(2)
(3)=
(4)
(5)=
Pro(4)+(3)
(1)- (2)
Total
Onration
Net
require- hand requireAlloof
Ware- ments, stock, ments, excess, cation,
house units
units
units
units
units
a
b
1
2,428
400 2,028
463
2,491
2
1,470
350 1,120
282
1,402
3
926
0
926
181
1,107
c
Total 4,824
4,074
926
5,000
aTotal
14
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Monthly
avg., units
Std. dev.,
units
Retailer 1
202.5
16.8
Retailer 2
100.5
15.6
Retailer 3
302.5
18.0
Combined
605.5
32.4
15
Retailer 1
218
188
225
217
176
187
221
212
210
203
188
185
202.5
16.8
Retailer 2
101
87
123
101
95
97
93
131
76
101
87
114
100.5
15.6
Retailer 3
268
296
321
312
301
294
285
305
289
303
324
332
302.5
18.0
Combined
587
571
669
630
572
578
599
648
575
607
599
631
605.5
32.4
16
Example (Contd)
Solution
Based on reorder point inventory control, the retailers
inventory statistics are
Retailer 1
Retailer 2
Retailer 3
Reorder qty, Q
312
220
381
61
35
87
167
120
202
2DW SW
QW =
= 2(605.5x12)(75) = 1,043.98, or 1,044 units
0.20(5)
ICW
17
18
C = $5/unit
P = 0.99 during lead time
Supply Chain Management
19
Processing time
= 1 , s 2p = 0 .1
Transport time
Inbound transport
No significant
inventory at pool
points and trucks
= 4 , s i2 = 1. 0
Outbound transport
Pool point
Transport time
X
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Distributor
= 2 , s o2 = 0 . 25
20
where
2
= sp2 + si2 + so2
sLT
= 0.1 + 1.0 + 0.25
= 1.35 days
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21
Now
s' = 7 x102 +1002 x1.35 = 14,200 =119.16 units
and
2(100)(10)
= 1208.3 units
(0.1/365)(5)
1208.3
Q*
'
+ z(s ) =
+ 2.33(119.16) = 882 units
AIL =
2
2
ROP = 978 units
Q*
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22
IT = Ii n
where
IT = amount of inventory at one location
Ii = amount of inventory at each of n locations
n = number of stocking points
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24
where
I2 = system inventory in n2 locations
I1 = system inventory in n1 locations
n2 = no. of new locations
n1 = no. of previous locations
So,
2
I2 = 3,000,000
= 2,449,490
3
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25
Inventory-Throughput Curve
Example
Suppose two warehouses with 390,000 lb. and
770,000 lb. of throughput respectively are to be
consolidated into a single warehouse with 390,000 +
770,000 = 1,160,000 lb. of annual throughput. How
much inventory is likely to be in the single warehouse?
The inventory-throughput curve developed from the
companys multiple warehouse stocks is shown in the
figure below.
Note Reading from the plot, the inventory in the
consolidated warehouse has dropped to 262,000 lb.
from 132,000 + 203,000 = 335,000 lb. in the two
warehouses.
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26
Inventory-Throughput Curve
Average inventory level, AIL (000 lb.)
i
450
400
350
AILi = 3.12Di0.628
300
262
250
203
200
150 132
100
Current
warehouse
50
Consolidated
warehouse
0
0
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200
400
600
800
1000
1200
1400
Annual warehouse throughput, Di (000 lb.)
Supply Chain Management
1600
1800
27
Annual
Average
warehouse
inventory
throughput, $
level, $
21,136,032
2,217,790
16,174,988
2,196,364
78,559,012
9,510,027
17,102,486
2,085,246
88,228,672 11,443,489
40,884,400
5,293,539
TO ratio =
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Warehouse
no.
7
8
9
10
11
12
Totals
$425,295,236
= 9.7
$43,701,344
Supply Chain Management
Annual
warehouse
throughput, $
43,105,917
47,136,632
24,745,328
57,789,509
16,483,970
26,368,290
425,295,236
Average
inventory
level, $
6,542,079
5,722,640
2,641,138
6,403,076
1,991,016
2,719,330
43,701,344
$ are at cost
28
Economies of Scale
Supply / Demand
Variability
Seasonal
Variability
Cycle Inventory
Safety Inventory
Seasonal Inventory
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