Créer une présentation
Télécharger la présentation

Télécharger la présentation
## Operations Management

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**Operations Management**Chapter 4 - Forecasting PowerPoint presentation to accompany Heizer/Render Principles of Operations Management, 6e Operations Management, 8e © 2006 Prentice Hall, Inc.**??**What is Forecasting? • Process of predicting a future event • Underlying basis of all business decisions • Production • Inventory • Personnel • Facilities**Forecasting Time Horizons**• Short-range forecast • Up to 1 year, generally less than 3 months • Purchasing, job scheduling, workforce levels, job assignments, production levels • Medium-range forecast • 3 months to 3 years • Sales and production planning, budgeting • Long-range forecast • 3+ years • New product planning, facility location, research and development**Influence of Product Life Cycle**• Introduction and growth require longer forecasts than maturity and decline • As product passes through life cycle, forecasts are useful in projecting • Staffing levels • Inventory levels • Factory capacity Introduction – Growth – Maturity – Decline**Introduction Growth Maturity Decline**Best period to increase market share R&D engineering is critical Practical to change price or quality image Strengthen niche Poor time to change image, price, or quality Competitive costs become critical Defend market position Cost control critical Company Strategy/Issues Fax machines CD-ROM Internet Drive-through restaurants Color printers Sales 3 1/2” Floppy disks Flat-screen monitors DVD Product Life Cycle Figure 2.5**Introduction Growth Maturity Decline**OM Strategy/Issues Product Life Cycle Product design and development critical Frequent product and process design changes Short production runs High production costs Limited models Attention to quality Forecasting critical Product and process reliability Competitive product improvements and options Increase capacity Shift toward product focus Enhance distribution Standardization Less rapid product changes – more minor changes Optimum capacity Increasing stability of process Long production runs Product improvement and cost cutting Little product differentiation Cost minimization Overcapacity in the industry Prune line to eliminate items not returning good margin Reduce capacity Figure 2.5**Types of Forecasts**• Economic forecasts • Address business cycle – inflation rate, money supply, housing starts, etc. • Technological forecasts • Predict rate of technological progress • Impacts development of new products • Demand forecasts • Predict sales of existing product**The Realities!**• Forecasts are seldom perfect • Most techniques assume an underlying stability in the system • Product family and aggregated forecasts are more accurate than individual product forecasts**Forecasting Approaches**Qualitative Methods • Used when situation is vague and little data exist • New products • New technology • Involves intuition, experience • e.g., forecasting sales on Internet**Forecasting Approaches**Quantitative Methods • Used when situation is ‘stable’ and historical data exist • Existing products • Current technology • Involves mathematical techniques • e.g., forecasting sales of color televisions**Overview of Qualitative Methods**• Jury of executive opinion • Pool opinions of high-level executives, sometimes augment by statistical models • Delphi method • Panel of experts, queried iteratively**Overview of Qualitative Methods**• Sales force composite • Estimates from individual salespersons are reviewed for reasonableness, then aggregated • Consumer Market Survey • Ask the customer**Time-Series Models**Associative Model Overview of Quantitative Approaches • Naive approach • Moving averages • Exponential smoothing • Trend projection • Linear regression**Time Series Forecasting**• Set of evenly spaced numerical data • Obtained by observing response variable at regular time periods • Forecast based only on past values • Assumes that factors influencing past and present will continue influence in future**Trend**Cyclical Seasonal Random Time Series Components**Naive Approach**• Assumes demand in next period is the same as demand in most recent period • e.g., If May sales were 48, then June sales will be 48 • Sometimes cost effective and efficient**∑ demand in previous n periods**n Moving average = Moving Average Method • MA is a series of arithmetic means • Used if little or no trend • Used often for smoothing • Provides overall impression of data over time**Actual 3-Month**Month Shed Sales Moving Average January 10 February 12 March 13 April 16 May 19 June 23 July 26 10 12 13 (10 + 12 + 13)/3 = 11 2/3 Moving Average Example (12 + 13 + 16)/3 = 13 2/3 (13 + 16 + 19)/3 = 16 (16 + 19 + 23)/3 = 19 1/3**Weightedmoving average**∑(weight for period n) x (demand in period n) ∑ weights = Weighted Moving Average • Used when trend is present • Older data usually less important • Weights based on experience and intuition**Weights Applied Period**3 Last month 2 Two months ago 1 Three months ago 6 Sum of weights Actual 3-Month Weighted Month Shed Sales Moving Average January 10 February 12 March 13 April 16 May 19 June 23 July 26 10 12 13 [(3 x 13) + (2 x 12) + (10)]/6 = 121/6 Weighted Moving Average [(3 x 16) + (2 x 13) + (12)]/6 = 141/3 [(3 x 19) + (2 x 16) + (13)]/6 = 17 [(3 x 23) + (2 x 19) + (16)]/6 = 201/2**Potential Problems With Moving Average**• Increasing n smooths the forecast but makes it less sensitive to changes • Do not forecast trends well • Require extensive historical data**Exponential Smoothing**• Form of weighted moving average • Weights decline exponentially • Most recent data weighted most • Requires smoothing constant () • Ranges from 0 to 1 • Subjectively chosen • Involves little record keeping of past data**Exponential Smoothing**New forecast = last period’s forecast + a(last period’s actual demand – last period’s forecast) Ft = Ft – 1 +a(At – 1 - Ft – 1) where Ft = new forecast Ft – 1 = previous forecast a = smoothing (or weighting) constant (0 a 1)**Exponential Smoothing Example**Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant a = .20**New forecast = 142 + .2(153 – 142)**Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant a = .20**Exponential Smoothing Example**Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant a = .20 New forecast = 142 + .2(153 – 142) = 142 + 2.2 = 144.2 ≈ 144 cars**Choosing **The objective is to obtain the most accurate forecast no matter the technique We generally do this by selecting the model that gives us the lowest forecast error Forecast error = Actual demand - Forecast value = At - Ft**Mean Absolute Deviation (MAD)**MAD = ∑ |actual - forecast| n Common Measure of Error**Forecast**including (FITt) = trend exponentially exponentially smoothed (Ft) + (Tt) smoothed forecast trend Exponential Smoothing with Trend Adjustment When a trend is present, exponential smoothing must be modified**Exponential Smoothing with Trend Adjustment**Ft = a(At - 1) + (1 - a)(Ft - 1 + Tt - 1) Tt = b(Ft - Ft - 1) + (1 - b)Tt - 1 Step 1: Compute Ft Step 2: Compute Tt Step 3: Calculate the forecast FITt= Ft+ Tt**Forecast**Actual Smoothed Smoothed Including Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt 1 12 11 2 13.00 2 17 3 20 4 19 5 24 6 21 7 31 8 28 9 36 10 Exponential Smoothing with Trend Adjustment Example Table 4.1**Forecast**Actual Smoothed Smoothed Including Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt 1 12 11 2 13.00 2 17 3 20 4 19 5 24 6 21 7 31 8 28 9 36 10 Exponential Smoothing with Trend Adjustment Example Step 1: Forecast for Month 2 F2 = aA1 + (1 - a)(F1 + T1) F2 = (.2)(12) + (1 - .2)(11 + 2) = 2.4 + 10.4 = 12.8 units Table 4.1**Forecast**Actual Smoothed Smoothed Including Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt 1 12 11 2 13.00 2 17 12.80 3 20 4 19 5 24 6 21 7 31 8 28 9 36 10 Exponential Smoothing with Trend Adjustment Example Step 2: Trend for Month 2 T2 = b(F2 - F1) + (1 - b)T1 T2 = (.4)(12.8 - 11) + (1 - .4)(2) = .72 + 1.2 = 1.92 units Table 4.1**Forecast**Actual Smoothed Smoothed Including Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt 1 12 11 2 13.00 2 17 12.80 1.92 3 20 4 19 5 24 6 21 7 31 8 28 9 36 10 Exponential Smoothing with Trend Adjustment Example Step 3: Calculate FIT for Month 2 FIT2 = F2 + T1 FIT2 = 12.8 + 1.92 = 14.72 units Table 4.1**Forecast**Actual Smoothed Smoothed Including Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt 1 12 11 2 13.00 2 17 12.80 1.92 14.72 3 20 4 19 5 24 6 21 7 31 8 28 9 36 10 Exponential Smoothing with Trend Adjustment Example 15.18 2.10 17.28 17.82 2.32 20.14 19.91 2.23 22.14 22.51 2.38 24.89 24.11 2.07 26.18 27.14 2.45 29.59 29.28 2.32 31.60 32.48 2.68 35.16 Table 4.1**35 –**30 – 25 – 20 – 15 – 10 – 5 – 0 – Actual demand (At) Product demand Forecast including trend (FITt) | | | | | | | | | 1 2 3 4 5 6 7 8 9 Time (month) Exponential Smoothing with Trend Adjustment Example Figure 4.3**^**y = a + bx ^ where y = computed value of the variable to be predicted (dependent variable) a = y-axis intercept b = slope of the regression line x = the independent variable Trend Projections Fitting a trend line to historical data points to project into the medium-to-long-range Linear trends can be found using the least squares technique**Actual observation (y value)**Deviation7 Deviation5 Deviation6 Deviation3 Values of Dependent Variable Deviation4 Deviation1 Deviation2 ^ Trend line, y = a + bx Time period Least Squares Method Figure 4.4**Actual observation (y value)**Deviation7 Deviation5 Deviation6 Deviation3 Values of Dependent Variable Deviation4 Deviation1 Deviation2 ^ Trend line, y = a + bx Time period Least Squares Method Least squares method minimizes the sum of the squared errors (deviations) Figure 4.4**Sxy - nxy**Sx2 - nx2 b = ^ y = a + bx a = y - bx Least Squares Method Equations to calculate the regression variables**Time Electrical Power**Year Period (x) Demand x2 xy 1999 1 74 1 74 2000 2 79 4 158 2001 3 80 9 240 2002 4 90 16 360 2003 5 105 25 525 2004 6 142 36 852 2005 7 122 49 854 ∑x = 28 ∑y = 692 ∑x2 = 140 ∑xy = 3,063 x = 4 y = 98.86 3,063 - (7)(4)(98.86) 140 - (7)(42) a = y - bx = 98.86 - 10.54(4) = 56.70 ∑xy - nxy ∑x2 - nx2 b = = = 10.54 Least Squares Example**Time Electrical Power**Year Period (x) Demand x2 xy 1999 1 74 1 74 2000 2 79 4 158 2001 3 80 9 240 2002 4 90 16 360 2003 5 105 25 525 2004 6 142 36 852 2005 7 122 49 854 Sx = 28 Sy = 692 Sx2 = 140 Sxy = 3,063 x = 4 y = 98.86 The trend line is ^ y = 56.70 + 10.54x 3,063 - (7)(4)(98.86) 140 - (7)(42) a = y - bx = 98.86 - 10.54(4) = 56.70 Sxy - nxy Sx2 - nx2 b = = = 10.54 Least Squares Example**Trend line,**y = 56.70 + 10.54x 160 – 150 – 140 – 130 – 120 – 110 – 100 – 90 – 80 – 70 – 60 – 50 – ^ Power demand | | | | | | | | | 1999 2000 2001 2002 2003 2004 2005 2006 2007 Year Least Squares Example**Seasonal Variations In Data**The multiplicative seasonal model can modify trend data to accommodate seasonal variations in demand Find average historical demand for each season Compute the average demand over all seasons Compute a seasonal index for each season Estimate next year’s total demand Divide this estimate of total demand by the number of seasons, then multiply it by the seasonal index for that season**Demand Average Average Seasonal**Month 2003 2004 2005 2003-2005 Monthly Index Jan 80 85 105 90 94 Feb 70 85 85 80 94 Mar 80 93 82 85 94 Apr 90 95 115 100 94 May 113 125 131 123 94 Jun 110 115 120 115 94 Jul 100 102 113 105 94 Aug 88 102 110 100 94 Sept 85 90 95 90 94 Oct 77 78 85 80 94 Nov 75 72 83 80 94 Dec 82 78 80 80 94 Seasonal Index Example**Demand Average Average Seasonal**Month 2003 2004 2005 2003-2005 Monthly Index Jan 80 85 105 90 94 Feb 70 85 85 80 94 Mar 80 93 82 85 94 Apr 90 95 115 100 94 May 113 125 131 123 94 Jun 110 115 120 115 94 Jul 100 102 113 105 94 Aug 88 102 110 100 94 Sept 85 90 95 90 94 Oct 77 78 85 80 94 Nov 75 72 83 80 94 Dec 82 78 80 80 94 average 2003-2005 monthly demand average monthly demand Seasonal index = = 90/94 = .957 Seasonal Index Example 0.957**Demand Average Average Seasonal**Month 2003 2004 2005 2003-2005 Monthly Index Jan 80 85 105 90 94 0.957 Feb 70 85 85 80 94 0.851 Mar 80 93 82 85 94 0.904 Apr 90 95 115 100 94 1.064 May 113 125 131 123 94 1.309 Jun 110 115 120 115 94 1.223 Jul 100 102 113 105 94 1.117 Aug 88 102 110 100 94 1.064 Sept 85 90 95 90 94 0.957 Oct 77 78 85 80 94 0.851 Nov 75 72 83 80 94 0.851 Dec 82 78 80 80 94 0.851 Seasonal Index Example**Demand Average Average Seasonal**Month 2003 2004 2005 2003-2005 Monthly Index Jan 80 85 105 90 94 0.957 Feb 70 85 85 80 94 0.851 Mar 80 93 82 85 94 0.904 Apr 90 95 115 100 94 1.064 May 113 125 131 123 94 1.309 Jun 110 115 120 115 94 1.223 Jul 100 102 113 105 94 1.117 Aug 88 102 110 100 94 1.064 Sept 85 90 95 90 94 0.957 Oct 77 78 85 80 94 0.851 Nov 75 72 83 80 94 0.851 Dec 82 78 80 80 94 0.851 Forecast for 2006 1,200 12 1,200 12 Jan x .957 = 96 Feb x .851 = 85 Seasonal Index Example Expected annual demand = 1,200