Theory at a Glance (For IES, GATE, PSU)

Transcription

1 1. Forecasting Theory at a Glance (For IES, GATE, PSU) Forecasting means estimation of type, quantity and quality of future works e.g. sales etc. It is a calculated economic analysis. 1. Basic elements of forecasting: 1. Trends. Cycles 3. Seasonal Variations 4. Irregular Variations. Sales forecasting techniques: a. Historic estimation b. Sales force estimation c. Trend line (or Time-series analysis) technique d. Market survey e. Delphi Method f. Judge mental techniques g. Prior knowledge h. Forecasting by past average i. Forecasting from last period's sales j. Forecasting by Moving average k. Forecasting by weighted moving average l. Forecasting by Exponential smoothing m. Correlation Analysis n. Linear Regression Analysis. I. Average method: Forecast sales for next period = Average sales for previous period Example: Period No Sales Forecast sales for Period No = = 7 6 II. Forecast by Moving Average: Page 4 of 318

2 In this method the forecast is neither influenced by very old data nor does it solely reflect the figures of the previous period. Example: Year Period Sales Four-period average forecasting Forecast for 1988 period = 40 = 50 4 Forecast for 1988 period = = 50 4 III. Weighted Moving Average: A weighted moving Average allows any weights to be placed on each element, providing of course, that the sum of all weights equals one. Example: Period Sales Month Month- 90 Month Month-4 95 Month Forecast (weights 40%, 30%, 0%, 10% of most recent month) Forecast for month-5 would be: F 5 = = 97.5 Forecast for month-6 would be: F 6 = = 10.5 IV. Exponential Smoothing: New forecast = α (latest sales figure) + (1 α ) (old forecast) [VIMP] Where: α is known as the smoothing constant. The size of α should be chosen in the light of the stability or variability of actual sales, and is normally from 0.1 to 0.3. The smoothing constant, α, that gives the equivalent of an N-period moving average can be calculated as follows, α =. N + 1 For e.g. if we wish to adopt an exponential smoothing technique equivalent to a nineperiod moving average then, α = = Page 5 of 318

3 Basically, exponential smoothing is an average method and is useful for forecasting one period ahead. In this approach, the most recent past period demand is weighted most heavily. In a continuing manner the weights assigned to successively past period demands decrease according to exponential law. Generalized equation: 0 1 k 1 k Ft= α. ( 1 α) dt 1 + α. ( 1 α) dt + α. ( 1 α) dt α ( 1 α) dt k+ ( 1 α) Ft k [Where k is the number of past periods] It can be seen from above equation that the weights associated with each demand of equation are not equal but rather the successively older demand weights decrease by factor (1 α). α 1 α 0, α 1 α 1, α 1 α, α 1 α 3 In other words, the successive terms ( ) ( ) ( ) ( ) decreases exponentially. This means that the more recent demands are more heavily weighted than the remote demands. Exponential smoothing method of Demand Forecasting: (ESE-06) (i) Demand for the most recent data is given more weightage. (ii) This method requires only the current demand and forecast demand. (iii) This method assigns weight to all the previous data. V. Regression Analysis: Regression analysis is also known as method of curve fitting. On this method the data on the past sales is plotted against time, and the best curve called the Trend line or Regression line or Trend curve. The forecast is obtained by extrapolating this trend line or curve. For linear regression y = a+ bx Σy bσx a = n nσxy Σx Σy b = nσx ( )( ) ( Σx) Standard error = Σ ( y y1 ) ( n ) Sales Past data Time Forecast Page 6 of 318

4 OBJECTIVE QUESTIONS (GATE, IES, IAS) Previous 0-Years GATE Questions GATE-1. GATE-. GATE-3. GATE-4. Which one of the following forecasting techniques is not suited for making forecasts for planning production schedules in the short range? [GATE-1998] (a) Moving average (b) Exponential moving average (c) Regression analysis (d) Delphi A moving average system is used for forecasting weekly demand. F1(t) and F(t) are sequences of forecasts with parameters m1 and m, respectively, where m1 and m (m1 > m) denote the numbers of weeks over which the moving averages are taken. The actual demand shows a step increase from d1 to d at a certain time. Subsequently, [GATE-008] (a) Neither F1(t) nor F(t) will catch up with the value d (b) Both sequences F1(t) and F(t) will reach d in the same period (c) F1(t) will attain the value d before F(t) (d) F(t) will attain the value d before F1(t) When using a simple moving average to forecast demand, one would (a) Give equal weight to all demand data [GATE-001] (b) Assign more weight to the recent demand data (c) Include new demand data in the average without discarding the earlier data (d) Include new demand data in the average after discarding some of the earlier demand data Which of the following forecasting methods takes a fraction of forecast error into account for the next period forecast? [GATE-009] (a) Simple average method (b) Moving average method (c) Weighted moving average method (d) Exponential smoothening method GATE-5. The demand and forecast for February are 1000 and 1075, respectively. Using single exponential smoothening method (smoothening coefficient = 0.5), forecast for the month of March is: [GATE-010] (a) 431 (b) 9587 (c) (d) GATE-6. The sales of a product during the last four years were 860, 880, 870 and 890 units. The forecast for the fourth year was 876 units. If the forecast for the fifth year, using simple exponential smoothing, is equal to the forecast using a three period moving average, the value of the exponential smoothing constant a is: [GATE-005] Page 7 of 318

5 1 1 ( a) ( b) ( c) ( d ) GATE-7. For a product, the forecast and the actual sales for December 00 were 5 and 0 respectively. If the exponential smoothing constant (α) is taken as 0., then forecast sales for January, 003 would be: [GATE-004] (a) 1 (b) 3 (c) 4 (d) 7 GATE-8. GATE-9. GATE-10. GATE-11. The sales of cycles in a shop in four consecutive months are given as 70, 68, 8, and 95. Exponentially smoothing average method with a smoothing factor of 0.4 is used in forecasting. The expected number of sales in the next month is: [GATE-003] (a) 59 (b) 7 (c) 86 (d) 136 In a forecasting model, at the end of period 13, the forecasted value for period 14 is 75. Actual value in the periods 14 to 16 are constant at 100. If the assumed simple exponential smoothing parameter is 0.5, then the MSE at the end of period 16 is: [GATE-1997] (a) (b) (c) (d) The most commonly used criteria for measuring forecast error is: (a) Mean absolute deviation (b) Mean absolute percentage error (c) Mean standard error (d) Mean square error [GATE-1997] In a time series forecasting model, the demand for five time periods was 10, 13, 15, 18 and. A linear regression fit resulted in an equation F = t where F is the forecast for period t. The sum of absolute deviations for the five data is: [GATE-000] (a). (b) 0. (c) 1. (d) 4.3 Previous 0-Years IES Questions IES-1. IES-. IES-3. Which one of the following is not a purpose of long-term forecasting? [IES 007] (a) To plan for the new unit of production (b) To plan the long-term financial requirement. (c) To make the proper arrangement for training the personnel. (d) To decide the purchase programme. Which one of the following is not a technique of Long Range Forecasting? [IES-008] (a) Market Research and Market Survey (b) Delphi (c) Collective Opinion (d) Correlation and Regression Assertion (A): Time series analysis technique of sales-forecasting can be applied to only medium and short-range forecasting. Reason (R): Qualitative information about the market is necessary for long-range forecasting. [IES-001] (a) Both A and R are individually true and R is the correct explanation of A (b) Both A and R are individually true but R is not the correct explanation of A (c) A is true but R is false (d) A is false but R is true Page 8 of 318