supply chain management lecture 10. outline today –finish chapter 6 (decision tree analysis)...
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Supply Chain Management
Lecture 10
Outline
• Today– Finish Chapter 6 (Decision tree analysis)– Start chapter 7
• Tomorrow– Homework 2 due before 5:00pm
• Next week– Chapter 7 (Forecasting)
Example: Decision Tree Analysis
• New product with uncertain demand ($85 profit/unit)– Annual demand expected to go up by 20% with
probability 0.6– Annual demand expected to go down by 20% with
probability 0.4– Use discount factor k = 0.1
Example
5. Represent the tree, identifying all states as well as all transition probabilities
D=144
D=96
D=64
D=120
D=80
D=100
0.6
0.4
Period 0
Period 2
0.6
0.4
0.6
0.4
Period 1 P = 12240
P = 8160
P = 5440P = 80*85+(0.6*8160+0.4*5440)/1.1 = 13229
P = 120*85+(0.6*12240+0.4*8160)/1.1 = 19844
P = 100*85+(0.6*19844+0.4*13229)/1.1 = 24135
Example
5. Represent the tree, identifying all states as well as all transition probabilities
D=144
D=96
D=64
D=120
D=80
D=100
0.6
0.4
Period 0
Period 2
0.6
0.4
0.6
0.4
Period 1
Calculate the NPV of each possible scenario separately
Example
5. Represent the tree, identifying all states as well as all transition probabilities
D=144
D=96
D=64
D=120
D=80
D=100
0.6
0.4
Period 0
Period 2
0.6
0.4
0.6
0.4
Period 1
Calculate the NPV of each possible scenario separately
Scenario C_0 C_1 C_2 NPV Prob100, 120, 144 100*85 (120*85)/1.1 (144*85)/1.21 27888 0.36 10040100, 120, 96 100*85 (120*85)/1.1 (96*85)/1.21 24517 0.24 5884100, 80, 96 100*85 (80*85)/1.1 (96*85)/1.21 21426 0.24 5142100, 80, 64 100*85 (80*85)/1.1 (64*85)/1.21 19178 0.16 3069
24135
Decision Trees (Summary)
• A decision tree is a graphic device used to evaluate decisions under uncertainty
1. Identify the duration of each period and the number of time periods T to be evaluated
2. Identify the factors associated with the uncertainty
3. Identify the representation of uncertainty
4. Identify the periodic discount rate k
5. Represent the tree, identifying all states and transition probabilities
6. Starting at period T, work back to period 0 identify the expected cash flows at each step• (Alternatively, calculate the NPV of each possible scenario
separately)
Decision Trees
• Using decision trees to evaluate network design decisions– Should the firm sign a long-term contract for
warehousing space or get space from the spot market as needed
– What should the firm’s mix of long-term and spot market be in the portfolio of transportation capacity
– How much capacity should various facilities have? What fraction of this capacity should be flexible?
Example: Decision Tree Analysis
• Three options for Trips Logistics1. Get all warehousing space from the spot market as
needed
2. Sign a three-year lease for a fixed amount of warehouse space and get additional requirements from the spot market
3. Sign a flexible lease with a minimum change that allows variable usage of warehouse space up to a limit with additional requirement from the spot market
Example: Decision Tree Analysis
• Trips Logistics input data– Evaluate each option over a 3 year time horizon (1
period is 1 year)• Demand D may go up or down each year by 20% with
probability 0.5• Warehouse spot price p may go up or down by 10%
with probability 0.5• Discount rate k = 0.1
Example
5. Represent the tree, identifying all states
D=100
p=$1.20
Period 0
D=120
p=$1.32
D=120
p=$1. 08
D=80
p=$1.32
D=80
p=$1.08
Period 1
D=144
p=$1.45
D=144
p=$1.19
D=96
p=$1.45
D=144
p=$0.97
D=96
p=$1.19
D=96
p=$0.97
D=64
p=$1.45
D=64
p=$1.19
D=64
p=$0.97
Period 2
0.25
0.25
0.25
0.25
0.250.25
0.25
0.25
Example – Option 1 (Spot)
6. Starting at period T, work back to period 0 identify the expected cash flows at each step• C(D = 144,000, p = 1.45, 2) = 144,000 x 1.45
= $208,800 • R(D = 144,000, p = 1.45, 2) = 144,000 x 1.22
= $175,680• P(D = 144,000, p = 1.45, 2) = R – C
= 175,680 – 208,800
= –$33,120
D=144
p=$1.45
D=144
p=$1.19
D=96
p=$1.45
D=144
p=$0.97
D=96
p=$1.19
D=96
p=$0.97
D=64
p=$1.45
D=64
p=$1.19
D=64
p=$0.97
Period 2
Cost
Revenue
Profit
Example – Option 1 (Spot)
6. Starting at period T, work back to period 0 identify the expected cash flows at each step
D=144
p=$1.45
D=144
p=$1.19
D=96
p=$1.45
D=144
p=$0.97
D=96
p=$1.19
D=96
p=$0.97
D=64
p=$1.45
D=64
p=$1.19
D=64
p=$0.97
Period 2
Revenue Cost ProfitR(D =, p =, 2) C(D =, p =, 2) P(D =, p =, 2)
D = 144 p = 1.45 144,000x1.22 144,000x1.45 ($33,120)D = 144 p = 1.19 144,000x1.22 144,000x1.19 $4,320D = 144 p = 0.97 144,000x1.22 144,000x0.97 $36,000D = 96 p = 1.45 96,000x1.22 96,000x1.45 ($22,080)D = 96 p = 1.19 96,000x1.22 96,000x1.19 $2,880D = 96 p = 0.97 96,000x1.22 96,000x0.97 $24,000D = 64 p = 1.45 64,000x1.22 64,000x1.45 ($14,720)D = 64 p = 1.19 64,000x1.22 64,000x1.19 $1,920D = 64 p = 0.97 64,000x1.22 64,000x0.97 $16,000
Example – Option 1 (Spot)
6. Starting at period T, work back to period 0 identify the expected cash flows at each step• EP(D = 120, p = 1.22, 1) =
0.25xP(D = 144, p = 1.45, 2) +0.25xP(D = 144, p = 1.19, 2) +0.25xP(D = 96 p = 1.45, 2) +0.25xP(D = 96, p = 1.19, 2)
= –$12,000 • PVEP(D = 120, p = 1.22, 1) =
EP(D = 120, p = 1.22, 1)/(1+k) = –12,000/1.1 = –$10,909
D=144
p=$1.45
D=144
p=$1.19
D=96
p=$1.45
D=96
p=$1.19
D=120
p=$1.32
0.250.25
0.25
0.25
Period 1
Period 2
Example – Option 1 (Spot)
6. Starting at period T, work back to period 0 identify the expected cash flows at each step• P(D = 120, p = 1.32, 1) =
R(D = 120, p = 1.22, 1) –C(D = 120, p = 1.32, 1) +PVEP(D = 120, p = 1.22, 1)
= $146,400 - $158,400 + (–$10,909) = –$22,909
D=144
p=$1.45
D=144
p=$1.19
D=96
p=$1.45
D=96
p=$1.19
D=120
p=$1.32
0.250.25
0.25
0.25
Period 1
Period 2
Example – Option 1 (Spot)
6. Starting at period T, work back to period 0 identify the expected cash flows at each step
D=144
p=$1.45
D=144
p=$1.19
D=96
p=$1.45
D=144
p=$0.97
D=96
p=$1.19
D=96
p=$0.97
D=64
p=$1.45
D=64
p=$1.19
D=64
p=$0.97
D=120
p=$1.32
D=120
p=$1. 08
D=80
p=$1.32
D=80
p=$1.32
0.250.25
0.25
0.25
Period 1
Period 2Revenue Cost Profit
R(D =, p =, 1) C(D =, p =, 1) PVEP P(D =, p =, 1)D = 120 p = 1.32 120,000x1.22 120,000x1.32 -12,000/1.1 ($22,909)D = 120 p = 1.08 120,000x1.22 120,000x1.08 16,800/1.1 $32,073D = 80 p = 1.32 80,000x1.22 80,000x1.32 -8,000/1.1 ($15,273)D = 80 p = 1.08 80,000x1.22 80,000x1.08 11,200/1.1 $21,382
Example – Option 1 (Spot)
6. Starting at period T, work back to period 0 identify the expected cash flows at each step
D=144
p=$1.45
D=144
p=$1.19
D=96
p=$1.45
D=144
p=$0.97
D=96
p=$1.19
D=96
p=$0.97
D=64
p=$1.45
D=64
p=$1.19
D=64
p=$0.97
D=120
p=$1.32
D=120
p=$1. 08
D=80
p=$1.32
D=80
p=$1.32
D=100
p=$1.20
0.25
0.25
0.25
0.25
0.250.25
0.25
0.25
Period 0
Period 1
Period 2Revenue Cost Profit
R(D =, p =, 1) C(D =, p =, 1) PVEP P(D =, p =, 1)D = 100 p = 1.20 100,000x1.22 100,000x1.20 3818/1.1 $5,471
NPV(Spot) = $5,471
Example: Decision Tree Analysis
• Three options for Target.com1. Get all warehousing space from the spot market as
needed
2. Sign a three-year lease for a fixed amount of warehouse space and get additional requirements from the spot market– Get 100,000 sq ft. of warehouse space at $1 per
square foot– Additional space purchased from spot market
3. Sign a flexible lease with a minimum change that allows variable usage of warehouse space up to a limit with additional requirement from the spot market
Example – Option 2 (Fixed lease)
6. Starting at period T, work back to period 0 identify the expected cash flows at each step
D=144
p=$1.45
D=144
p=$1.19
D=96
p=$1.45
D=144
p=$0.97
D=96
p=$1.19
D=96
p=$0.97
D=64
p=$1.45
D=64
p=$1.19
D=64
p=$0.97
D=120
p=$1.32
D=120
p=$1. 08
D=80
p=$1.32
D=80
p=$1.32
D=100
p=$1.20
0.25
0.25
0.25
0.25
0.250.25
0.25
0.25
Period 0
Period 1
Period 2
Example – Option 2 (Fixed lease)
6. Starting at period T, work back to period 0 identify the expected cash flows at each step• P(D =, p =, 2) = R(D =, p =, 2) – C(D =, p =, 2)• P(D =, p =, 2) = Dx1.22 – (100,000x1.00 + Sxp)
Space Space ProfitLeased Spot price(S) P(D =, p =, 2)
D = 144 p = 1.45 100,000 sq.ft. 44,000 sq.ft. $11,800D = 144 p = 1.19 100,000 sq.ft. 44,000 sq.ft. $23,320D = 144 p = 0.97 100,000 sq.ft. 44,000 sq.ft. $33,000D = 96 p = 1.45 100,000 sq.ft. 0 sq.ft. $17,120D = 96 p = 1.19 100,000 sq.ft. 0 sq.ft. $17,120D = 96 p = 0.97 100,000 sq.ft. 0 sq.ft. $17,120D = 64 p = 1.45 100,000 sq.ft. 0 sq.ft. ($21,920)D = 64 p = 1.19 100,000 sq.ft. 0 sq.ft. ($21,920)D = 64 p = 0.97 100,000 sq.ft. 0 sq.ft. ($21,920)
8
Example – Option 2 (Fixed lease)
6. Starting at period T, work back to period 0 identify the expected cash flows at each step• P(D =, p =, 1) = R(D =, p =, 1) – C(D =, p =, 1) +
PVEP(D =, p =, 1)• P(D =, p =, 1) = Dx1.22 – (100,000x1.00 + Sxp) +
EP(D =, p =, 1)/(1+k)
Space ProfitPVEP Spot price(S) P(D =, p =, 1)
D = 120 p = 1.32 17,360/1.1 20,000 sq.ft. $35,782D = 120 p = 1.08 17,120/1.1 20,000 sq.ft. $45,382D = 80 p = 1.32 -21,920/1.1 0 sq.ft. ($4,582)D = 80 p = 1.08 -21,920/1.1 0 sq.ft. ($4,582)
Example – Option 2 (Fixed lease)
6. Starting at period T, work back to period 0 identify the expected cash flows at each step• P(D =, p =, 0) = R(D =, p =, 0) – C(D =, p =, 0) +
PVEP(D =, p =, 0)• P(D =, p =, 0) = 100,000x1.22 – 100,000x1.00 +
16,364/1.1
Space ProfitPVEP Spot price(S) P(D =, p =, 1)
D = 100 p = 1.20 18,000/1.1 0 sq.ft. $38,364
NPV(Fixed lease) = $38,364
Example: Decision Tree Analysis
• Three options for Target.com1. Get all warehousing space from the spot market as needed
2. Sign a three-year lease for a fixed amount of warehouse space and get additional requirements from the spot market
3. Sign a flexible lease with a minimum change that allows variable usage of warehouse space up to a limit with additional requirement from the spot market– $10,000 upfront payment– Use anywhere between 60,000 and 100,000 sq ft. at $1 per
sq ft.– Additional space purchased from spot market
Example – Option 3 (Flexible lease)
• Flexible lease rules– Up-front payment of $10,000– Flexibility of using between 60,000 and 100,000 sq.ft.
at $1.00 per sq.ft. per year– Additional space requirements from spot market
Example – Option 3 (Flexible lease)
6. Starting at period T, work back to period 0 identify the expected cash flows at each step
D=144
p=$1.45
D=144
p=$1.19
D=96
p=$1.45
D=144
p=$0.97
D=96
p=$1.19
D=96
p=$0.97
D=64
p=$1.45
D=64
p=$1.19
D=64
p=$0.97
D=120
p=$1.32
D=120
p=$1. 08
D=80
p=$1.32
D=80
p=$1.32
D=100
p=$1.20
0.25
0.25
0.25
0.25
0.250.25
0.25
0.25
Period 0
Period 1
Period 2
Example – Option 3 (Flexible lease)
6. Starting at period T, work back to period 0 identify the expected cash flows at each step• P(D =, p =, 2) = R(D =, p =, 2) – C(D =, p =, 2)• P(D =, p =, 2) = Dx1.22 – (Wx1.00 + Sxp)
Space Space ProfitLease $1.00(W) Spot price(S) P(D =, p =, 2)
D = 144 p = 1.45 100,000 sq.ft. 44,000 sq.ft. $11,800D = 144 p = 1.19 100,000 sq.ft. 44,000 sq.ft. $23,320D = 144 p = 0.97 100,000 sq.ft. 44,000 sq.ft. $34,200D = 96 p = 1.45 96,000 sq.ft. 0 sq.ft. $21,120D = 96 p = 1.19 96,000 sq.ft. 0 sq.ft. $21,120D = 96 p = 0.97 60,000 sq.ft. 36,000 sq.ft. $22,200D = 64 p = 1.45 64,000 sq.ft. 0 sq.ft. $14,080D = 64 p = 1.19 64,000 sq.ft. 0 sq.ft. $14,080D = 64 p = 0.97 60,000 sq.ft. 4,000 sq.ft. $14,200
Example – Option 3 (Flexible lease)
6. Starting at period T, work back to period 0 identify the expected cash flows at each step• P(D =, p =, 1) = R(D =, p =, 1) – C(D =, p =, 1) +
PVEP(D =, p =, 1)• P(D =, p =, 1) = Dx1.22 – (Wx1.00 + Sxp) +
EP(D =, p =, 1)/(1+k)
Space Space ProfitPVEPLease $1.00(W) Spot price(S) P(D =, p =, 1)
D = 120 p = 1.32 19360/1.1 100,000 sq.ft. 0 sq.ft $37,600D = 120 p = 1.08 25,210/1.1 100,000 sq.ft. 0 sq.ft $47,718D = 80 p = 1.32 17,600/1.1 80,000 sq.ft. 0 sq.ft $33,600D = 80 p = 1.08 17,900/1.1 80,000 sq.ft. 0 sq.ft $33,873
20,00020,000
Example – Option 3 (Flexible lease)
6. Starting at period T, work back to period 0 identify the expected cash flows at each step• P(D =, p =, 0) = R(D =, p =, 0) – C(D =, p =, 0) +
PVEP(D =, p =, 0)• P(D =, p =, 0) = 100,000x1.22 – 100,000x1.00 +
38,198/1.1
Space Space ProfitPVEPLease $1.00(W) Spot price(S) P(D =, p =, 1)
D = 100 p = 1.20 38,198/1.1 100,000 sq.ft. 0 sq.ft. $56,725
NPV(Flexible lease) = 56,725 – 10,000 = $46,725
From Design to Planning
• Network design– C4 Designing Distribution Networks– C5 Network Design in the Supply Chain– C6 Network Design in an Uncertain Environment
• Planning in a supply chain– C7 Demand Forecasting in a Supply Chain– C8 Aggregate Planning in a Supply Chain– C9 Planning Supply and Demand
Demand Forecasting
• How does BMW know how many Mini Coopers it will sell in North America?
• How many Prius cars should Toyota build to meet demand in the U.S. this year? Worldwide?
• When is it time to tweak production, upward or downward, to reflect a change in the market?
What factors influence customer demand?
Factors that Affect Forecasts
• Past demand• Time of year/month/week• Planned advertising or marketing efforts • Planned price discounts • State of the economy• Market conditions • Actions competitors have taken
Example: Demand Forecast for Milk• A supermarket has experienced the following weekly
demand (in gallons) over the last ten weeks– 109, 116, 108, 103, 97, 118, 120, 127, 114, and 122
What is a reasonable demand forecast for milk for the upcoming week?
If demand turned out to be 125 what can you say about the demand forecast?
When could using average demand as a forecast lead to an inaccurate forecast?
1) Characteristics of Forecasts
• Forecasts are always wrong!– Forecasts should include an expected value and a
measure of error (or demand uncertainty)• Forecast 1: sales are expected to range between 100
and 1,900 units• Forecast 2: sales are expected to range between 900
and 1,100 units
2) Characteristics of Forecasts
• Long-term forecasts are less accurate than short-term forecasts– Less easy to consider other variables
• Hard to include the effects of weather in a forecast
– Forecast horizon is important, long-term forecast have larger standard deviation of error relative to the mean
3) Characteristics of Forecasts
• Aggregate forecasts are more accurate than disaggregate forecasts
SKU A SKU BForecast 75 25Actual 25 75Accuracy 0% 0%
SKU A SKU B TotalForecast 75 25 100Actual 25 75 100Accuracy 0% 0% 100%
3) Characteristics of Forecasts
• Aggregate forecasts are more accurate than disaggregate forecasts– They tend to have a smaller standard deviation of
error relative to the mean
Monthly sales SKU
Monthly sales product line
4) Characteristics of Forecasts
• Information gets distorted when moving away from the customer– Bullwhip effect
Characteristics of Forecasts
1. Forecasts are always wrong!
2. Long-term forecasts are less accurate than short-term forecasts
3. Aggregate forecasts are more accurate than disaggregate forecasts
4. Information gets distorted when moving away from the customer
Role of Forecasting
Push Push Push
Push Push
Push
Pull
Pull
Pull
Manufacturer Distributor Retailer CustomerSupplier
Is demand forecasting more important for a push or pull system?
Types of Forecasts
• Qualitative– Primarily subjective, rely on judgment and opinion
• Time series– Use historical demand only
• Causal– Use the relationship between demand and some
other factor to develop forecast
• Simulation– Imitate consumer choices that give rise to demand
Components of an Observation
• Quarterly demand at Tahoe Salt
0
10,000
20,000
30,000
40,000
50,000
1, 2 1, 3 1, 4 2, 1 2, 2 2, 3 2, 4 3, 1 3, 2 3, 3 3, 4 4, 1
Quarter
Dem
and
Actual Actual demand (D)
0
10,000
20,000
30,000
40,000
50,000
1, 2 1, 3 1, 4 2, 1 2, 2 2, 3 2, 4 3, 1 3, 2 3, 3 3, 4 4, 1
Quarter
Dem
and
Actual
Components of an Observation
• Quarterly demand at Tahoe Salt
Level (L) and Trend (T)
0
10,000
20,000
30,000
40,000
50,000
1, 2 1, 3 1, 4 2, 1 2, 2 2, 3 2, 4 3, 1 3, 2 3, 3 3, 4 4, 1
Quarter
Dem
and
Actual
Components of an Observation
• Quarterly demand at Tahoe Salt
Seasonality (S)
Components of an Observation
Observed demand =
Systematic component + Random component
L Level (current deseasonalized demand)T Trend (growth or decline in demand)S Seasonality (predictable seasonal fluctuation)
Time Series Forecasting
0
10,000
20,000
30,000
40,000
50,000
1, 2 1, 3 1, 4 2, 1 2, 2 2, 3 2, 4 3, 1 3, 2 3, 3 3, 4 4, 1 4, 2 4, 3 4, 4 5, 1
Quarter
Dem
and
Actual
Forecast demand for thenext four quarters.