3 session 3a risk_pooling
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Transcript of 3 session 3a risk_pooling
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Dr. RAVI SHANKARProfessor
Department of Management Studies
Indian Institute of Technology DelhiHauz Khas, New Delhi 110 016, India
Phone: +91-11-26596421 (O); 2659-1991(H); (0)-+91-9811033937 (m)Fax: (+91)-(11) 26862620
Email: [email protected]://web.iitd.ac.in/~ravi1
SESSION#3: TUTORIAL ON RISK POOLING (CFVG: 2012)
A TUTORIAL ON RISK POOLING
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RISK POOLINGRisk pooling is an important concept in supply chain management. The idea of risk pooling is executed by a centralized distribution system which caters to the requirements of all the markets in a given region instead of separate warehouse allocated for different markets.
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Market Two
Risk Pooling
• Consider these two systems:
Supplier
Warehouse One
Warehouse Two
Market One
Market Two
Supplier Warehouse
Market One
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Supplier
Warehouse
Retailers
Centralized Systems
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Decentralized System
Supplier
Warehouses
Retailers
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Demand Forecasts
• The three principles of all forecasting techniques:
– Forecasting is always wrong
– The longer the forecast horizon the worst is the
forecast
– Aggregate forecasts are more accurate
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The Effect of
Demand Uncertainty• Most companies treat the world as if it were predictable:
– Production and inventory planning are based on forecasts of demand made far in advance of the selling season
– Companies are aware of demand uncertainty when they create a forecast, but they design their planning process as if the forecast truly represents reality
• Recent technological advances have increased the level
of demand uncertainty:
– Short product life cycles
– Increasing product variety
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Market one
Market two
Factory
Central
warehouse
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Warehouse 1
Warehouse 2
Factory
Decentralized Warehouses
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Market one
Market two
Factory
Centralised
warehouse at
Ayutthaya
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Market Two
ABC Chiang Pai
Market One
Market Two
ABC Chiang Pai
Market One
Prachin Buri Warehouse
Pathumthani Warehouse
Central
warehouse:
Ayutthaya
Market Pathumthani
Market Prachin Buri
Factory: ABC
Central
warehouse
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Market Two
ABC company
Market One
Market Two
ABC company
Market One
Prachin Buri Warehouse
Pathumthani Warehouse
Central
warehouse
(Ayutthaya)
Market one
Market two
Market one
Market two
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WEEK 1 2 3 4 5 6 7 8
Pathumthani 68(-17) 37(+14) 45(+6) 58(-7) 16(+35) 32(+19) 72(-21) 80(-29)
Prachin Buri 87(-27) 62(-3) 55(+4) 67(-8) 12(+47) 42(+17) 69(-10) 81(-22)
TOTAL 155(-45) 99(+11) 100(+10) 125(-15) 28(+82) 74(+36) 141(-31) 161(-51)
PRODUCT A
0
10
20
30
40
50
60
70
80
90
100
1 2 3 4 5 6 7 8
WEEK
AV
ER
AG
E W
EE
KL
Y D
EM
AN
D
DEMAND Pathumthani
DEMAND Prachin Buri
HISTORICAL DEMAND DATA
51
59
110
Average
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Theoretical Approach
• Consider two markets
– Risk Polling by Aggregating Demand by
Centralized procurement, centralized
warehousing, centralized distribution like
super stores etc
– Risk Polling by Aggregating time horizon by
combining orders as discussed in previous
slide
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A Detail Analysis of
RISK POOLING Case
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The Basic EOQ Model
We assumed that, we will only keep half the inventory over a year then
The total carry cost/yr = Cc x (Q/2). Total order cost = Co x (D/Q)
Then , Total cost = 2Q
CQDCTC co +=
Finding optimal Q*
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Cost Relationships for Basic EOQ(Constant Demand, No Shortages)
TC
–A
nn
ual
Co
st
Total Cost
CarryingCost
OrderingCost
EOQ balances carryingcosts and ordering costs in this model.
Q* Order Quantity (how much)
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The Basic EOQ Model
• EOQ occurs where total cost curve is at minimum value and carrying cost equals
ordering cost:
•Where is Q* located in our model?
c
o
co
CDCQ
QCQDCTC
2
2
*
min
=
+=
(How to obtain this?)Then, *c
o
co
CDCQ
QCQDCTC
2
2
*
min
=
+=
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A Revision of model discussed in Sesion-3:
Model with “re-order points”• The reorder point is the inventory level at which a new order is placed.
• Order must be made while there is enough stock in place to cover demand during lead time.
• Formulation: R = dL, where d = demand rate per time period, L = lead time
Then R = dL = (10,000/311)(10) = 321.54
Working days/yr
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Reorder Point• Inventory level might be depleted at slower or faster rate during lead time.
• When demand is uncertain, safety stock is added as a hedge against stockout.
Two possible scenarios
Safety stock!
No Safety
stocks!
We should then ensure
Safety stock is secured!
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Determining Safety Stocks Using Service Levels
• We apply the Z test to secure its safety level,
)( LZLdR dσ+=
Reorder point
Safety stock
Average sample demand
How these values are represented in the diagram of normal distribution?
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Reorder Point with Variable Demand
stocksafety
yprobabilit level service toingcorrespond deviations standard ofnumber
demanddaily ofdeviation standard the
timelead
demanddaily average
pointreorder
where
=
=
=
=
=
=
+=
LZ
Z
L
d
R
LZLdR
d
d
d
σ
σ
σ
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Reorder Point with Variable Demand
Example
Example: determine reorder point and safety stock for service level of 95%.
26.1. : formulapoint reorder in termsecond isstock Safety
yd 1.3261.26300)10)(5)(65.1()10(30
1.65 Zlevel, service 95%For
dayper yd 5 days, 10 L day,per yd 30 d
=+=+=+=
=
===
LZLdR
d
dσ
σ
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A detail treatment of
this case study
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TERMINOLOGY
• AVG: Average daily demand faced by the distributor.
• STD: standard deviation of the daily demand faced by the distributor.
• L: Replenishment lead time from the supplier to the distributor in days
• K: Fixed cost (set up cost) incurred every time the warehouse places an order, it includes transportation cost.
• h: Cost of holding one unit of the product in the inventory for one day at the warehouse.
• α: Service level -the probability of not stocking out during lead time.
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• Average demand during lead time=L×AVG. This ensures that if a distributor places an order the system has enough inventory to cover expected demand during lead time.
• Safety stock= z×STD× this is the amount of inventory distributor needs to keep to meet deviations from average demand during lead time.
• z: Safety factor which is chosen from statistical table to ensure that probability of stock out is exactly 1-α
• Reorder level (s) = average demand during lead time + safety stock
=L×AVG + z×STD×Whenever the inventory level drops below reorder
level the distributor should place new order to raise itsinventory.
L
L
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• . Order quantity (Q): It is the number of items ordered each time places an order that minimizes the average total cost per unit of time distributor.
Q=
• Order-up-to level (S): Since there is variability in demand the distributor places an order for Q items whenever inventory is below reorder level (s).
S= Q + s
2K AVG
h
×
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• Average inventory = Q/2 + z STD
• Coefficient of variation =
×× L
STD
AVG L×
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A View of (s, S) Policy
Time
Inven
tory
Lev
el
S
s
0
Lead
Time
Lead
Time
Inventory Position
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EXAMPLE OF RISK
POOLINGLet us illustrate this with an example of a Chiang Paibased company ABC that produces certain type of products and distributes them in the South Thailand region .The current distribution system partitions S-Thailand region into two markets each of which has a warehouse.
1. One warehouse is located in Prachin Buri
2. Another one located in Pathumthani.
alternative strategy of centralized distribution system replaces two warehouses by a single warehouse located between the two cities in Ayutthaya that will serve all customer orders in both markets
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Market Two
Consider these two systems:
ABC company
Pathumthani Warehouse
Prachin Buri. Warehouse
Market One
Market Two
ABC companyCentral
warehouse
Market OneMarket one
Market two
Market two
Market one
Chiang Rai
Chiang Rai
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ASSUMPTIONS
• Manufacturing facility has sufficient capacity to
satisfy any warehouse demand
• Lead time for delivery to each warehouse is
about one week and is assumed to be constant.
• Delivery time does not change significantly if we
adopt a centralized distribution system.
• Service level of 95% that is the probability of
stocking out is 5% is maintained.
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DATA ANALYSIS
Now with analysis of weekly demand for two different products, product A and product B produced by ABC company for last 8 weeks in both market zones we will be able to decide which distribution strategy will be more efficient and cost effective.
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WEEK 1 2 3 4 5 6 7 8
Pathum 68 37 45 58 16 32 72 80
Prachine 87 62 55 67 12 42 69 81
TOTAL 155 99 100 125 28 74 141 161
PRODUCT A
0
10
20
30
40
50
60
70
80
90
100
1 2 3 4 5 6 7 8
WEEK
AV
ER
AG
E W
EE
KL
Y D
EM
AN
D
DEMAND Pathum
DEMAND Prachine
HISTORICAL DEMAND DATA FOR PRODUCT A
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WEEK 1 2 3 4 5 6 7 8
Pathum 0 0 1 3 2 4 0 1
Prachine 1 0 2 0 0 3 1 1
TOTAL 1 0 3 3 2 7 1 2
PRODUCT B
00.5
1
1.52
2.5
33.5
4
4.5
1 2 3 4 5 6 7 8
WEEK
AV
ER
AG
E D
EM
AN
D
DEMAND Pathum DEMAND Prachine
HISTORICAL DEMAND DATA FOR PRODUCT B
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ANALYSIS OF HISTORICAL DATA
PRODUCT AVERAGEDEMAND
STANDARDDEVIATION
COEFFICIENT OF
VARIATION
Pathum A 51 20.70 0.41
Prachin B 1.38 1.41 1.02
Pathum A 59.38 22.23 0.32
Prachin B 1 1 1
CENTRAL A 110.38 39.14 0.35
CENTRAL B 2.38 1.99 0.84
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SAMPLE CALCULATIONS
FOR PRODUCT A IN Pathumthani WAREHOUSE
1. Average demand = (68+37+45+58+16+32+72+80)/8=51
2. Standard deviation of demand =
= 20.7
3. Coefficient of variation = 20.7/51 = 0.41
2 2 2(68 51) (51 37) .............. (80 51)
8
− + − + −
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GENERALIZATIONS
• average demand for product A is much higher than product B which is a slow moving product.
• Both standard deviation (absolute) and coefficient of variation (relative to average demand) are measure of variability of demand but we find that STD for product A is higher but coefficient of variation of product B is higher.
• For centralized distribution average demand is simply the sum of the demand faced by each of existing warehouse
• However the variability of demand as measured by STD or COV faced by central warehouse is lower than that faced by the two existing ones.
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NUMERICAL VALUES
• Safety factor (Z) =1.65
• Fixed cost for both the products (Co) = Rs 3500
• Inventory holding cost (Cc) = Rs 18.5 per unit per week.
• Cost of transportation from warehouse to a customer – Current distribution system = Rs 50 per product
– Centralized distribution system = Rs 60 per product.
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INVENTORY LEVELS
PRODUCT AVERAGE DEMAND DURINGLEAD TIME
SAFETY STOCK
(SS)
REORDERPOINT
(s)
ORDERQUANTITY
(Q)
ORDERUPTOLEVEL(S)
AVERAGE
INVENTORY
Pathum A 51 34.16 85 139 224 104
Prachine B 1.38 2.33 4 23 27 14
Pathum A 59.38 36.68 96 150 246 112
Prachine B 1 1.65 3 19 22 11
CENTRAL A 110.38 64.58 175 204 379 167
CENTRAL B 2.38 3.28 6 30 36 18
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4. Safety stock =1.65 20.7 = 34.16
5. Reorder point = 51 + 34.16 = 85.16
6. Order quantity = = 139
7. Order up to level = 139 +85 = 224
8. Average inventory = 139/2 +34.16 = 103.66
× × 1
2 3500 51
18.5
× ×
SAMPLE CALCULATIONSFOR PRODUCT A IN Pathumthani WAREHOUSE
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% REDUCTION IN
INVENTORY
REDUCTION IN AVERAGE INVENTORY
PRODUCT A = = 22.7%
PRODUCT B = = 28%
(104 112 167)100
(104 112)
+ −×
+
(14 11 18)100
(14 11)
+ −×
+
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NORMAL DISTRIBUTIONAverage mean = 0
Standard deviation = 1
X axis- safety factor
Shaded area under curve= service level
Z=1.65P(z)=.95
Z=0
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Demand Variability: Example 1
Product Demand
150
75
225
100
150
50
125
6148 53
104
45
0
50
100
150
200
250
Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar
Month
Demand
(000's)
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Reminder:
The Normal Distribution
0 10 20 30 40 50 60Average = 30
Standard Deviation = 5
Standard Deviation = 10
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ANALYSIS AT DIFFERENT
SERVICE LEVELS
When average inventory for different level of service is calculated corresponding to varying value of z it was found that there exists a trade-off between service level and reduction in inventory through risk pooling.
SERVICE LEVEL (%)
90 91 92 93 94 95 96 97 98 99 99.9
Z 1.29 1.34 1.41 1.48 1.56 1.65 1.75 1.88 2.05 2.33 3.08
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PERCENTAGE REDUCTION IN AVERAGE INVENTORY VS
SERVICE LEVEL
0
5
10
15
20
25
30
90 93 96 99
SERVICE LEVEL
% R
ED
UC
TIO
N I
N A
VG
INV
EN
TO
RY
PRODUCTAPRODUCTB
SERVICE
LEVEL (%)90 91 92 93 94 95 96 97 98 99 99.9
PRODUCT A
24 23.7 23.4 23.1 23 22.7 22.3 21.8 21.7 21.2 19.5
PRODUCT B
27.12 27.07 27.0 26.94 26.89 26.82 26.72 26.59 26.44 26.2 25.65
% REDUCTION IN AVERAGE INVENTORY
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Following generalizations are made
• If a company goes for higher level of service it has to compromise with the % of reduction in the inventory level and vice versa.
• To provide high service level company has to maintain high inventory too.
• % reduction in inventory decreases with increase in service level.
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IDEAL SITUATION
This works best for
– High coefficient of variation, which reduces required
safety stock.
– Negatively correlated demand as in such a case the
high demand from one customer will be offset by low demand from another