It service operations 1

Forecasting Demand for Services

Forecasting Models

• Subjective ModelsDelphi Methods

• Time Series ModelsMoving AveragesExponential Smoothing

• Causal ModelsRegression Models

DELPHI METHOD

• Rationale– Anonymous written responses encourage

honesty and avoid that a group of experts are dominated by only a few members

DELPHI METHOD

• Approach

Coordinator Sends Initial Questionnaire

Each expertwrites response(anonymous)

Coordinatorperformsanalysis

Coordinatorsends updatedquestionnaire

Coordinatorsummarizesforecast

Consensusreached?

YesNo

DELPHI METHOD• Main advantages

– Generate consensus– Can forecast long-term trend without

availability of historical data

• Main drawbacks – Slow process – Experts are not accountable for their

responses– Little evidence that reliable long-term

forecasts can be generated with Delphi or other methods

DELPHI METHOD

• Typical application– Long-term forecasting– Technology forecasting

Interactive Exercise: Delphi ForecastingQuestion: In what future election will a woman become president of the united states?

Year 1st Round Positive Arguments 2nd Round Negative Arguments 3rd Round

2008

2012

2016

2020

2024

2028

2032

2036

2040

2044

2048

2052

Never

Total

TIME SERIES PROJECTION METHODS

• These methods generate forecasts on the basis of an analysis of the historical time series.

• The important time series projection methods are:– Moving Average Method– Exponential Smoothing Method– Trend Projection Method

Moving Averages • Moving averages are useful if we can

assume that market demands will stay fairly steady over time. Moving average can be defined as the summation of demands of total periods divided by the total number of periods.

Mathematically, • Moving average = ∑ Demand in previous n periods

n

9

Moving Average• Include n most recent observations• Weight equally• Ignore older observations

weight

today

123...n

1/n

10

ExampleMonth Actual Washing

machine sales, units Three-month moving average

January 10

February 12

March 13

April 16

May 19

June 23

July 26

August 30

September 28

October 18

November 16

December 14 11


machine sales, units

Three-month moving average

January 10

February 12

March 13

April 16 (10 + 12 + 13) / 3 = 11.67

May 19

June 23

July 26

August 30

September 28

October 18

November 16

December 14 12



January 10

February 12

March 13

April 16 (10 + 12 + 13) / 3 = 11.67

May 19 (12 + 13 + 16) / 3 = 13.67

June 23

July 26

August 30

September 28

October 18

November 16

December 14 13



January 10

February 12

March 13

April 16 (10 + 12 + 13) / 3 = 11.67

May 19 (12 + 13 + 16) / 3 = 13.67

June 23 (13 + 16 + 19) / 3 = 16

July 26

August 30

September 28

October 18

November 16

December 14 14



Three-month moving average

January 10

February 12

March 13

April 16 (10 + 12 + 13) / 3 = 11.67

May 19 (12 + 13 + 16) / 3 = 13.67

June 23 (13 + 16 + 19) / 3 = 16

July 26 (16 + 19 + 23) / 3 = 19.33

August 30 (19 + 23 + 26) / 3 = 22.67

September 28 (23 + 26 + 30) / 3 = 26.33

October 18 (26 + 30 + 28) / 3 = 28

November 16 (30 + 28 + 18) / 3 = 25.33

December 14 (28 + 18 +16) / 3 = 20.67 15

Weighted Moving Averages• When there is a detectable trend or pattern,

weights can be used to place more emphasis on recent values. This makes the techniques more responsive to changes since more recent periods may be more heavily weighted. Deciding which weights to use requires some experience and a bit of luck.

• Choice of weights is somewhat arbitrary since there is not set formula to determine them.

16

Weighted Moving AveragesMathematically,

Weighted Moving average =

∑(weight for period n) x (Demand in period n) ∑weights

17

Weighted Moving Averages

• Include all past observations• Weight recent observations much more

heavily than very old observations:

weight

today

Decreasing weight given to older observations


machine sales, units Three-month weighted moving average

January 10

February 12

March 13

April 16

May 19

June 23

July 26

August 30

September 28

October 18

November 16

December 14 19

Example

Weighting the past three months as follows:

Weights applied Period

3 Last month

2 Two months ago

1 Three months ago

6 Sum of weights

20



Three-month weighted moving average

January 10

February 12

March 13

April 16

May 19

June 23

July 26

August 30

September 28

October 18

November 16

December 14 21




January 10

February 12

March 13

April 16 (1 x 10 + 2 x 12 + 3 x 13) / 6 = 12.16

May 19

June 23

July 26

August 30

September 28

October 18

November 16

December 14 22




January 10

February 12

March 13

April 16 (1 x 10 + 2 x 12 + 3 x 13) / 6 = 12.16

May 19 (1 x 12 + 2 x 13 + 3 x 16) / 6 = 14.33

June 23

July 26

August 30

September 28

October 18

November 16

December 14 23




January 10

February 12

March 13

April 16 (1 x 10 + 2 x 12 + 3 x 13) / 6 = 12.16

May 19 (1 x 12 + 2 x 13 + 3 x 16) / 6 = 14.33

June 23 (1 x 13 + 2 x 16 + 3 x 19) / 6 = 17

July 26

August 30

September 28

October 18

November 16

December 14 24




January 10

February 12

March 13

April 16 (1 x 10 + 2 x 12 + 3 x 13) / 6 = 12.16

May 19 (1 x 12 + 2 x 13 + 3 x 16) / 6 = 14.33

June 23 (1 x 13 + 2 x 16 + 3 x 19) / 6 = 17

July 26 (1 x 16 + 2 x 19+3x23) / 6 = 20.5

August 30 (1x19+2x23+3x26)/6=23.83

September 28 (1x23+2x26+3x30)/6=27.5

October 18 (1x26+2x30+3x28)/6=28.33

November 16 (1x30+2x28+3x18)/6=23.33

December 14 (1x28+2x18+3x16)/6=18.67 25

Limitations

• less sensitive to real changes in the data.

• cannot pick up trends very well.

• require extensive records of past data.

26

Exponential Smoothing A new forecast is based on the forecast of

the previous period.

The following relationship exists between the two:

New forecast = Last period’s forecast + α (Last period’s actual demand – last period’s forecast)

Where, α denotes a weight, or smoothing constant.

27

Exponential SmoothingMathematically :

Ft = Ft-1 + α (At-1

– Ft-1 ) 0 < =α < =1

where

Ft = New forecast

F t-1 = Previous forecast

α= Smoothing constant (0 <= α <= 1)

At-1 = Previous period’s actual demand

• The smoothing constant, α, is generally in the range from .05 to .50 for business applications.

28

29

Week t Sales (1000’s of gallons)

Exponential smoothing forecast Ft using α = .2


1 17

2 21

3 19

4 23

5 18

6 16

7 20

8 18

9 22

10 20

11 15

12 22

30




1 17 17 17

2 21

3 19

4 23

5 18

6 16

7 20

8 18

9 22

10 20

11 15

12 22

31




1 17 17 17

2 21 17+.2(17-17)=17 17+.5(17-17)=17

3 19

4 23

5 18

6 16

7 20

8 18

9 22

10 20

11 15

12 22

32




1 17 17 17

2 21 17+.2(17-17)=17 17+.5(17-17)=17

3 19 19+.2(21-17)=17.8 19+.5(21-17)=19

4 23

5 18

6 16

7 20

8 18

9 22

10 20

11 15

12 22

33

Week t Sales (1000’s of gallons



1 17 17 17

2 21 17+.2(17-17)=17 17+.5(17-17)=17

3 19 17+.2(21-17)=17.8 17+.5(21-17)=19

4 23 17.8 + .2(19 – 17.8) = 18.04 19 + .5(19 – 19) = 19

5 18 18.04 + .2(23 – 18.04) = 19.03 19 + .5(23 – 19) = 21

6 16 19.03 + .2(18 – 19.03) = 18.83 21 + .5(18 – 21) = 19.5

7 20 18.83 + .2(16 – 18.83) = 18.26 19.5 + .5(16 – 19.5) = 17.75

8 18 18.26 + .2(20 – 18.26) = 18.61 17.75 + .5(20 – 17.75) = 18.88

9 22 18.61 + .2(18 – 18.61) = 18.49 18.88 + .5(18 – 18.88) = 18.44

10 20 18.49 + .2(22 – 18.49) = 19.19 18.44 + .5(22 – 18.44) = 20.22

11 15 19.19 + .2(20 – 19.19) = 19.35 20.22 + .5(20 – 20.22) = 20.11

12 22 19.35 + .2(22 – 19.35) = 18.48 20.11 + .5(22 – 20.11) = 21.06

Selecting the smoothing constant

• The exponential smoothing approach is easy to use, and has been successfully applied in many organizations. Selection of a suitable constant α is the pre-requisite for the success of smoothing technique.

34

The forecast error The overall accuracy of a forecasting

model can be determined by comparing the forecasted values with the actual or observed values.

Forecast error = Demand – Forecast

35

Measures of forecast error Mean absolute deviation (MAD) • This is computed by taking the sum of the

absolute values of the individual forecast errors and dividing by the number of periods of data (n):

MAD= ∑ |Forecast errors| / n

Mean squared error (MSE) • MSE is the average of the squared

differences between the forecasted and observed values. The formula is:

MSE = ∑ (Forecast errors)2 / n 36

37

Week t Sales (1000’s of gallons



1 17 17 17

2 21 17+.2(17-17)=17 17+.5(17-17)=17

3 19 17+.2(21-17)=17.8 17+.5(21-17)=19

4 23 17.8 + .2(19 – 17.8) = 18.04 19 + .5(19 – 19) = 19

5 18 18.04 + .2(23 – 18.04) = 19.03 19 + .5(23 – 19) = 21

6 16 19.03 + .2(18 – 19.03) = 18.83 21 + .5(18 – 21) = 19.5

7 20 18.83 + .2(16 – 18.83) = 18.26 19.5 + .5(16 – 19.5) = 17.75

8 18 18.26 + .2(20 – 18.26) = 18.61 17.75 + .5(20 – 17.75) = 18.88

9 22 18.61 + .2(18 – 18.61) = 18.49 18.88 + .5(18 – 18.88) = 18.44

10 20 18.49 + .2(22 – 18.49) = 19.19 18.44 + .5(22 – 18.44) = 20.22

11 15 19.19 + .2(20 – 19.19) = 19.35 20.22 + .5(20 – 20.22) = 20.11

12 22 19.35 + .2(22 – 19.35) = 18.48 20.11 + .5(22 – 20.11) = 21.06

38

Week t Sales 1000’s of gallons

RF with α = .2 RF with α = .5

1 17 17 17

2 21 17 17

3 19 18 19

4 23 18 19

5 18 19 21

6 16 19 20

7 20 18 18

8 18 19 19

9 22 18 18

10 20 19 20

11 15 19 20

12 22 18 21

Trend Projections. • This technique fits a trend line to a

series of historical data points and then projects the line into the future for medium - to long – range forecasts.

• Several mathematical trend equations can be developed (for example, exponential and quadratic), but we will discuss a linear (straight line) trends only.

39

Trend Projections

Using the standard method of Least Square

Assuming Time period as independent variable

And actual demand as dependent variable

40

The least square method • A least squares line is described in terms of its y –

intercept (the height at which it intercepts the y – axis) and its slope (the angle of the line). If we can compute y – intercept and slope, we can express the line as

Y = a + bX

where

y = Computed value of the variable to be predicted (called the dependent variable)

a = y – axis intercept

b = slope of the regression line

X = independent variable (which is time here)

41

X axis time

Y axis demand

Intercept

X axis time

Y axis demand

Slope

X axis time

Y axis demand

X axis time

Y axis demand

X axis time

Y axis demand

The least square method

Slope b=

Intercept a =Y- b X

X=∑Xi/n Y=∑Yi/n47

∑Xi Yi - n X Y

∑Xi 2

- n X2

Xi=Time periods(i=1,2,3…,n)

Yi=Actual demand during period Xi

Example

The demand for electrical power at Delhi over the period 1990 – 1996 is shown below, in megawatts. Let us fit a straight – line trend to these data and forecast 1997 demand

48

Year 1990 1991 1992 1993 1994 1995 1996

Electrical power Demand

74 79 80 90 105 142 122

Solution

49

Year Time Period(X)

Electrical power Demand(Y)

X2 XY

Solution

50

Year Time Period(X)

Electrical power Demand(Y)

X2 XY

1990 1 74

1991 2 79

1992 3 80

1993 4 90

1994 5 105

1995 6 142

1996 7 122

Solution

51

Year Time Period(X)

E8lectrical power Demand(Y)

X2 XY

1990 1 74 1

1991 2 79 4

1992 3 80 9

1993 4 90 16

1994 5 105 25

1995 6 142 36

1996 7 122 49

Solution

52

Year Time Period(X)


X2 XY

1990 1 74 1 74

1991 2 79 4 158

1992 3 80 9 240

1993 4 90 16 360

1994 5 105 25 525

1995 6 142 36 852

1996 7 122 49 854

Solution

53

Year Time Period(X)


X2 XY

1990 1 74 1 74

1991 2 79 4 158

1992 3 80 9 240

1993 4 90 16 360

1994 5 105 25 525

1995 6 142 36 852

1996 7 122 49 854

∑X= ∑Y= ∑X2 = ∑XY =

Solution

54

Year Time Period(X)


X2 XY

1990 1 74 1 74

1991 2 79 4 158

1992 3 80 9 240

1993 4 90 16 360

1994 5 105 25 525

1995 6 142 36 852

1996 7 122 49 854

∑X=28 ∑Y=692 ∑X2 =140 ∑XY =3063

Solution

55

Year Time Period(X)


X2 XY

1990 1 74 1 74

1991 2 79 4 158

1992 3 80 9 240

1993 4 90 16 360

1994 5 105 25 525

1995 6 142 36 852

1996 7 122 49 854

∑X=28 ∑Y=692 ∑X2 =140 ∑XY =3063

X=∑Xi/n = 28/7 =4

Y=∑Yi/n =692/7 =98.86

Solution

56

Year Time Period(X)


X2 XY

1990 1 74 1 74

1991 2 79 4 158

1992 3 80 9 240

1993 4 90 16 360

1994 5 105 25 525

1995 6 142 36 852

1996 7 122 49 854

∑X=28 ∑Y=692 ∑X2 =140 ∑XY =3063

∑Xi Yi - n X Y

∑Xi 2

- n X2Slope b=

3063 – 7 x 4 x 98.86

140 – 7 x 42

294.92

28

=

= = 10.54

Solution

57

Year Time Period(X)


X2 XY

1990 1 74 1 74

1991 2 79 4 158

1992 3 80 9 240

1993 4 90 16 360

1994 5 105 25 525

1995 6 142 36 852

1996 7 122 49 854

∑X=28 ∑Y=692 ∑X2 =140 ∑XY =3063

Intercept a =Y- b X=98.86 – 10.54(4) = 56.7

Demand in 1997

• Y=a + b X

• Y= 56.7+10.54 X

• Y= 56.7+10.54 (8)

• Y=141.02

• Then we estimate the demand in 1997 is 141 megawatts.

58

CASUAL METHODS

• Casual methods seek to develop forecasts on the basis of cause-effects relationships specified in an explicit, quantitative manner.– Chain Ratio Method– Consumption Level Method– End Use Method– Leading Indicator Method– Econometric Method

Watling Line

Waiting Realities

• Inevitability of Waiting: Waiting results from variations in arrival rates and service rates

• Economics of Waiting: High utilization purchased at the price of customer waiting. Make waiting productive (salad bar) or profitable (drinking bar).

Laws of Service

• Maister’s First Law:Customers compare expectations with perceptions.

• Maister’s Second Law:Is hard to play catch-up ball.

• Skinner’s Law:The other line always moves faster.

• Jenkin’s Corollary:However, when you switch to another other line, the line you left moves faster.

Remember Me

• I am the person who goes into a restaurant, sits down, and patiently waits while the wait-staff does everything but take my order.

• I am the person that waits in line for the clerk to finish chatting with his buddy.

• I am the one who never comes back and it amuses me to see money spent to get me back.

• I was there in the first place, all you had to do was show me some courtesy and service.

The Customer

Waiting Line

• It is estimated that Americans spend a total of 37 billion hours a year waiting in lines.

• Places we wait in line...▪ stores ▪ hotels ▪ post offices▪ banks ▪ traffic lights ▪ restaurants▪ airports ▪ theme parks ▪ on the

phone• Waiting lines do not always contain people...

▪ returned videos▪ subassemblies in a manufacturing plant▪ electronic message on the Internet

• Queuing theory deals with the analysis and management of waiting lines.

Psychology of Waiting• That Old Empty Feeling: Unoccupied time goes

slowly• A Foot in the Door: Pre-service waits seem longer

that in-service waits• The Light at the End of the Tunnel: Reduce anxiety

with attention• Excuse Me, But I Was First: Social justice with FCFS

queue discipline• They Also Serve, Who Sit and Wait: Avoids idle

service capacity

Concept of loss of business due to customers’ waiting

• Cost analysis of provision of faster servicing to reduce queue length

• Marginal cost of extra provisioning during rush hours

Waiting Lines - Queuing Theory

The Purpose of Queuing Models

• Queuing models are used to: –describe the behavior of queuing

systems

–determine the level of service to provide

–evaluate alternate configurations for providing service

Queuing System Cost

• Cost of providing the service also known as service cost

• Cost of not providing the service also known as waiting cost

Trade-off

Service Level

Total Expected Cost

Cost of providing service

Cost of waiting time

OptimalService Level

Co

st o

f o

per

atin

g s

ervi

ce f

acil

ity

• Arrival pattern

• Service pattern

• Queue discipline

• Customer’s behavior

Important factors of Queuing Situations

Essential Features of Queuing Systems

DepartureQueue

discipline

Arrival process

Queueconfiguration

Serviceprocess

Renege

Balk

Callingpopulation

No futureneed for service

Queuing System: General Structure

• Arrival Process• According to source• According to numbers• According to time

Arrival Process Structure

Static Dynamic

AppointmentsPriceAccept/Reject BalkingReneging

Randomarrivals withconstant rate

Random arrivalrate varying

with time

Facility-controlled

Customer-exercised

control

Arrival process

Queuing System: General Structure

• Service System• Single server facility• Multiple, parallel facilities with single queue• Multiple, parallel facilities with multiple queues• Service facilities in a parallel

Common Queuing System Configurations

Waiting Line Server 1

Server 2

Server 3

Waiting Line

Waiting Line

CustomerLeaves

CustomerLeaves

CustomerLeaves

...

...

...

CustomerArrives

CustomerLeaves

...Waiting Line

Server 1

Server 2

Server 3

CustomerLeaves

CustomerLeaves

CustomerArrives

CustomerArrives

...

Waiting Line Server

CustomerLeaves

CustomerArrives

...

Waiting Line Server 2

CustomerLeaves Server 1

• Queue Discipline• Static

– First come first served

• Dynamic– Status of queue– Customer attribute

Queue Discipline

Queuediscipline

Static(FCFS rule)

Dynamic

selectionbased on status

of queue

Selection basedon individual

customerattributes

Number of customers

waitingRound robin Priority Preemptive

Processing timeof customers

(SPT rule)

• Customer Behavior• Balking• Reneging• Jockeying• Collusion