Lecture 4 - The Value of Information.pdf

CHAPTER 5:VALUE OF INFORMATION

E. OldenkampSession 419 April 2016

HOW VARIABLE IS DEMAND FOR DIAPERS?

2

NEWBORN BABIES PER YEAR IN THE NL

3

Pampers demand pattern

• Steady purchase rate at the customer end• Early 1900s extreme and increasing demand variations from the

retailer to the distributor• Reasons:

– infrequent ordering– changes in prices– that is: lack of information upstream about actual customer

orders• Old SC model: replenishment took at both the distribution and

supplier side several weeks• Retailers order only when product was missing from the shelves• P&G’s procurement from suppliers based on historical sales data

4

P&G’S DIAPERS CASEconsumer sales at retailer

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retailer's orders to distributor

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distributor's orders to P&G

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P&G's orders with 3M

5

• P&G initiated the use of VMI systems involving 3M andWal-Mart

• Effect:– lower operating costs at Wal-Mart– increase in P&G’s market share (more room at Wal-

Mart)– P&G provided POS data to its suppliers:“This allows the suppliers to better plan their production and deliever raw and packingmaterial on a just-in-time bases”– demand driven supply chain– everybody in the SC accessed the same data

P&G’s diapers case

6

BULLWHIP EFFECT (BWE)

Order variability keeps amplifying as we move UP the SC.

7

4-STAGE SUPPLY CHAIN1,000 units

1,100 units

1,210 units

1,331 units

1,464 units

+10%

+10%

+10%

+10%

total safety stock:

1,105 units

8

CAUSES OF THE BULLWHIP EFFECT

• Four major causes:– forecasting based on order and not customer demand– ordering in large lots– price fluctuations (forward buying)– false orders

• Long lead times magnify the effect

9


• Four major causes:– demand forecasting– batch ordering– price fluctuations– false orders


How does forecasting

increase the BWE?

10

DEMAND FORECASTING

Consider a simple supply chain…• single retailer• single wholesaler

Retailer WholesalerDt

Qt

L

11

DEMAND FORECASTING – MA

• p-period moving average:

�𝐷𝐷𝑡𝑡 =1𝑝𝑝�𝑖𝑖=1

𝑝𝑝𝐷𝐷𝑡𝑡−𝑖𝑖 and �𝜎𝜎𝑡𝑡2 =

1𝑝𝑝 − 1�𝑖𝑖=1

𝑝𝑝(𝐷𝐷𝑡𝑡−𝑖𝑖−�𝐷𝐷𝑡𝑡)2.

• Periodic review (𝑆𝑆 − 1, 𝑆𝑆) policy (dynamic):

𝑆𝑆𝑡𝑡 = 𝐿𝐿 + 𝑟𝑟 × �𝐷𝐷𝑡𝑡 + z × 𝐿𝐿 + 𝑟𝑟 × �𝜎𝜎𝑡𝑡• How to measure the bullwhip effect?

𝐵𝐵𝐵𝐵𝐵𝐵 = var 𝑄𝑄𝑡𝑡var 𝐷𝐷𝑡𝑡

12


timeL

safetystock

tt-1

𝑺𝑺𝒕𝒕

𝑺𝑺𝒕𝒕−𝟏𝟏 𝑸𝑸𝒕𝒕 = 𝑺𝑺𝒕𝒕 − 𝑺𝑺𝒕𝒕−𝟏𝟏 +𝑫𝑫𝒕𝒕−𝟏𝟏

L13

DEMAND FORECASTING – MASimulation• Normal demand with 𝐴𝐴𝐴𝐴𝐴𝐴 = 20 and 𝑆𝑆𝑆𝑆𝐷𝐷 = 4• Forecast: 5-period MA (𝑝𝑝 = 5)• 𝐿𝐿 = 3• var 𝐷𝐷𝑡𝑡 = 16.48, var 𝑄𝑄𝑡𝑡 = 65.0 ⇒ BWE = 3.94

14


• Perform the simulation 10,000 times:

– average 𝐵𝐵𝐵𝐵𝐵𝐵 = 4.74

• Lower bound on bullwhip effect

BWE = var 𝑄𝑄𝑡𝑡var 𝐷𝐷𝑡𝑡 ≥ 1+

2𝐿𝐿𝑝𝑝 + 2𝐿𝐿

2

𝑝𝑝2

𝐿𝐿 = 3 and 𝑝𝑝 = 5What is the BWE at the wholesaler?

lower bound is 2.9215


0

2

4

6

8

10

12

0 10 20 30

low

er b

ound

BW

E

p

L=1L=3L=5

5

2.92

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• Consider a multi-stage supply chain– stage k places order Qk to stage k+1– Lk is the lead time between stage k and k+1

RetailerD=Q0

L1Wholesaler Distributor

Q1

L2

Q2Factory

L3

Q3

17


Decentralized: each stage bases order on previous stage’s demand• Retailer does not share demand forecast with

wholesaler• Wholesaler forecasts demand by retailer’s orders• Distributor forecasts demand by wholesaler’s orders

How to measure the bullwhip effect?

𝐵𝐵𝐵𝐵𝐵𝐵𝑘𝑘 = var 𝑄𝑄𝑡𝑡𝑘𝑘var 𝐷𝐷𝑡𝑡

= var 𝑄𝑄𝑡𝑡1var 𝐷𝐷𝑡𝑡

× var 𝑄𝑄𝑡𝑡2var 𝑄𝑄𝑡𝑡1

×⋯× var 𝑄𝑄𝑡𝑡𝑘𝑘var 𝑄𝑄𝑡𝑡𝑘𝑘−1

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Simulation• Normal demand with 𝐴𝐴𝐴𝐴𝐴𝐴 = 20 and 𝑆𝑆𝑆𝑆𝐷𝐷 = 4• Forecast: 5-period MA (𝑝𝑝 = 5)• 5 stages: customer, retailer, wholesaler, DC, MF• 𝐿𝐿1 = 3, 𝐿𝐿2= 5, 𝐿𝐿3= 2, 𝐿𝐿4= 4• BWE1= 4, BWE2=38.3, BWE3= 86.8, BWE4=187.4

19


• Perform the simulation 10,000 times:– average BWE1 = 4.73– average BWE2 = 34.81– average BWE3 = 119.72– average BWE4 = 514.15

• Lower bound on bullwhip effect

𝐵𝐵𝐵𝐵𝐵𝐵𝑘𝑘 =var 𝑄𝑄𝑡𝑡𝑘𝑘var 𝐷𝐷𝑡𝑡

≥ 1 + 2𝐿𝐿1𝑝𝑝 + 2𝐿𝐿12

𝑝𝑝2 1 + 2𝐿𝐿2𝑝𝑝 + 2𝐿𝐿22

𝑝𝑝2 ⋯ 1 + 2𝐿𝐿𝑘𝑘𝑝𝑝 + 2𝐿𝐿𝑘𝑘2

𝑝𝑝2

𝐿𝐿1 = 3, 𝐿𝐿2 = 5, 𝐿𝐿3 = 2, 𝐿𝐿4 = 4, and 𝑝𝑝 = 5.What is the lower bound of the BWE at each stage?

20


• Retailer

– 𝐵𝐵𝐵𝐵𝐵𝐵1 ≥ 1 + 2×35 + 2×32

52 = 2.92• Wholesaler

– 𝐵𝐵𝐵𝐵𝐵𝐵2 ≥ 1 + 2×35 + 2×32

52 1 + 2×55 + 2×52

52 = 14.6• Distributor

– 𝐵𝐵𝐵𝐵𝐵𝐵3 ≥ 2.92 × 5.0 × 2.12 = 30.952• Manufacturer

– 𝐵𝐵𝐵𝐵𝐵𝐵4 ≥ 2.92 × 5.0 × 2.12 × 3.88 = 120.094

𝐿𝐿1 = 3, 𝐿𝐿2 = 5, 𝐿𝐿3 = 2, 𝐿𝐿4 = 4, and 𝑝𝑝 = 521


• Perform the simulation 10,000 times:– average BWE1 = 4.73– average BWE2 = 34.81– average BWE3 = 119.72 – average BWE4 = 514.15

≥ 2.92≥ 14.60≥ 30.95≥ 120.09

22

DEMAND FORECASTING – ES

• Demand forecast with Exponential Smoothing

�𝐷𝐷𝑡𝑡 = 𝛼𝛼𝐷𝐷𝑡𝑡−1 + (1− 𝛼𝛼)�𝐷𝐷𝑡𝑡−1• Periodic review (𝑆𝑆 − 1, 𝑆𝑆) policy:

𝑆𝑆𝑡𝑡 = 𝐿𝐿 + 𝑟𝑟 × �𝐷𝐷𝑡𝑡 + z × 𝐿𝐿 + 𝑟𝑟 × �𝜎𝜎𝑡𝑡• How to measure the bullwhip effect?

𝐵𝐵𝐵𝐵𝐵𝐵 = var 𝑄𝑄𝑡𝑡var 𝐷𝐷𝑡𝑡

≥ 1 + 2𝛼𝛼𝐿𝐿 + 2𝛼𝛼2𝐿𝐿22−𝛼𝛼

𝛼𝛼 = 0.3 and L=3 ⟹ lower bound = 3.75

23

DEMAND FORECASTING – ES

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low

er b

ound

BW

E

L=1L=3L=5

𝜶𝜶0.3

3.75

24

DEMAND FORECASTING – ES• Consider again a multi-stage supply chain

– stage k places order Qk to stage k+1– Lk is the lead time between stage k and k+1

RetailerD=Q0

L1Wholesaler Distributor

Q1

L2

Q2Factory

L3

Q3

𝐵𝐵𝐵𝐵𝐵𝐵𝑘𝑘 =var 𝑄𝑄𝑡𝑡𝑘𝑘var 𝑄𝑄𝑡𝑡0

≥ 1 + 2𝛼𝛼𝐿𝐿1 +2𝛼𝛼2𝐿𝐿122− 𝛼𝛼 1 + 2𝛼𝛼𝐿𝐿2 +

2𝛼𝛼2𝐿𝐿222− 𝛼𝛼 ⋯ 1 + 2𝛼𝛼𝐿𝐿𝑘𝑘 +

2𝛼𝛼2𝐿𝐿𝑘𝑘22− 𝛼𝛼

25

• Both forecasts have the same variance of the forecast errors when

𝛼𝛼 = 2𝑝𝑝 + 1

• Filling in the numbersVar(𝑄𝑄𝑀𝑀𝑀𝑀)Var(D) ≥ 1 + 2L

p + 2L2p2

Var(𝑄𝑄𝐸𝐸𝐸𝐸)Var(D) ≥ 1 + 4L

p + 1 +4L2

p(p + 1)

COMPARISON OF THE TWO FORECASTING TECHNIQUES

MA: 𝑝𝑝 = 5 and 𝐿𝐿 = 3 ⇒ lower bound = 2.92ES: α = 0.333 and 𝐿𝐿 = 3 ⇒ lower bound = 4.20

26

COMPARISON OF THE TWO FORECASTING TECHNIQUES

0

2

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14

0 10 20 30

low

er b

ound

BW

E

p

MA - L=1MA - L=3MA - L=5EX - L=1EX - L=3EX - L=5

27


• Four major causes:– demand forecasting– ordering in large lotsizes– price fluctuations– false orders


How does batch ordering increase the

BWE?

28




How do price fluctuations increase the

BWE?

29

PRICE FLUCTUATIONS (1)

Point-of-Sales Data

30


Point-of-Sales Data – after removing promotions

31

Point-of-Sales Data – after removing promotions and trend


32




How do false orders

increase the BWE?

33




How do longer lead times

magnify the BWE?

34

COUNTERACT THE BULLWHIP EFFECT

1. Avoid independent demand forecasting by different SC actors

2. Break order batches3. Stabilize prices4. Eliminate false orders

35

IMPACT OF CENTRALIZED INFORMATION

Moving average:• Decentralized

𝐵𝐵𝐵𝐵𝐵𝐵 = Var 𝑄𝑄𝑘𝑘Var 𝐷𝐷 ≥ �

𝑖𝑖=1

𝑘𝑘1 + 2𝐿𝐿𝑖𝑖

𝑝𝑝 + 2𝐿𝐿𝑖𝑖2𝑝𝑝2

• Centralized

𝐵𝐵𝐵𝐵𝐵𝐵 = Var 𝑄𝑄𝑘𝑘Var 𝐷𝐷 ≥ 1 + 2

𝑝𝑝�𝑖𝑖=1

𝑘𝑘𝐿𝐿𝑖𝑖 +

2𝑝𝑝2�𝑖𝑖=1

𝑘𝑘𝐿𝐿𝑖𝑖2

𝐿𝐿1 = 3, 𝐿𝐿2 = 5, 𝐿𝐿3 = 2, 𝐿𝐿4 = 4, and 𝑝𝑝 = 5What is the lower bound of the BWE at the SC partners?

36


• Retailer

– 𝐵𝐵𝐵𝐵𝐵𝐵1 ≥ 1 + 25 × 3 +

225 × 9 = 2.92

• Wholesaler

– 𝐵𝐵𝐵𝐵𝐵𝐵2 ≥ 1 + 25 × 3 + 5 + 2

25 × 9 + 25 = 6.92• Distributor

– 𝐵𝐵𝐵𝐵𝐵𝐵3 ≥ 1 + 25 × 3 + 5 + 2 + 2

25 × 9 + 25 + 4 = 8.04• Manufacturer

– 𝐵𝐵𝐵𝐵𝐵𝐵4 ≥ 1 + 25 × 3 + 5 + 2 + 4 + 2

25 × 9 + 25 + 4 + 16 = 10.92

37

• Perform the simulation 10,000 times:– average BWE1 = 4.73– average BWE2 = 8.37– average BWE3 = 9.41 – average BWE4 = 11.67

≥ 2.92≥ 6.92≥ 8.04≥ 10.92

MOVING AVERAGE

38

LOWER BOUNDS OF BWE -- MA

0

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25

30

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er b

ound

BW

E

p

k=1Dec - k=3Dec - k=5Cen - k=3Cen - k=5

39

decentralized centralized

simulation lower bound simulation lower bound

Retailer 4.73 2.92 4.73 2.92

Wholesaler 34.81 14.60 8.37 6.92

Distributor 119.72 30.95 9.41 8.04

Manufacturer 514.15 120.09 11.67 10.92

MOVING AVERAGE

40

IMPACT OF CENTRALIZED INFORMATION

Exponential smoothing:• Decentralized

𝐵𝐵𝐵𝐵𝐵𝐵 = Var 𝑄𝑄𝑘𝑘Var 𝐷𝐷 ≥ �

𝑖𝑖=1

𝑘𝑘1 + 2α𝐿𝐿𝑖𝑖 +

2𝛼𝛼2𝐿𝐿𝑖𝑖22− 𝛼𝛼

• Centralized

𝐵𝐵𝐵𝐵𝐵𝐵 = Var 𝑄𝑄𝑘𝑘Var 𝐷𝐷 ≥ 1 + 2𝛼𝛼�

𝑖𝑖=1

𝑘𝑘𝐿𝐿𝑖𝑖 +

2𝛼𝛼22− 𝛼𝛼�𝑖𝑖=1

𝑘𝑘𝐿𝐿𝑖𝑖2

41

EXPONENTIAL SMOOTHING

0

10

20

30

40

50

0 0.2 0.4 0.6 0.8 1

low

er b

ound

BW

E

alpha

k=1Dec - k=3Dec - k=5Cen - k=3Cen - k=5

42

MANAGERIAL INSIGHTS

• Variance increases up the supply chain in both centralized and decentralized cases

• Variance increases:– additively with centralized case

– multiplicatively with decentralized case

• Centralizing can significantly reduce the bullwhip effect – although cannot eliminate it completely!

43


1. Avoid independent demand forecasting by different SC actors

2. Break order batches3. Stabilize prices4. Eliminate false orders

44

BREAK ORDER BATCHES

• Reduce replenishment costs• Economies of scale in transportation• Use third-party logistics companies

• P&G requires all orders from retailers to be full TL: combination of products reduces lot size

Think about EOQ model: Q*= 2DKh

→ reduction of fixed order cost by factor k2, results in reduction order size of only factor k

45


1. Avoid multiple demand forecast updates2. Break order batches3. Stabilize prices4. Eliminate false orders

46

SHORT TERM DISCOUNTING

Qd

Q*

t

inve

ntor

y le

vel

Identify Qd that maximizes the reduction in total cost(material cost + order cost + holding cost)

47

Assumptions• Discount will only be offered once• Order quantity Qd is a multiple of Q*• Retailer takes no action of influence the demand

Notation• C = wholesale price• d = discount on wholesale price• h = holding cost % of wholesale price


EOQ model: 𝑄𝑄∗ = 2𝐷𝐷𝐷𝐷ℎ𝐶𝐶

48


• Estimate total cost of ordering 𝑄𝑄𝑑𝑑 in discount period• TC 𝑄𝑄𝑑𝑑 = material cost + order cost + inventory cost

= 𝐶𝐶 − 𝑑𝑑 𝑄𝑄𝑑𝑑 + 𝐾𝐾 + 𝑄𝑄𝑑𝑑2 𝐶𝐶 − 𝑑𝑑 ℎ 𝑄𝑄𝑑𝑑

𝐷𝐷

discount period = 𝑄𝑄𝑑𝑑𝐷𝐷

Qd

Q*

t

inve

ntor

y le

vel

49

SHORT TERM DISCOUNTING• Estimate total cost of ordering 𝑄𝑄∗ in discount period• TC 𝑄𝑄∗ = material cost + order cost + inventory cost

= 𝐶𝐶𝑄𝑄𝑑𝑑 + 𝐾𝐾 𝑄𝑄𝑑𝑑𝑄𝑄∗ +

𝑄𝑄∗2 ℎ𝐶𝐶 𝑄𝑄𝑑𝑑

𝐷𝐷

= 𝐶𝐶𝑄𝑄𝑑𝑑 + 𝑄𝑄𝑑𝑑𝐷𝐷 2𝐷𝐷𝐾𝐾ℎ𝐶𝐶 (since 𝑄𝑄∗ = 2𝐷𝐷𝐷𝐷

ℎ ).

discount period = 𝑄𝑄𝑑𝑑𝐷𝐷

Qd

Q*

t

inve

ntor

y le

vel

50

• Cost difference: 𝐹𝐹 𝑄𝑄𝑑𝑑 = TC 𝑄𝑄𝑑𝑑 − TC 𝑄𝑄∗

• Take the derivative and set to zero

𝐹𝐹′ 𝑄𝑄𝑑𝑑 = 0 ⇒ 𝑄𝑄𝑑𝑑 = 𝑑𝑑𝐷𝐷ℎ 𝐶𝐶−𝑑𝑑 + 𝐶𝐶𝑄𝑄∗

𝐶𝐶−𝑑𝑑


51

• D = 120,000/year• C = $3• h = 20% (annual)• K = $100


− Q* = 6,324 units− cycle time = 0.63 months

Assume a promotion is offered (d=$0.15)

• Qd = dD(C−d)h +

CQ∗

C−d

= 0.15 × 120,000(3−0.15) × 0.2 + 3 × 6,324

3 − 0.15

= 38,236 units

cycle time = 3.82 months

52

CAMPBELL SOUP COMPANY

• Flagship product: cans of condensed soup• Backwards integration

53

CUSTOMER DEMAND

Types:• retailer (45%)• wholesaler (47%)• other (8%)

54

SUMMARY BULLWHIP EFFECT

Cause of bullwhip

Information sharing Channel alignment Operational efficiency

demand forecast update

- understanding system dynamics

- use POS data- EDI- internet

- VMI- discount for

information sharing- direct shipping

- lead time reduction- echelon based

inventory control

order batching

- EDI- Internet

- discount for truckload assortment

- delivery appointments- consolidation- logistics outsourcing

- reduction in fixed cost of ordering by EDI or electronic commerce

pricefluctuations

- EDLC - EDLP

false orders - sharing sales, capacity, and inventory data

- allocation based on past sales

55

Documents

Lecture 4 - The Value of Information.pdf