Managing Flow Variability: Safety Inventory
Centralization and ROP
1
At- Ft; Decentralized vs. Centralized
P1
P2
P3
P4
P5
Total
1
2
4
-3
4
-2
5
2
0
0
5
0
1
6
3
2
5
-2
1
0
6
4
-1
2
-4
1
-2
-4
5
1
-4
-4
4
3
0
6
-2
-1
4
5
1
7
7
4
-5
0
5
-5
-1
8
-2
2
2
0
-4
-2
9
-4
1
1
4
3
5
10
-1
-1
-4
-2
4
-4
11
4
1
3
2
0
10
12
2
0
-4
-3
2
-3
13
-4
-1
2
-1
-4
-8
14
0
-5
4
5
-2
2
15
-5
4
4
0
-4
-1
16
4
2
2
1
3
12
17
-3
2
-2
5
-3
-1
18
3
1
-3
-1
3
3
19
2
3
-3
-5
3
0
20
0
-3
1
-1
-4
-7
21
-3
4
-4
0
5
2
22
4
1
-5
4
0
4
23
0
-4
-5
0
-5
-14
24
-2
0
-2
-4
-2
-10
25
2
5
-2
5
-1
9
26
4
5
5
0
1
15
27
2
1
4
1
-1
7
28
0
-3
3
0
-2
-2
29
3
-2
-1
-1
-4
-5
30
-2
1
-4
-4
0
-9
4
5
5
5
5
15
Month
Managing Flow Variability: Safety Inventory
Centralization and ROP
2
What is the optimal inventory
level at each WH?
Warehouse A
Demand
N~(100,10^2)
Central Warehouse
Warehouse B
Demand
N~(100,10^2)
What is the
optimal target
inventory level at
Demand N~(100,10^2)
Demand N~(100,10^2)
CWH?
Managing Flow Variability: Safety Inventory
Physical Centralization
3
Demand in the two warehouses are independent. Both warehouses
have the same distribution for their lead time demand.
LTD1: N(LTD, σLTD )
LTD2: N(LTD, σLTD )
Both warehouses have identical service levels
To provide desired SL, each location must carry Isafety = zσLTD
Isafety = zσLTD
z is determined by the desired service level
The total safety inventory in the decentralized system is
I
D
Safety
 2 z LTD
Managing Flow Variability: Safety Inventory
Independent Lead time demands at two locations
4
LTDC = LTD1 + LTD2
LTDC = LTD + LTD = 2 LTD
C
VarLTD
  2 LTD   2 LTD  2 2 LTD
C
 LTD
 2 LTD
I
C
Safety
 z 2 LTD
I
D
Safety
 2 z LTD
Centralization reduced the safety inventory by a factor of 1/√2
Managing Flow Variability: Safety Inventory
Independent Lead time demands at two locations
5
GE lighting operating 7 warehouses throughout Europe. A warehouse
with average lead time demand of 20,000 units with a standard
deviation of 5,000 units and a 95% service level. What would be the
impact on safety inventory if they are replaced Centralize Europe
Warehouse. Isafety = 1.65×5000= 8250
I
D
safety
 7  8,250  57,750
C
I safety
 1.65  7  5000  21,827
Decrease in safety inventory by a factor of
Centralization of N locations:
7  2.65
c
I safety
 z N  LTD
Independent demand in N locations: Total safety inventory to
provide a specific SL increases not by N but by √N
Managing Flow Variability: Safety Inventory
independent Lead time demands at N locations
6
In Waiting Line; Centralization (Polling) leads to flow time reduction and
throughput improvement.
In Inventory; Centralization leads to reduction in Cycle Inventory,
reduction in Safety Inventory, and flow time reduction.
If centralization of stocks reduces inventory, why doesn’t everybody do it?
– Longer response time
– Higher shipping cost
– Less understanding of customer needs
– Less understanding of cultural, linguistics, and regulatory barriers
These disadvantages may reduce the demand.
Managing Flow Variability: Safety Inventory
Dependent Demand
7
Does centralization offer similar
benefits when demands in
multiple locations are correlated?
120
100
80
60
40
LTD1 and LTD2 are statistically
identically distributed but correlated
with a correlation coefficient of ρ .
20
0
0
10
20
30
40
50
60
70
80
90
100
No Correlation: ρ close to 0
C
( LTD
) 2   2 LTD   2 LTD  2  LTD LTD
C
2
( LTD
) 2   2 LTD   2 LTD  2  LTD
 2(1   ) 2 LTD
C
 LTD
 2(1   ) LTD
C
I safety
 z  2(1   ) LTD
If LTD1 and LTD2 are independent   =0
C
I safety
 z  2 LTD
Managing Flow Variability: Safety Inventory
+ Correlation, + Perfect Correlation
8
100
120
90
100
80
70
80
60
50
60
40
40
30
20
20
10
0
0
0
10
20
30
40
50
60
70
80
90
100
Positive Correlation: ρ close to 1
0
10
20
30
40
50
60
70
80
90
100
Perfect Positive Correlation: ρ = +1
120
100
90
100
80
70
80
60
50
60
40
40
30
20
20
10
0
0
0
10
20
30
40
50
60
70
80
90
100
Negative Correlation: ρ close to -1
0
10
20
30
40
50
60
70
80
90
100
Perfect Negative Correlation: ρ = -1
Managing Flow Variability: Safety Inventory
Correlation
9
C
I safety
 2(1   )  z   LTD
D
I safety
 2  z   LTD
The safety inventory in the two-location decentralized system is larger
than in the centralized system by a factor of
2/
2(1   ) 
2 /(1   )
If demand is positively fully correlated, ρ = 1, centralization
offers no benefits in the reduction of safety inventory
Benefits of centralization increases as the demand on the two
locations become negatively correlated. The best case is  = -1,
where we do not need safety inventory at all
Managing Flow Variability: Safety Inventory
Principle of Aggregation and polling Inventory
10
Inventory benefits  due to principle of aggregation.
Statistics: Standard deviation of sum of random variables is less than
the sum of the individual standard deviations.
Physical consolidation is not essential, as long as available inventory is
shared among various locations  Polling Inventory
–
Virtual Centralization
–
Specialization
–
Component Commonality
–
Delayed Differentiation
–
Product Substitution
Managing Flow Variability: Safety Inventory
Virtual Centralization
11
Virtual Centralization: inventory polling in a network of locations is
facilitated using information regarding availability of goods and subsequent
transshipment of goods between locations to satisfy demand.
Location A
Exceeds Available stock
Location B
Less than Available stock
1. Information about product demand and availability must be available
at both locations
2. Shipping the product from one location to a customer at another
location must be fast and cost effective
polling is achieved by keeping the inventories at decentralized locations.
Managing Flow Variability: Safety Inventory
Specialization, Substitution
12
Demand for both products exist in both locations. But a large
portion of demand for P1 is in location A, while a large portion
of demand for P2 is in location B.
Location A
Location B
Product P1
Product P2
Both locations keep average inventory.
Safety inventory is kept only in the specialized warehouse
One other possibility to deal with variability is product substitution.
Managing Flow Variability: Safety Inventory
Component Commonality
13
Up to now we have discussed aggregating demand across various geographic
locations, either physical or virtual
Aggregating demand across various products has the same benefits.
Computer manufacturers: offer a wide range of models, but few components,
CPU, RMA, HD, CD/DVD drive, are used across product lines.
Replace Make-to-stock with make Make-to-Order
Commonality + MTO:
Commonality: Safety inventory of the common components much less than
safety inventory of unique components stored separately.
MTO: Inventory cost is computed in terms of WIP cost not in terms of
finished good cost (which is higher).
Managing Flow Variability: Safety Inventory
Postponement (Delayed Differentiation)
14
Forecasting Characteristic: Forecasts further into the future tends to be
less accurate than those of more imminent events.
Since shorter-range forecasts are more accurate, operational decisions
will be more effective if supply is postponed closer to the point of
actual demand.
Two Alternative processes (each activity takes one week)
 Alternative A: (1) Coloring the fabric, (2) assembling T-shirts
 Alternative B: (1) Assembling T-shirts, (2) coloring the fabric
No changes in flow time. Alternative B postponed the color difference
until one week closer to the time of sale. Takes advantage of the
forecasting characteristic: short-Range forecast more accurate.
Managing Flow Variability: Safety Inventory
Postponement (Delayed Differentiation)
15
Two advantages: Taking advantage of two demand forecasting
characteristics
 Commonality Advantage: At week 0; Instead of forecast for each
individual item, we forecast for aggregates item – uncolored Tshirt. Forecast for aggregate demand is more accurate than forecast
for individual item. It is easier to more accurately forecast total
demand for different colored T-shirts for next week than the week
after the next.
 Postponement Advantage: Instead of forecasting for each
individual items two weeks ahead, we do it at week 1. Shorter rang
forecasts are more accurate. It is easier to more accurately forecast
demand for different colored T-shirts for next week than the week
after the next.
Managing Flow Variability: Safety Inventory
Lessons Learned
16
Levers for Reducing Safety Capacity
 Reduce demand variability through improved forecasting
 Reduce replenishment lead time
 Reduce variability in replenishment lead time
 poll safety inventory for multiple locations or products
 Exploit product substitution
 Use common components
 Postpone product-differentiation processing until closer to the
point of actual demand