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					            TM 631 Optimization
                  Fall 2008
          Dr. Frank Joseph Matejcik
12th Session: Ch. 27 on disk
Forecasting
12/01/08




Frank Matejcik SD School of Mines & Technology   1
                       Activities
• Review assignments and resources
• Hand back exams
• Assignment
   – weird way of numbering problems
   Chapter 27
   27.4-2, 27.5-3, 27.6-2, 27.6-3, & 27.8-2

• Chapter 27 On Disk H & L

Frank Matejcik SD School of Mines & Technology   2
             Tentative Schedule
          Chapters Assigned                Chapters Assigned
9/01/2008   Holiday             11/17/2008 9 9.3-3, 9.4-1, 9.5-6
9/08/2008   1, 2 ________       11/24/2008 9 9.6-1, 9.8-1
9/15/2008 3 3.1-8,3.2-4,3.6-3 12/01/2008 27 27.4-2, 27.5-3,
9/22/2008 4 4.3-6, 4.4-6, 4.7-6 27.6-2, 27.6-3, & 27.8-2
9/29/2008   6 6.3-1, 6.3-5,     12/08/2008 18
            and 6.8-3(abce) 12/15/2008 Final
10/06/2008 Exam 1
10/13/2008 Holiday
10/20/2008 8 8.1-5, 8.1-6, 8.2-6, 8.2-7(ab), 8.2-8
10/27/2008 8 8.4 Answers in Slides
11/03/2008 21
11/10/2008 Exam 2
 Frank Matejcik SD School of Mines & Technology   3
             Web Resources
• Class Web site on the HPCnet system
• http://sdmines.sdsmt.edu/sdsmt/directory/co
  urses/2008fa/tm631M021
• May use D2L, also. It has a password
  protection
• Answers found from the Fall 2006 site
  http://sdmines.sdsmt.edu/sdsmt/directory/co
  urses/2006fa/tm631021 Look at the Answer
  Link and the User guide and password for
  the answer link.

 Frank Matejcik SD School of Mines & Technology   4
             Ch. 27 Forecasting
• Questions in Forecasting
   – Economic growth over the next year?
   – Where is the stock market headed?
   – What about interest rates?
   – How will consumer tastes be changing?
   – What will be the hot new products?
• Forecasts generally wrong (inaccurate)
• Business depends on management
  spotting trends and responding
Frank Matejcik SD School of Mines & Technology   5
             Ch. 27 Forecasting
• historical data allow use of statistical
  forecasting methods
   – Time series
   – Regression Analysis
• judgmental forecasting methods that
  solely use expert judgment also are
  available.


Frank Matejcik SD School of Mines & Technology   6
  27.1 Forecasting Applications
• Large Application Areas from Articles
   – Sales Forecasting
   – Forecasting the Need for Spare Parts
   – Forecasting Production Yields
   – Forecasting Economic Trends
   – Forecasting Staffing Needs
   – Other (specialty methods)
• Summary table

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         27.1 Sales Forecasting
• Underestimating demand may lead to
   1. lost sales
   2. unhappy customers
   3. competitors gain in the marketplace
• Overestimating demand leads to
   1.   Excessive inventory costs
   2.   Forced price reductions
   3.   Unneeded production or storage capacity
   4.   Lost opportunities to market other goods

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         27.1 Sales Forecasting
• Merit Brass Company supplies the pipe,
  valve, & fittings industry. 1990 project
   – statistical sales forecasting
   – finished-goods inventory management
• Improvements in customer service (as
  measured by product availability)
• Simultaneously achieving substantial cost
  reductions.

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         27.1 Sales Forecasting
• Spanish electric utility, Hidroeléctrica
  Español, used OR models to manage
  reservoirs used for hydroelectric power.
• A sophisticated statistical forecasting
  method is used to forecast energy demand
  on both a short-term and long-term basis.
• A hydrological forecasting model
  generates the forecasts of reservoir
  inflows.

Frank Matejcik SD School of Mines & Technology   10
         27.1 Sales Forecasting
• Airline companies depend heavily on the
  high fares for short notice travel on while
  discount fares help fill the seats.
• Allocating seats to the different fare
  classes is done to maximize revenue.
• American Airlines uses statistical
  forecasting of the demand at each fare.


Frank Matejcik SD School of Mines & Technology   11
     27.1 Forecasting the Need for
             Spare Parts
• IBM’s spare-parts inventory Sec. 18.8
   – valued in the billions of dollars
   – many thousand different parts
• American Airlines maintains spare parts
   – A missing parts lead to cancelled flights
   – 5,000 different types of rotatable parts (e.g.,
     landing gear and wing flaps)
   – Average value of $5,000 per item
   – PC based system using 18 month records

Frank Matejcik SD School of Mines & Technology   12
27.1 Forecasting Production Yields
• For high-technology products, the yield
  frequently is well under 100 percent.
• Albuquerque Microelectronics Operation,
  The 1st phase in production, the wafer fab
  process, would yield 0 to 40% (at start)
  and would increase to 35 to 75%.
• A statistical forecasting method that
  included this trend was used to forecast
  the production yield.

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27.1 Forecasting Economic Trends
• Forecasting economic trends on a regional,
  national, or international level.
   –   Nation’s gross domestic product
   –   Rate of inflation
   –   Unemployment rate
   –   Balance of trade
• Econometric models
   – developed in governmental agencies, university
     research centers, large corporations, and consulting
     firms
   – Many factors influence the economy. Some models
     include hundreds of variables and equations. Except
     for their size and scope, these models resemble the
     methods used for sales forecasting, etc.
Frank Matejcik SD School of Mines & Technology   14
27.1 Forecasting Economic Trends
• Forecasts by the U.S. Congressional Budget Office
   – Guide Congress in developing the federal budgets
   – Helps businesses assess economic outlook.
• U.S. Department of Labor contracted the
  unemployment insurance econometric forecasting model
  (UIEFM).
   – Used by state employment security agencies
   – Projects fundamental economic factors
       • unemployment rates
       • wage levels
       • the size of the labor force covered by unemployment insurance
   – UIEFM forecasts state payments in unemployment insurance.
   – By projecting tax inflows for the state’s unemployment insurance,
     UIEFM forecasts fund balances

Frank Matejcik SD School of Mines & Technology          15
27.1 Forecasting Staffing Needs
• American economy is a shifting emphasis
  to services: travel, tourism, entertainment,
  legal aid, health services, financial,
  educational, design, maintenance, etc.
• Forecasting “sales” becomes forecasting
  the demand for services, which then
  translates into forecasting staffing needs.


Frank Matejcik SD School of Mines & Technology   16
27.1 Forecasting Staffing Needs
• One of the fastest-growing service industries in
  the U.S. is call centers: providing technical
  assistance, making a travel reservations, filling
  an order for goods, or booking services, etc.
  There are several hundred thousand call centers
  in the United States.
• Providing too few agents to answer the
  telephone leads to
   – unhappy customers
   – lost calls
   – lost business.
• Too many agents cause excessive personnel
  costs.

Frank Matejcik SD School of Mines & Technology   17
27.1 Forecasting Staffing Needs
• Personnel scheduling at United Airlines
   – 4,000 reservations sales representatives
   – 11 reservations offices
   – 1,000 customer service agents at its Planning
     system was developed to design the work
     schedules including statistical forecasting of
     staffing requirements
       •   annual savings of over $6 million
       •   improved customer service
       •   reduced support staff requirements
       •   10 largest airports,
Frank Matejcik SD School of Mines & Technology   18
27.1 Forecasting Staffing Needs
• Taco Bell
   – 4,000 company-owned and franchised
     restaurants
   – Labor-management system makes statistical
     forecasting of the customers arriving in each
     15-minute interval. It saved $13 million in
     labor costs and improved customer service.




Frank Matejcik SD School of Mines & Technology   19
27.1 Forecasting Staffing Needs
• L.L. Bean is a retailer of outdoor goods &
  apparel.
   – Over 70 % of sales are from a call center.
   – Two 800 numbers, one for placing orders and
     the other for inquiries & problems.
   – Separate statistical forecasting models were
     developed to forecast staffing requirements
     for the two 800 numbers. Saved L.L. Bean
     $300,000 annually.

Frank Matejcik SD School of Mines & Technology   20
    27.1 Other (Summary slide)




Frank Matejcik SD School of Mines & Technology   21
                     27.1 Other
• Special Methods are used for
   – forecasting weather
   – the stock market
   – prospects for new products (before market
     testing)
• Not covered in this book



Frank Matejcik SD School of Mines & Technology   22
   27.2 Judgmental Forecasting
• Judgmental forecasting methods
   –   Subjective
   –   Intuition
   –   Expert opinion
   –   Experience
   –   Qualitative
   –   Used when no data are available
   –   Some decision makers prefer a judgmental method
   –   Combination of formal statistical method and
       judgmental forecasting methods can be used

Frank Matejcik SD School of Mines & Technology   23
   27.2 Judgmental Forecasting
• 1. Manager’s opinion:
   – Most informal of the methods
   – A single manager’s best judgment
   – Some data may be available to help.
   – Sometimes solely experience and an intimate
     knowledge of the current conditions




Frank Matejcik SD School of Mines & Technology   24
   27.2 Judgmental Forecasting
2. Jury of executive opinion:
   – Similar to managers opinion
   – A small group of high-level managers who
     pool their best judgment
   – Used for more critical forecasts where several
     executives share responsibility
   – Provides different types of expertise.



Frank Matejcik SD School of Mines & Technology   25
   27.2 Judgmental Forecasting
• 3. Sales force composite:
   – For a company employs a sales force
   – A bottom-up approach
   – Each salesperson provides an estimate of
     what sales in his region.
   – Managerial review at each level
   – Aggregated into a corporate sales forecast



Frank Matejcik SD School of Mines & Technology   26
   27.2 Judgmental Forecasting
• 4. Consumer market survey:
   – More grass-roots approach than sales force
     composite
   – Survey customers regarding the future
     purchasing plans and response d to new
     features
   – Helpful for designing new products
   – For initial sales forecasts
   – Helpful for planning a marketing campaign
Frank Matejcik SD School of Mines & Technology   27
   27.2 Judgmental Forecasting
• 5. Delphi method:
   – A panel of experts in different locations
     independently fill out a series of
     questionnaires
   – Each expert then can evaluate this group
     information in adjusting responses next time
   – Normally is used only at the highest levels of
     a corporation
   – Long-range forecasts of broad trends
• All methods must fit the organization
Frank Matejcik SD School of Mines & Technology   28
               27.3 Time Series
• A time series is a series of observations
  over time of some quantity of interest (a
  random variable). Thus, if Xi is the random
  variable of interest at time i, and if
  observations are taken at times
  i = 1, 2, . . . , t, then the observed values
  {X1 = x1, X2 = x2, . . . , Xt = xt} are a time
  series.

Frank Matejcik SD School of Mines & Technology   29
               27.3 Time Series




Frank Matejcik SD School of Mines & Technology   30
               27.3 Time Series
• constant level
• linear trend
• seasonal effect




Frank Matejcik SD School of Mines & Technology   31
               27.3 Time Series




Frank Matejcik SD School of Mines & Technology   32
               27.3 Time Series
• Xi = A + ei, for i = 1, 2, . . . ,
   – Xi is the random variable observed at time i,
   – A is the constant level of the model,
   – ei is the random error occurring at time i




Frank Matejcik SD School of Mines & Technology   33
               27.3 Time Series
• Let Ft+1 = forecast of the values of the time
  series at time t + 1, given the observed
  values, X1 = x1, X2 = x2, . . . , Xt = xt.
• Because of the random error et+1, it is
  impossible for Ft+1 to predict the value Xt+1
  = xt+1 precisely, but the goal is to have Ft+1
  estimate the constant level A = E(Xt+1)


Frank Matejcik SD School of Mines & Technology   34
    27.4 Forecasting for Constant-
               Levels
• Are an idealized representation of the
  actual situation. For the real time series, at
  least small shifts in the value of A may be
  occurring occasionally. Each of the
  following methods reflects a different
  assessment of how recently (if at all) a
  significant shift may have occurred.


Frank Matejcik SD School of Mines & Technology   35
      27.4 Last-Value Forecasting
                Method
• Imprecise; i.e., its variance is large;
  sample size is1.
• It is worth considering if
   1. The constant-level assumption is “shaky”
      and the process is changing rapidly or
   2. the assumption that et has constant variance
      is unreasonable
– Sometimes is called the naive method

Frank Matejcik SD School of Mines & Technology   36
       27.4 Averaging Forecasting
                Method
• Uses all the data points in the time series
  and simply averages these points.




• Because of a natural reluctance to use
  very old data, this procedure generally is
  limited to young processes.

Frank Matejcik SD School of Mines & Technology   37
          27.4 Moving-Average
• The moving-average estimator combines
  the advantages of the last value and
  averaging estimators in that it uses only
  recent history and it uses multiple
  observations.




Frank Matejcik SD School of Mines & Technology   38
    27.4 Exponential Smoothing
• a (0 < a < 1) is the smoothing constant.




Frank Matejcik SD School of Mines & Technology   39
    27.4 Exponential Smoothing




• Excel formulas are easy to develop.
• Can use Excel template or IOR
Frank Matejcik SD School of Mines & Technology   40
          27.5 Seasonal Effects In
                Forecasting
• It is fairly common for a time series to
  have a seasonal pattern
• Example: Christmas gifts
• Violates the assumption of a constant-
  level model
• Cycle need not be a year, a week for retail
• Fortunately, it is relatively straightforward
  to make seasonal adjustments
Frank Matejcik SD School of Mines & Technology   41
   27.5 Computer Club Warehouse
• Ex. COMPUTER CLUB WAREHOUSE
  (CCW) sells from a call center.
• In general, the seasonal factor for any
  period of a year (a quarter, a month, etc.)
  measures how that period compares to the
  overall average
• Seasonal factor
• Other procedures
• Excel template for seasonal factors.
Frank Matejcik SD School of Mines & Technology   42
   27.5 Computer Club Warehouse




Frank Matejcik SD School of Mines & Technology   43
   27.5 Computer Club Warehouse




Frank Matejcik SD School of Mines & Technology   44
    27.5 Seasonally Adjusted Time
               Series




Frank Matejcik SD School of Mines & Technology   45
    27.5 Seasonally Adjusted Time
               Series




Frank Matejcik SD School of Mines & Technology   46
        27.5 General Procedure
1. Seasonally adjust each value in the time series:




2. Select a time series forecasting method.
3. Apply this method to the seasonally adjusted
   time series to obtain a forecast of the next
   seasonally adjusted value (or values).
4. Multiply this forecast by the corresponding
   seasonal factor to obtain a forecast of the next
   actual value (without seasonal adjustment).
Frank Matejcik SD School of Mines & Technology   47
       27.6 Exponential Smoothing
        Method for a Linear Trend
• Suppose the observed time series is a linear trend
  superimposed with random fluctuations the slope,
  B, is called the trend factor. The model is
             Xi = A + Bi + ei, for i 1, 2, . . . ,
  –   Xi is the random variable observed at time i,
  –   A is a constant,
  –   B is the trend factor, and
  –   ei is the random error occurring at time i (with expected
      value of zero & constant variance).
• Advantages of Exponential Smoothing Method
Frank Matejcik SD School of Mines & Technology   48
        27.6 Adapting Exponential
               Smoothing




Frank Matejcik SD School of Mines & Technology   49
        27.6 Adapting Exponential
               Smoothing




Frank Matejcik SD School of Mines & Technology   50
        27.6 Adapting Exponential
               Smoothing
• Getting started requires two initial
  estimates
• x0 = initial estimate of the expected value
  of the time series (A) if the conditions just
  prior to beginning forecasting were to
  remain unchanged without any trend;
• T1 initial estimate of the trend of the time
  series (B) just prior to beginning
  forecasting.

Frank Matejcik SD School of Mines & Technology   51
        27.6 Adapting Exponential
               Smoothing




• Excel templates are given
Frank Matejcik SD School of Mines & Technology   52
       27.6 Application to CCW




Frank Matejcik SD School of Mines & Technology   53
       27.6 Application to CCW




Frank Matejcik SD School of Mines & Technology   54
       27.6 Application to CCW




Frank Matejcik SD School of Mines & Technology   55
  27.6 Forecasting More Than One
        Time Period Ahead
• For n periods ahead use

• It looks like a line

  27.7 Time Series Forecasting With
            CB Predictor
  Skip for this class

Frank Matejcik SD School of Mines & Technology   56
        27.8 Forecasting Errors




Frank Matejcik SD School of Mines & Technology   57
     27.9 Box-Jenkins Methods
• Developed by G.E.P. Box & G.M. Jenkins.
• An alternative name is the ARIMA method,
  which is an acronym for autoregressive
  integrated moving average.
• Sophisticated & complex technique, so
  book has only a conceptual overview (not
  applicable for solving problems)
• Not on exam

Frank Matejcik SD School of Mines & Technology   58
      27.10 Causal Forecasting
• Causal forecasting obtains a forecast of
  the quantity of interest (the dependent
  variable) by relating it directly to one or
  more other quantities (the independent
  variables) that drive the quantity of
  interest.




Frank Matejcik SD School of Mines & Technology   59
      27.10 Causal Forecasting




Frank Matejcik SD School of Mines & Technology   60
       27.10 Linear Regression
• X represents the independent variable
  and
• Y represents the dependent variable of
  interest.




Frank Matejcik SD School of Mines & Technology   61
27.10 Method of Least Squares




Frank Matejcik SD School of Mines & Technology   62
      27.10 Confidence Interval
      Estimation of E(Y|x = x*)
             Predictions
• Skip for our class




Frank Matejcik SD School of Mines & Technology   63
   27.11 Forecasting In Practice




Frank Matejcik SD School of Mines & Technology   64
               27.12 Conclusions

• The future success of any business
  depends on forecasting.
• Judgmental forecasting methods can be
  important.
• If historical data are available develop a
  statistical forecast.
• After forecasting begins, monitor
  performance

Frank Matejcik SD School of Mines & Technology   65

				
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