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The document discusses different forecasting methods including subjective models like the Delphi method, time series models like moving averages and exponential smoothing, and causal models like regression analysis. It provides details on the Delphi method and exponential smoothing approach. The Delphi method generates consensus forecasts through anonymous questionnaires while exponential smoothing generates new forecasts as a weighted average of the previous forecast and last period's actual value. The document compares simple and weighted moving averages and outlines how to calculate errors to evaluate forecast accuracy.

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Forecasting Demand for Services
Forecasting Models • Subjective Models Delphi Methods • Time Series Models Moving Averages Exponential Smoothing • Causal Models Regression 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 expert writes response (anonymous) Coordinator performs analysis Coordinator sends updated questionnaire Coordinator summarizes forecast Consensus reached? 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 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
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
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
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
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
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
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
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 Averages Mathematically, 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
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
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
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
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
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
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
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
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 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 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 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 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 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 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
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 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 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/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
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) 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
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 =
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
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
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
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
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 Optimal Service Level Costofoperatingservicefacility
• Arrival pattern • Service pattern • Queue discipline • Customer’s behavior Important factors of Queuing Situations
Essential Features of Queuing Systems Departure Queue discipline Arrival process Queue configuration Service process Renege Balk Calling population No future need 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 Random arrivals with constant rate Random arrival rate 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 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
• Queue Discipline • Static – First come first served • Dynamic – Status of queue – Customer attribute
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)
• Customer Behavior • Balking • Reneging • Jockeying • Collusion

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It service operations 1

  • 1.
  • 2.
    Forecasting Models • SubjectiveModels 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 SendsInitial Questionnaire Each expert writes response (anonymous) Coordinator performs analysis Coordinator sends updated questionnaire Coordinator summarizes forecast Consensus reached? YesNo
  • 5.
    DELPHI METHOD • Mainadvantages – 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 • Typicalapplication – Long-term forecasting – Technology forecasting
  • 7.
    Interactive Exercise: DelphiForecasting 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 • Movingaverages 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 • Includen most recent observations • Weight equally • Ignore older observations weight today 123...n 1/n 10
  • 11.
    Example Month Actual Washing machinesales, 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 machinesales, 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 machinesales, 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 machinesales, 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 machinesales, 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, WeightedMoving average = ∑(weight for period n) x (Demand in period n) ∑weights 17
  • 18.
    Weighted Moving Averages • Includeall 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 machinesales, 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 pastthree 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 machinesales, 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 machinesales, 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 machinesales, 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 machinesales, 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 machinesales, 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 sensitiveto real changes in the data. • cannot pick up trends very well. • require extensive records of past data. 26
  • 27.
    Exponential Smoothing A newforecast 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’sof 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’sof 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’sof 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’sof 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’sof 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 smoothingconstant • 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 Theoverall 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 forecasterror 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’sof 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’sof 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. • Thistechnique 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 thestandard method of Least Square Assuming Time period as independent variable And actual demand as dependent variable 40
  • 41.
    The least squaremethod • 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 Yaxis demand Intercept
  • 43.
    X axis time Yaxis demand Slope
  • 44.
    X axis time Yaxis demand
  • 45.
    X axis time Yaxis demand
  • 46.
    X axis time Yaxis demand
  • 47.
    The least squaremethod 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 forelectrical 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.
  • 50.
    Solution 50 Year Time Period(X) Electrical power Demand(Y) X2 XY 1990 174 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 174 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 174 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 174 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 174 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 174 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 174 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 174 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 • Casualmethods 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.
  • 61.
    Waiting Realities • Inevitabilityof 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 • Iam 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 • Itis 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 lossof 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 ofQueuing 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 ExpectedCost 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 ofQueuing Systems Departure Queue discipline Arrival process Queue configuration Service process Renege Balk Calling population No future need for service
  • 72.
    Queuing System: GeneralStructure • Arrival Process • According to source • According to numbers • According to time
  • 73.
    Arrival Process Structure StaticDynamic AppointmentsPriceAccept/Reject BalkingReneging Random arrivals with constant rate Random arrival rate varying with time Facility- controlled Customer- exercised control Arrival process
  • 74.
    Queuing System: GeneralStructure • 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 SystemConfigurations 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 basedon 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