Operations management- least square methods and time series, and differrent forecasting methods including numericals for practice with solution. Third module contents for the subject operations management for ktu .

Operations management- least square methods and time series, and differrent forecasting methods including numericals for practice with solution. Third module contents for the subject operations management for ktu .

1. MODULE 3

2. Demand forecast The demand forecast gives the expected level of demand for goods or services. This is the basic input for business planning and control. Hence, the decisions for all the functions of any corporate house are influenced by the demand forecast Prediction is an estimate of future event through subjective considerations other than just the past data. For prediction, a good subjective estimation is based on managers skill, experience and judgement. There is an influence of one’s own perception and bias in prediction. So it is less accurate and has low reliability. Forecasting is an estimate of future event achieved by systematically combining and casting forward in a predetermined way data about the past.

3. NEED FOR DEMAND FORECASTING Majority of the activities of the industries depend upon the future sales. Projected demand for the future assists in decision-making with respect to investment in plant and machinery, market planning and programmes . To schedule the production activity to ensure optimum utilisation of plant’s capacity. To prepare material planning to take up replenishment action to make the materials available at right quantity and right time. To provide an information about the relationship between demand for different products in order to obtain a balanced production in terms of quantity required of different products as a function of time. Forecasting is going to provide a future trend which is very much essential for product design and development.

4. FORECASTING METHODS Judgemental techniques Time Series methods. Causal methods (Econometric Forecasting).

5. JUDGEMENTAL TECHNIQUES. Opinion Survey Method: Executive Opinion Method: Customer and Distributor Surveys: Marketing Trials: Market Research: Delphi Technique:

6. Time series method The time series methods does not study the factors that influence the demand and in this method all the factors that shape the demand are grouped into one factor-time and demand is expressed as a series of data with respect to time. The time series analysis consists of determining the trend underlying the demand and extrapolate the future trend. Statistical methods are used to determine the trend.

7. Time series consists of four components: 1. Trend (T): The long period 2. Cyclical Fluctuations 3.Seasonal Variations 4. Irregular Variations

8. LEAST SQUARE METHOD OF FORECASTING (Regression Analysis) This is the mathematical method of obtaining “the line of best fit between the dependent variable (usually demand) and an independent variable. This method is called least square method as the sum of the square of the deviations of the various points from the line of best fit is minimum or least. It gives the equation of the line for which the sum of the squares of vertical distances between the actual values and the line values are at minimum”

9. where b is the slope of the line a is the y-intercept. The values of the constants a and b are determined by the two simultaneous equations. …..(1) = a + b …….(2) To compute the values of a and b ( i ) Calculate the deviation (x) for each period and also the sum of deviations. (ii) Find the value of (iii) Find the value of (iv) Calculate the values of a and b (v) Make the sum of deviations = 0   In a simple regression analysis, the relationship between the dependent variable y and some independent variable x can be represented by a straight line.  

10. Substituting the value of = 0 in equations (1) and (2) We get, = Na = b which gives the values of a and b as a = /N b = / Note: If the Time Series consists of odd number of years to make = 0, the middle value of the time series is taken as the Origin. If the time series consists of even number of years, the midway period between two middle periods is taken as origin to make = 0.  

11. PROBLEM2

12. Least square method when the sum of the deviations is not zero ( )  

13. a=15.07 b=3.11

14. Measures of Forecast Accuracy Demand forecast influences most of the decisions in all the functions. Hence, it must be estimated with the highest level of precision. Some common measures are inevitable to measure the accuracy of a forecasting technique. This measure may be an aggregate error (deviation) of the forecast values from the actual demands. The different types of errors which are generally computed are as presented below. Mean Absolute Deviation (MAD) Mean Square Error (MSE) Mean Forecast Error (MFE) Mean Absolute Percent Error (MAPE)

15. 1. Mean Absolute Deviation (MAD) It is the mean of absolute deviations of forecast demands from actual demand values Where, Dt = Actual demand for the period t Ft = Forecast demand for the period t n = Number of time period used.

16. 2. Mean Square Error (MSE). Mean square error is the mean of the squares of the deviations of the forecast demands from the actual demand values. Usually, the effects on operations of small errors are not serious. These errors may be smoothed out by inventory or overtime work. It will be difficult to have smoothed values for forecast even if there are few large errors. Consequently, a method of measuring errors that penalizes large errors more than small errors is sometime desired. The mean square error (MSE) provides this type of measure of forecast error.

17. 3. Mean Forecast Error (MFE) Mean forecast error (MFE) is the mean of the deviations of the forecast demands from the actual demands. Where, n = Total number of errors used.

18. 4.Mean Absolute Percentage Error (MAPE) Mean absolute percentage error (MAPE) is the mean of the percent deviations of the forecast demands from the actual demands.

19. QUANTITATIVE FORECASTING TECHNIQUES

20. Simple Moving Average Method A simple moving average is a method of computing the average of a specified number of the most recent data values in a series At each period, fresh average is computed at the end of each period by adding the demand of the most recent period and deleting the data of the old-period since the data in this method changes from period to period, it is called moving average method. The formula to compute the simple moving average (SMA) (n period )is as follows. Where, M t = Simple moving average at the end of period t (It is to be used as a forecast for period t + 1 ). D t = Actual demand in period t. n = Number of periods included in each average.  

21. Mean Forecast Error (MFE) = –0.889 Mean Absolute Deviation (MAD) = 16.37 The values printed under column M(t) are obtained as: Moving Average Period (n) = 3 M(3) = (95 + 100 + 87)/3 = 94 M(4) = (100 + 87 + 123)/3 = 103.33 The forecast for period 13 would be: F13 = M12 = 92

22. Comments: In most cases, this method is applied to forecast for only one period into the future. The forecaster must wait until demand entries are available for making the first forecast. This method is applicable only for horizontal demand data patterns. This model requires to store the first n observed values, which consumes considerable amount of computer storage space if the demands of several products are to be forecasted. Greater smoothing effect could be obtained by including more observations in the moving average.

23. 2. Weighted Moving Average Method Equal weights were assigned to all periods in the computation of the simple moving average. The weighted moving average assigns more weight to some demand values (usually the more recent ones) than to others. W 3 =0.5,W 2 =0.3,W 1 =0.2

24. where i = 1, 2, 3 if we use three periods moving averages. i = 3 corresponds to the most recent time period and i = 1 corresponds to the oldest time period. W t = Weight for the time period t. In the example, W 1 = 0.2, W 2 = 0.3 and W 3 = 0.5

25. 3. Simple (Single) Exponential Smoothing Method Exponential smoothing method requires only the current demand and the forecasted demand for the current month. Simple moving average method gives the equal weightage to the all the periods. Exponential smoothing is distinguished by the fact that it assigns weight to all the previous data and the pattern of weights assigned are of exponential form ) Where, F t = Smoothed average forecast for period t. F t–1 = Previous period forecast. = Smoothing constant, weight given to previous data (0 < < 1). D t–1 = Previous period demand.  

26. A firm uses simple exponential smoothing with a = 0.2 to forecast demand. The forecast for the first week of January was 400 units, whereas actual demand turned out to be 450 units. (a) Forecast the demand for the second week of January. (b) Assume that the actual demand during the second week of January turned out to be 460 units. Forecast the demand up to February third week, assuming the subsequent demands as 465, 434, 420, 498, and 462 units. Example 1

27. Solution. The forecast for the second week of January is computed as shown below. F t = F t – 1 + a (D t – 1 – F t – 1 ) F 2 = 400 + 0.2 (450 – 400) = 410 units. (b) The workings for the remaining weeks are shown in tabular form.

28. Trend Adjusted Exponential Smoothing Simple exponential smoothing method fails to responds to trends A trend in a time series is a systematic increase or decrease in the average of the series overtime. When there is a significant presence of a trend, there is a need to modify the exponential smoothing approach.  

29. Where, α = smoothing parameter for the average. = smoothing parameter for the trend.  

30. Problem A pathological laboratory conducts on an average 28 blood tests per week during last one month. The trend over that period was 3 additional patients per week. This week’s demand was for 27 blood tests. Assume α = 0.2 and = 0.2 to calculate forecast for next week.  

31. A = 28 patients and T = 3 patients. The forecast for next week is computed as follows: A 1 = 0.20 (27) + 0.80 (28 + 3) = 30.2 T 1 = 0.20 (30.2 – 28) + 0.80 (3) = 2.8 F 2 = 30 + 2.8 = 33 patient tests. If the actual number of patients in week 2 proved to be 44, the updated forecast for week 3 is A 2 = (0.2) (44) + 0.80 (30.2 + 2.8) = 35.2 T 2 = (0.20) (35.2 – 30.2) + 0.80 (2.8) = 3.2 F 3 = 35.2 + 3.2 38 blood tests.