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Practice Problems Problem 1: Auto sales at Carmen’s Chevrolet are shown below. Develop a 3-week moving average and develop a forecast for Week 7. Week 1 2 3 4 5 6 7 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e Auto Sales 8 10 9 11 10 13 — 4-1 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Problem 1: Practice Problems demand in previous n periods Moving average = n Auto sales at Carmen’s Chevrolet are shown below. Develop a 3-week moving average and develop a forecast for Week 7. Week 1 2 3 4 5 6 7 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e Auto Sales 8 10 9 11 10 13 — 4-2 3–Week Moving Average (8 + 10 + 9)/3 = 9 (10 + 9 + 11)/3 = 10 (9 + 11 + 10)/3 = 10 (11 + 10 + 13)/3 = 111/3 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Practice Problems Problem 2: Carmen’s decides to forecast auto sales by weighting the three weeks as follows: Weights Applied 3 2 1 6 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e Period Last week Two weeks ago Three weeks ago Total 4-3 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Practice Problems Week Auto Sales 3–Week Moving Average 1 8 10 Problem 2: 2 3 9 4 to forecast auto11 (3*9 +the 2*10 + 1*8)/6 = 9as1/6 Carmen’s decides sales by weighting three weeks 5 10 (3*11 + 2*9 + 1*10)/6 = 101/6 follows: 6 13 (3*10 + 2*11 + 1*9)/6 = 101/6 7 — (3*13 + 2*10 + 1*11)/6 = 112/3 Weights Applied Period 3 Last week 2 Two weeks ago 1 Three weeks ago 6 Total (weight for period n)(demand in period n) Moving average = weights PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-4 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Practice Problems Problem 3: A firm uses simple exponential smoothing with = 0.1 to forecast demand. The forecast for the week of January 1 was 500 units whereas the actual demand turned out to be 450 units. Calculate the demand forecast for the week of January 8. Ft = Ft-1 + (At-1 – Ft-1) = 500 + 0.1(450 – 500) = 495 units PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-5 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Practice Problems Problem 4: Exponential smoothing is used to forecast automobile battery sales. Two values of are examined, = 0.8 and = 0.5. Evaluate the accuracy of each smoothing constant. Which is preferable? (Assume the forecast for January was 22 batteries.) Actual sales are given below: Month Actual Battery Sales January 20 February 21 March 15 April 14 May 13 June 18 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-6 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Practice Problems |deviations| MAD = n Problem 4: Exponential smoothing is used to forecast automobile battery sales. Two values of are examined, = 0.8 and = 0.5. Evaluate the accuracy of each smoothing constant. Which is preferable? (Assume the forecast for January was 22 batteries.) Actual sales are given below: Absolute Absolute Month Actual Battery Sales Forecast =Deviation 0.8 Forecast =Deviation 0.5 2 2 January 20 22 22 1 0 February 21 20 21 6 6 March 15 21 21 2 4 April 14 16 18 1 3 May 13 14 16 3 1.5 June 18 13 14.5 MAD = 2.56 MAD = 2.67 = 15 = 16 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-7 Practice Problems Problem 5: Use the sales data given below to determine: (a) the least squares trend line, and (b) the predicted value for 2003 sales. Year 1996 1997 1998 1999 2000 2001 2002 Sales (Units) 100 110 122 130 139 152 164 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-8 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Practice Problems x 28 x= n = =4 y = a + bx = 89.16 + 10.46x 7 Problem 5: y 917 y= n = = 131 7 Use the sales data given below to determine: (a) the least squares trend line, 3961 – (7)(4)(131) xy – nxy 293 and (b) bthe predicted value for 2003 sales. = = = = 10.46 140 – (7)(42) x2 – nx2 28 Year Sales (Units) Time Period X2 XY a = y – bx = 131 – (10.46*4) = 89.16 1996 100 1 1 100 1997 110 2 4 220 1998 122 3 9 366 1999 130 4 16 520 Sales in 2003 =589.16 + 10.46*8 2000 139 25 = 172.84 695 2001 152 6 36 912 2002 164 7 49 1148 917 28 140 3961 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-9 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Practice Problems Problem 6: Given the forecast demand and actual demand for 10-foot fishing boats, compute the tracking signal and MAD. Year 1 2 3 4 5 6 Forecast Demand 78 75 83 84 88 85 Actual Demand 71 80 101 84 60 73 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-10 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Problem 6: Practice Problems |Forecast errors| MAD = n = 70 = 11.7 6 Given the forecast demand and actual demand for 10-foot fishing boats, compute the tracking signal and MAD. Year 1 2 3 4 5 6 Forecast Demand 78 75 83 84 88 85 Actual Demand 71 80 101 84 60 73 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e Error –7 5 18 0 –28 –12 4-11 RSFE –7 –2 16 16 –12 –24 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Problem 6: Practice Problems RSFE Tracking Signal = MAD = –24 = 2.1 MADs 11.7 Given the forecast demand and actual demand for 10-foot fishing boats, compute the tracking signal and MAD. Year 1 2 3 4 5 6 Forecast Demand 78 75 83 84 88 85 Actual Demand 71 80 101 84 60 73 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e Cummulative |Error| Error 7 7 5 12 18 30 0 30 28 58 12 70 4-12 MAD 7.0 6.0 10.0 7.5 11.6 11.7 Tracking Signal –1.0 –0.3 +1.6 +2.1 –1.0 –2.1 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Practice Problems Problem 7: Over the past year Meredith and Smunt Manufacturing had annual sales of 10,000 portable water pumps. The average quarterly sales for the past 5 years have averaged: spring 4,000, summer 3,000, fall 2,000 and winter 1,000. Compute the quarterly index. PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-13 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Practice Problems Problem 7: Over the past year Meredith and Smunt Manufacturing had annual sales of 10,000 portable water pumps. The average quarterly sales for the past 5 years have averaged: spring 4,000, summer 3,000, fall 2,000 and winter 1,000. Compute the quarterly index. Equally dividing the annual sales of 10,000 units over the four seasons Spring Summer Fall Winter PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 10,000 / 4 = 2,500 4,000 / 2,500 = 1.6 3,000 / 2,500 = 1.2 2,000 / 2,500 = 0.8 1,000 / 2,500 = 0.4 4-14 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Practice Problems Problem 8: Using the data in Problem 7, Meredith and Smunt Manufacturing expects sales of pumps to grow by 10% next year. Compute next year’s sales and the sales for each quarter. PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-15 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Practice Problems Problem 8: Using the data in Problem 7, Meredith and Smunt Manufacturing expects sales of pumps to grow by 10% next year. Compute next year’s sales and the sales for each quarter. Next years sales should be 11,000 pumps (10,000*1.10 = 11,000) Spring Summer Fall Winter PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e (11,000 / 4)*1.6 = 4,400 (11,000 / 4)*1.2 = 3,300 (11,000 / 4)*0.8 = 2,200 (11,000 / 4)*0.4 = 1,100 4-16 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458