ch11 Operation Management Roberta Russell & Bernard W. Taylor

Chapter 11 Forecasting  Operations Management - 5 th  Edition  Roberta Russell & Bernard W. Taylor, III

Beni Asllani

Lecture Outline 

Strategic Role of Forecasting in Supply Chain Management and TQM



Components of Forecasting Demand



Time Series Methods



Forecast Accuracy



Regression Methods

Forecasting  

Predicting the Future Qualitative forecast methods 



subjective

Quantitative forecast methods 

based on mathematical formulas

Forecasting and Supply Chain Management 



Accurate forecasting determines how much inventory a company must keep at various points along its supply chain Continuous replenishment    



supplier and customer share continuously updated data typically managed by the supplier reduces inventory for the company speeds customer delivery

Variations of continuous replenishment    

quick response JIT (just-in-time) VMI (vendor-managed inventory) stockless inventory

Forecasting and TQM  

Accurate forecasting customer demand is a key to providing good quality service Continuous replenishment and JIT complement TQM 

 

eliminates the need for buffer inventory, which, in turn, reduces both waste and inventory costs, a primary goal of TQM smoothes process flow with no defective items meets expectations about on-time delivery, which is perceived as good-quality service

Types of Forecasting Methods 

Depend on 





time frame demand behavior causes of behavior

Time Frame 

Indicates how far into the future is forecast 

Short- to mid-range forecast  



typically encompasses the immediate future daily up to two years

Long-range forecast 

usually encompasses a period of time longer than two years

Demand Behavior  

Trend 



Random variations 



movements in demand that do not follow a pattern

Cycle 



a gradual, long-term up or down movement of demand

an up-and-down repetitive movement in demand

Seasonal pattern 

an up-and-down repetitive movement in demand occurring periodically

Forms of Forecast Movement    d   n   a   m   e    D

Random movement

   d   n   a   m   e    D

Time (a) Trend

Time (b) Cycle

   d   n   a   m   e    D

   d   n   a   m   e    D

Time (c) Seasonal pattern

Time (d) Trend with seasonal pattern

Forecasting Methods 

Qualitative 



Time series 



use management judgment, expertise, and opinion to predict future demand statistical techniques that use historical demand data to predict future demand

Regression methods 

attempt to develop a mathematical relationship between demand and factors that cause its behavior

Qualitative Methods 

Management, marketing, purchasing, and engineering are sources for internal qualitative forecasts



Delphi method 

involves soliciting forecasts about technological advances from experts

Forecasting Process 1. Identify the purpose of forecast

2. Collect historical data

3. Plot data and identify patterns

6. Check forecast accuracy with one or  more measures

5. Develop/compute forecast for period of  historical data

4. Select a forecast model that seems appropriate for data

7. Is accuracy of  forecast acceptable?

No

8b. Select new forecast model or  adjust parameters of  existing model

 Yes 8a. Forecast over  planning horizon

9. Adjust forecast based on additional qualitative information and insight

10. Monitor results and measure forecast accuracy

Time Series 

Assume that what has occurred in the past will continue to occur in the future



Relate the forecast to only one factor - time



Include 

moving average



exponential smoothing linear trend line



Moving Average 

Naive forecast 



Simple moving average 



demand the current period is used as next period’s forecast stable demand with no pronounced behavioral patterns

Weighted moving average 

weights are assigned to most recent data

Moving Average:  Naïve Approach MONTH Jan Feb Mar  Apr  May June July Aug Sept Oct Nov

ORDERS PER MONTH 120 90 100 75 110 50 75 130 110 90 -

FORECAST 120 90 100 75 110 50 75 130 110 90

Simple Moving Average

n

D

i  = 1 Di 

MAn =

n

where n

Di 

= number of periods in the moving average = demand in period i 

3-month Simple Moving Average 3

ORDERS MONTH Jan MONTH

PER

120

Feb

90

Mar 

100

Apr 

75

May

110

June

50

July

75

MOVING AVERAGE  –  –  – 103.3 88.3 95.0 78.3 78.3 85.0 105.0 110.0

i  = 1

MA3 =

=

Di 

3 90 + 110 + 130 3

= 110 orders for Nov

5-month Simple Moving Average ORDERS MONTH Jan MONTH

PER

120

Feb

90

Mar 

100

Apr 

75

May

110

June

50

July

75

MOVING AVERAGE  –  –  –  –  – 99.0 85.0 82.0 88.0 95.0 91.0

5 i  = 1

MA5  =

=

Di 

5

90 + 110 + 130+75+50 5 = 91 orders for Nov

Smoothing Effects 150 – 125 –

5-month

100 – 75 –   s   r   e    d   r    O 50 – 3-month

25 – Actual

0– | Jan

| Feb

| Mar 

| | | | Apr  May June July Month

| | Aug Aug Sept

| Oct

| Nov

Weighted Moving Average 

Adjusts moving average method to more closely reflect data fluctuations

WMAn =

W i  Di 

i  = 1

where

W i  = the weight for period i , between 0 and 100 percent W i  = 1.00

Weighted Moving Average Example MONTH 

WEIGHT 

DATA

17% 33% 50%

130 110 90

 August  September  October 

3

November Forecast

WMA3 = i  = 1 W i  Di 

= (0.50)(90) + (0.33)(110) + (0.17)(130) = 103.4 orders

Exponential Smoothing Exponential

   

Averaging method Weights most recent data more strongly Reacts more to recent changes Widely used, accurate method

Exponential Smoothing (cont.) Exponential F t +1 = α Dt  + (1 - α)F t  where: F t +1 = forecast for next period Dt  =

actual demand for present period

previously determined forecast F t = for present period

α = weighting factor, smoothing constant

Effect of Smoothing Constant 0.0 ≤ α ≤ 1.0 If α = 0.20, then F t +1 = 0.20 Dt  + 0.80 F t  If α = 0, then F t +1 = 0 Dt  + 1 F t 0 = F t  Forecast does not reflect recent data

If α = 1, then F t +1 = 1 Dt  + 0 F t = Dt  Forecast based only on most recent data

Exponential Smoothing (α=0.30) Exponential PERIOD DEMAND

MONTH

1

Jan

37

2

Feb

40

3

Mar 

41

4

Apr 

37

5

May

45

F 2 =

D1 + (1 -

= (0.30)(37) + (0.70)(37) = 37 F 3 =

D2 + (1 -

Jun

50

)F 2

= (0.30)(40) + (0.70)(37) = 37.9 F 13 =

D12 + (1 -

)F 12

= (0.30)(54) + (0.70)(50.84) = 51.79

6

)F 1

Exponential Smoothing Exponential (cont.) FORECAST, F t  + 1 PERIOD

MONTH

DEMAND

1 2 3 4 5 6 7 8 9 10 11 12 13

Jan Feb Mar  Apr  May Jun Jul Aug Sep Oct Nov Dec Jan

37 40 41 37 45 50 43 47 56 52 55 54  –

(

= 0.3)  – 37.00 37.90 38.83 38.28 40.29 43.20 43.14 44.30 47.81 49.06 50.84 51.79

(

= 0.5)  – 37.00 38.50 39.75 38.37 41.68 45.84 44.42 45.71 50.85 51.42 53.21 53.61

Exponential Smoothing (cont.) Exponential 70 – 60 –

Actual

= 0.50

50 – 40 –   s   r   e 30 –    d   r    O

= 0.30

20 – 10 – 0– | 1

| 2

| 3

| 4

| 5

| 6 Month

| 7

| 8

| 9

| 10

| 11

| 12

| 13

Adjusted Exponential Smoothing  AF t +1 = F t +1 + T t +1 where T = an exponentially smoothed trend factor  T t +1 = β(F t +1 - F t ) + (1 - β) T t  where T t = the last period trend factor  β = a smoothing constant for trend

Adjusted Exponential Smoothing (β=0.30) T 3 PERIOD DEMAND

MONTH

= (F 3 - F 2) + (1 - ) T 2 = (0.30)(38.5 - 37.0) + (0.70)(0) = 0.45

1

Jan

37

2

Feb

40

3

Mar 

41

4

Apr 

37

5

May

45

6

Jun

50

 AF 3 = F 3 + T 3 = 38.5 + 0.45 = 38.95 T 13

= (F 13 - F 12) + (1 - ) T 12 = (0.30)(53.61 - 53.21) + (0.70)(1.77) = 1.36

 AF 13 = F 13 + T 13 = 53.61 + 1.36 = 54.96

Adjusted Exponential Smoothing: Example PERIOD

MONTH

DEMAND

FORECAST Ft  +1

1 2 3 4 5 6 7 8 9 10 11 12 13

Jan Feb Mar  Apr  May Jun Jul Aug Sep Oct Nov Dec Jan

37 40 41 37 45 50 43 47 56 52 55 54  –

37.00 37.00 38.50 39.75 38.37 38.37 45.84 44.42 45.71 50.85 51.42 53.21 53.61

TREND Tt  +1

ADJUSTED FORECAST AFt  +1

 – 0.00 0.45 0.69 0.07 0.07 1.97 0.95 1.05 2.28 1.76 1.77 1.36

 – 37.00 38.95 40.44 38.44 38.44 47.82 45.37 46.76 58.13 53.19 54.98 54.96

Adjusted Exponential Smoothing Forecasts 70 – Adjusted forecast ( = 0.30)

60 –

Actual

50 – 40 –

   d   n   a 30 –   m   e    D20 –

Forecast ( = 0.50)

20

10 – 0– | 1

| 2

| 3

| 4

| 5

| | 6 7 Period

| 8

| 9

| 10

| 11

| 12

| 13

Linear Trend Line  y = a + bx where a = intercept b = slope of the line  x = time period  y = forecast for  demand for period  x

b

Σ xy - nxy = Σ x2 - nx2

a =  y - b x

where numb mber er of pe peri riod ods s n = nu  x =

Σ x

= mean of the  x values

n Σ y = mean of the  y values  y = n

Least Squares Example  x (PERIOD) (PERIOD)

 yy(DEMAND)

 xy xy

 x  x 2

1 2 3 4 5 6 7 8 9 10 11 12

73 40 41 37 45 50 43 47 56 52 55 54

37 80 123 148 225 300 301 376 504 520 605 648

1 4 9 16 25 36 49 64 81 100 121 144

78

557

3867

650

Least Squares Example (cont.) 78  x  = = 6.5 12 557  y = = 46.42 12  xy - nxy b = = 2 2  x  - nx 

3867 - (12)(6.5)(46.42) 650 - 12(6.5)2

a =  y - bx 

= 46.42 - (1.72)(6.5) = 35.2

=1.72

Linear trend line  y = 35.2 + 1.72 x Forecast for period 13  y = 35. 35.2 2 + 1.7 1.72( 2(13 13)) = 57. 57.56 56 un unit its s 70 – 60 – Actual 50 –    d40 –   n   a   m   e 30 –    D

Linear trend line

20 – 10 – 0–

| 1

| 2

| 3

| 4

| 5

| | 6 7 Period

| 8

| 9

| 10

| 11

| 12

| 13

Seasonal Adjustments  

Repetitive increase/ decrease in demand Use seasonal factor to adjust forecast

Seasonal factor = S i =

Di

∑D

Seasonal Adjustment (cont.) DEMAND (1000’S PER QUARTER)

S 1 = S 2 =

 YEAR

1

2 

3

4

Total 

2002 2003

12.6 14.1

8.6 10.3

6.3 7.5

17.5 18.2

45.0 50.1

2004 Total

15.3 42.0

10.6 29.5

8.1 21.9

19.6 55.3

53.6 148.7

D1

42.0 = = 0.28 D 148.7

D2

29.5 = = 0.20 D 148.7

S 3 = S 4 =

D3

21.9 = = 0.15 D 148.7

D4

55.3 = = 0.37 D 148.7

Seasonal Adjustment (cont.)

For 2005  y = 40.97 + 4.30 x = 40.97 + 4.30(4) = 58.17

SF 1 = (S 1) (F 5) = (0.28)(58.17) = 16.28 SF 2 = (S 2) (F 5) = (0.20)(58.17) = 11.63 SF 3 = (S 3) (F 5) = (0.15)(58.17) = 8.73 SF 4 = (S 4) (F 5) = (0.37)(58.17) = 21.53

Forecast Accuracy 

Forecast error 

difference between forecast and actual demand



MAD 



mean absolute deviation

MAPD 

mean absolute percent deviation



Cumulative error



Average error or bias

Mean Absolute Deviation (MAD) MAD =

Σ| Dt  - F t | n

where t  = period number  Dt  = demand in period t 

F t  = forecast for period t  n = total number of periods  = absolute value

MAD Example PERIOD 1 2 3 4 5 6 7 8 9 10 11 12

DEMAND, Dt  37 40 41 37 MA45D 50 43 47 56 52 55 54 557

= = =

F t  (α =0.3)

37.00 37.00 37.90 D38.83 t  - F  t  38.28 n 40.29 53.39 43.20 1143.14 44.30 4.85 47.81 49.06 50.84

Σ|

|

(Dt  - F t )

|Dt  - F t |

 – 3.00 3.10 -1.83 6.72 9.69 -0.20 3.86 11.70 4.19 5.94 3.15

 – 3.00 3.10 1.83 6.72 9.69 0.20 3.86 11.70 4.19 5.94 3.15

49.31

53.39

Other Accuracy Measures Mean absolute percent deviation (MAPD) MAPD =

 ∑  |Dt  - F t | ∑ |D  ∑ Dt 

Cumulative error  E =  ∑ et   Average error  E=

 ∑ et 

n

Comparison of Forecasts

FORECAST

MAD

MAPD

E 

(E )

4.85 4.04

9.6% 8.5%

49.31 33.21

4.48 3.02

Adjusted exponential smoothing ( = 0.50, = 0.30)

3.81

7.5%

21.14

1.92

Linear trend line

2.29

4.9%

 –

 –

Exponential smoothing ( Exponential smoothing (

= 0.30) = 0.50)

Forecast Control 

Tracking signal 

monitors the forecast to see if it is biased high or low

Tracking signal = 



∑(Dt  - F t ) MAD

E  = MAD

1 MAD ≈ 0.8 б Control limits of 2 to 5 MADs are used most frequently

Tracking Signal Values PERIOD

DEMAND Dt 

1 2 3 4 5 6 7 8 9 10 11 12

37 40 41 37 45 50 43 47 56 52 55 54

FORECAST, F t 

ERROR Dt  - F t 

E = E = (Dt  - F t )

37.00  –  – 37.00 3.00 3.00 37.90 3.10 6.10 38.83 -1.83 4.27 38.28 6.72 for period 10.99 3 Tracking signal 40.29 9.69 20.68 43.20 -0.20 20.48 6.10 43.14 TS3 = 3.86 =24.34 2.00 3.05 36.04 44.30 11.70 47.81 4.19 40.23 49.06 5.94 46.17 50.84 3.15 49.32

MAD

 – 3.00 3.05 2.64 3.66 4.87 4.09 4.06 5.01 4.92 5.02 4.85

TRACKING SIGNAL

 – 1.00 2.00 1.62 3.00 4.25 5.01 6.00 7.19 8.18 9.20 10.17

Tracking Signal Plot 3  –    ) 2    D    A    M    ( 1    l   a   n 0   g    i   s   g-1   n    i    k   c-2   a   r    T-3

 – Exponential smoothing (

 –

= 0.30)

 –  –  –  –

| 0

Linear trend line

| 1

| 2

| 3

| 4

| 5

| 6 Period

| 7

| 8

| 9

| 10

| 11

| 12

Statistical Control Charts σ=





∑(Dt  - F t )2 n-1

Using σ we can calculate statistical control limits for the forecast error  Control limits are typically set at ± 3σ

Statistical Control Charts 18.39 – 12.24 –

UCL = +3

6.12 – 0–   s   r   o   r   r -6.12 –    E -12.24 – -18.39 – LCL = -3 | 0

| 1

| 2

| 3

| 4

| 5

| 6 Period

| 7

| 8

| 9

| 10

| 11

| 12

Regression Methods 

Linear regression 



a mathematical technique that relates a dependent variable to an independent variable in the form of a linear equation

Correlation 

a measure of the strength of the relationship between independent and dependent variables

Linear Regression  y = a + bx

a =  y - b x b =

 xy - nxy  x 2 - nx 2

where a = intercept b = slope of the line  x =  y =

 x  = mean of the  x data n  y n = mean of the  y data

Linear Regression Example  x 

 yy

(WINS)

(ATTENDANCE)

 xy

 x  x 2

4 6 6 8 6 7 5 7

36.3 40.1 41.2 53.0 44.0 45.6 39.0 47.5

145.2 240.6 247.2 424.0 264.0 319.2 195.0 332.5

16 36 36 64 36 49 25 49

49

346.7

2167.7

311

Linear Regression Example (cont.) 49 = 6.125 8 346.9  y = = 43.36 8  x =

b =

∑ xy - nxy2 ∑ x2 - nx2

(2,167.7) - (8)(6.125)(43.36) = (311) - (8)(6.125)2 = 4.06 a =  y - bx = 43.36 - (4.06)(6.125) = 18.46

Linear Regression Example (cont.) Regression equation

Attendance forecast for 7 wins

 y = 18.46 + 4.06 x 

 y = 18.46 + 4.06(7) = 46.88, or 46,880

60,000 – 50,000 – 50,000 – 40,000 –      y

 ,   e 30,000 –   c   n   a    d   n 20,000 –   e    t    t    A

Linear regression line,  y = 18.46 + 4.06 x 

10,000 –

| 0

| 1

| 2

| 3

| 4

| | 5 6 Wins,  x 

| 7

| 8

| 9

| 10

Correlation and Coefficient of  Determination 

Correlation, r   



Measure of strength of relationship Varies between -1.00 and +1.00

Coefficient of determination, r 2 

Percentage of variation in dependent variable resulting from changes in the independent variable

Computing Correlation r =

r =

n∑ xy - ∑ x∑ y

[n∑ x2 - (∑ x)2] [n∑ y2 - (∑ y)2] (8)(2,167.7) - (49)(346.9)

[(8)(311) - (49)2] [(8)(15,224.7) - (346.9) 2] r = 0.947

Coefficient of determination r 2 = (0.947)2 = 0.897

Multiple Regression Study the relationship of demand to two or  more independent variables y = β0 + β1x1 + β2x2 … + βkxk  where

β0 = the intercept β 1, … , βk  = parameters for the independent variables x1, … , xk  = independent variables

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