supply chain management lecture 10. outline today –finish chapter 6 (decision tree analysis)...

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.