Service Operations

1. Forecasting Demand for
Services

2. Forecasting Models
• Subjective Models
Delphi Methods
• Time Series Models
Moving Averages
Exponential Smoothing
• Causal Models
Regression Models

3. DELPHI METHOD
• Rationale
– Anonymous written responses encourage
honesty and avoid that a group of experts are
dominated by only a few members

4. DELPHI METHOD
• Approach
Coordinator
Sends Initial
Questionnaire
Each expert
writes response
(anonymous)
Coordinator
performs
analysis
Coordinator
sends updated
questionnaire
Coordinator
summarizes
forecast
Consensus
reached?
YesNo

5. 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

6. DELPHI METHOD
• Typical application
– Long-term forecasting
– Technology forecasting

7. Interactive Exercise: Delphi Forecasting
Question: 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

8. 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

9. 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

10. Moving Average
• Include n most recent observations
• Weight equally
• Ignore older observations
weight
today
123...n
1/n
10

11. Example
Month 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

12. Example
Month Actual Washing
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

13. Example
Month Actual Washing
machine sales, units
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
July 26
August 30
September 28
October 18
November 16
December 14 13

14. Example
Month Actual Washing
machine sales, units
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
August 30
September 28
October 18
November 16
December 14 14

15. Example
Month Actual Washing
machine sales,
units
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

16. 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

17. Weighted Moving Averages
Mathematically,
Weighted Moving average =
∑(weight for period n) x (Demand in period n)
∑weights
17

18. 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

19. Example
Month Actual Washing
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

20. 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

21. Example
Month Actual Washing
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 21

22. Example
Month Actual Washing
machine sales,
units
Three-month weighted moving average
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

23. Example
Month Actual Washing
machine sales,
units
Three-month weighted moving average
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

24. Example
Month Actual Washing
machine sales,
units
Three-month weighted moving average
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

25. Example
Month Actual Washing
machine sales,
units
Three-month weighted moving average
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

26. Limitations
• less sensitive to real changes in the data.
• cannot pick up trends very well.
• require extensive records of past data.
26

27. 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

28. Exponential Smoothing
Mathematically :
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. 29
Week t Sales
(1000’s of gallons)
Exponential smoothing
forecast Ft using α = .2
Exponential smoothing forecast Ft
using α = .5
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. 30
Week t Sales
(1000’s of gallons)
Exponential smoothing
forecast Ft using α = .2
Exponential smoothing forecast Ft
using α = .5
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. 31
Week t Sales
(1000’s of gallons)
Exponential smoothing
forecast Ft using α = .2
Exponential smoothing forecast Ft
using α = .5
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. 32
Week t Sales
(1000’s of gallons)
Exponential smoothing
forecast Ft using α = .2
Exponential smoothing forecast Ft
using α = .5
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. 33
Week t Sales
(1000’s of gallons
Exponential smoothing forecast
Ft using α = .2
Exponential smoothing forecast
Ft using α = .5
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

34. 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

35. 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

36. 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. 37
Week t Sales
(1000’s of gallons
Exponential smoothing forecast
Ft using α = .2
Exponential smoothing forecast
Ft using α = .5
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. 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

39. 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

40. Trend Projections
Using the standard method of Least
Square
Assuming Time period as independent
variable
And actual demand as dependent
variable
40

41. 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

42. X axis time
Y axis demand
Intercept

43. X axis time
Y axis demand
Slope

44. X axis time
Y axis demand

45. X axis time
Y axis demand

46. X axis time
Y axis demand

47. The least square method
Slope b=
Intercept a =Y- b X
X=∑Xi/n Y=∑Yi/n 47
∑Xi Yi - n X Y
∑Xi
2
- n X2
Xi=Time periods(i=1,2,3…,n)
Yi=Actual demand during period Xi

48. 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

49. Solution
49
Year Time
Period(X)
Electrical
power
Demand(Y)
X2
XY

50. 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

51. 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

52. Solution
52
Year Time
Period(X)
E8lectrical
power
Demand(Y)
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

53. Solution
53
Year Time
Period(X)
E8lectrical
power
Demand(Y)
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 =

54. Solution
54
Year Time
Period(X)
E8lectrical
power
Demand(Y)
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

55. Solution
55
Year Time
Period(X)
E8lectrical
power
Demand(Y)
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

56. Solution
56
Year Time
Period(X)
E8lectrical
power
Demand(Y)
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 X2
Slope b=
3063 – 7 x 4 x 98.86
140 – 7 x 42
294.92
28
=
= = 10.54

57. Solution
57
Year Time
Period(X)
E8lectrical
power
Demand(Y)
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

58. 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

59. 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

60. Watling Line

61. 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).

62. 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.

63. 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

64. 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.

65. 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

66. 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

67. 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

68. Queuing System Cost
• Cost of providing the service also
known as service cost
• Cost of not providing the service also
known as waiting cost

69. Trade-off
Service Level
Total Expected Cost
Cost of providing service
Cost of waiting time
Optimal
Service Level
Costofoperatingservicefacility

70. • Arrival pattern
• Service pattern
• Queue discipline
• Customer’s behavior
Important factors of Queuing Situations

71. Essential Features of Queuing Systems
Departure
Queue
discipline
Arrival
process
Queue
configuration
Service
process
Renege
Balk
Calling
population
No future
need for
service

72. Queuing System: General Structure
• Arrival Process
• According to source
• According to numbers
• According to time

73. Arrival Process Structure
Static Dynamic
AppointmentsPriceAccept/Reject BalkingReneging
Random
arrivals with
constant rate
Random arrival
rate varying
with time
Facility-
controlled
Customer-
exercised
control
Arrival
process

74. 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

75. Common Queuing System Configurations
Waiting Line Server 1
Server 2
Server 3
Waiting Line
Waiting Line
Customer
Leaves
Customer
Leaves
Customer
Leaves
...
...
...
Customer
Arrives
Customer
Leaves
...
Waiting Line
Server 1
Server 2
Server 3
Customer
Leaves
Customer
Leaves
Customer
Arrives
Customer
Arrives
...
Waiting Line Server
Customer
Leaves
Customer
Arrives
...
Waiting Line Server 2
Customer
LeavesServer 1

76. • Queue Discipline
• Static
– First come first served
• Dynamic
– Status of queue
– Customer attribute

77. Queue Discipline
Queue
discipline
Static
(FCFS rule)
Dynamic
selection
based on status
of queue
Selection based
on individual
customer
attributes
Number of
customers
waiting
Round robin Priority Preemptive
Processing time
of customers
(SPT rule)

78. • Customer Behavior
• Balking
• Reneging
• Jockeying
• Collusion