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Supporting Slides

X. Supporting Slides. Systems for Planning & Control in Manufacturing: Systems and Management for Competitive Manufacture. Professor David K Harrison Glasgow Caledonian University Dr David J Petty The University of Manchester Institute of Science and Technology. ISBN 0 7506 49771. 0000.

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Supporting Slides

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  1. X Supporting Slides Systems for Planning & Control in Manufacturing: Systems and Management for Competitive Manufacture Professor David K Harrison Glasgow Caledonian University Dr David J Petty The University of Manchester Institute of Science and Technology ISBN 0 7506 49771 0000

  2. 10 Overview • Qualitative Analysis • Quantitative Analysis • Management Science • Operations Research 1001

  3. Define Problem Formulate a Clear and Unambiguous Statement of the Problem Develop Model Models can take several forms Acquire Data Accurate Input Data is Essential Develop Solution Algebraic or Numerical Solution Test Solution Validation Analyse Results Implications Implement Results 10 The Quantitative Analysis Process 1002

  4. Basic Probability - Definitions and 7 and Black and 10 • Basic Rules Draw a Card ME CE • Mutually Exclusive Face and Number • Events King and 7 and,, • Collectively Exhaustive 1003

  5. Basic Probability - Law of Addition - 1 10 • Take a Standard 52 Card Deck (No Jokers) • Draw a Card and Write Down Result • Replace Card • Draw a Second Card and Write Down Result • What are the Probabilities of Drawing:- • a) A Heart or a Diamond? • b) A Five or a Diamond? ? ? 1004

  6. Basic Probability - Law of Addition - 2 10 Adding Mutually Exclusive Events A B Adding Non Mutually Exclusive Events A B 1005

  7. Basic Probability - Independence 10 • Marginal or Simple Probability • Joint Probability Independent Events a b a • Conditional Probability Then b 1006

  8. 10 Statistically Dependent Events If a red ball is drawn, what is the probability that it will have a spot? 30 Blue 10 Spot 20 Plain 30 Red 6 Spot 24 Plain Bayes Theorem NOT Independent 1007

  9. Probability Trees 10 0 1 2 3 4 HHH (0.125) H HHHH (0.0625) HH (0.25) H HHHT (0.0625) T H HHT (0.125) H HHTH (0.0625) H (0.5) T HHTT (0.0625) T H HTH (0.125) H HTHH (0.0625) H HTHT (0.0625) T T HTT (0.125) H HTTH (0.0625) HT (0.25) T T HTTT (0.0625) THH (0.125) H THHH (0.0625) TH (0.25) H T THHT (0.0625) H THT (0.125) H THTH (0.0625) 0 1 2 3 4 T T THTT (0.0625) T TTH (0.125) H TTHH (0.0625) T (0.5) H T TTHT (0.0625) T TTT (0.125) H TTTH (0.0625) TT (0.25) T T TTTT (0.0625) 1 4 6 4 1 1008

  10. Probability Distributions 10 Throwing Four Coins Throwing a Die 0.2 0.15 0.3 Probability P(x) 0.1 Probability P(x) 0.2 0.1 0.05 0 1 2 3 4 1 2 3 4 5 6 Score x Score x 1009

  11. The Normal Distribution 10 M x1 x2 1010

  12. Statistical Formulae 10 1011

  13. Forecasting - Overview 11 • To Provide Information • To Anticipate Changes • Rationale Short Medium Long 1101

  14. Forecasting Approaches 11 Forecasting Intuition Extrapolation Prediction • Judgement • Conference • Survey • Delphi • Graphical • Moving Average • Exponential Smoothing • Regression • Multiple Regression 1102

  15. 11 Intuitive Forecasting Approaches • Judgment • Conference • Survey • Delphi The Opinion of One Person The Collective Opinion of a group of People Collecting the Independent Opinion of Several People Combining the Conference and Survey Approaches 1103

  16. Forecasting Exercise (1) 11 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 105 100 106 105 100 108 107 106 113 109 113 112 2001 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 114 118 116 115 114 117 116 122 120 122 121 125 2002 1104

  17. Forecasting Exercise (2) December 2002 Sales - 11 1105

  18. Analytical Extrapolation 11 • Moving • Average • Exponential Smoothing Forecast for next period is the average of previous n data points n = Number of data points k = Number of points used to average xi = Data element F(i+1) = Forecast for next period.  = Smoothing factor • Advantage • Simple Forecast is a weighted average (most recent is most important) of all data points • Advantage • Logical • Only two data elements needed Move up by 1106

  19. 11 Exponential Smoothing - 1 1107

  20. Exponential Smoothing - 2 11 Trend 1108

  21. Exponential Smoothing - 3 11 Seasonal 1109

  22. Exponential Smoothing - 4 11 Combined 1110

  23. Trend Correction 11 1st Order Smoothing 2nd Order Smoothing • Second Order Smoothing Correction “Anticipates” Changes in the Data. • Also Called Trend Correction 1111

  24. 11 Second Order Smoothing - 1 Random Random 1112

  25. Second Order Smoothing - 2 11 Trend Trend 1113

  26. Second Order Smoothing - 3 11 Seasonal 1114

  27. Second Order Smoothing - 4 11 Combined Combined 1115

  28. Regression Analysis - 1 11 Aftermarket Disc Brake Pads Sales + 5 Yrs vs Car Sales Now Student Attendance vs Student Marks ? • Is There a Correlation Between Students Marks and Attendance? • Is There a Correlation Between Car Sales Now and Demand for DBPs in 5 Years? 1116

  29. Regression Analysis - 2 11 y • What Line Will Minimise Total Distance? (x3, y3) (d4) (d3) (x4, y4) y=a+bx (d2) (x1, y1) (x2, y2) (d1) a x 1117

  30. Regression Analysis – 3 11 1118

  31. 11 Use of Regression Analysis • Inside the company • Inside the Industry • Outside the Industry 1119

  32. Correlation Coefficients No Correlation 11 Positive Correlation 0 < r < 1 Perfect Positive r =+1 Perfect Negative r =-1 Negative Correlation 0 > r > -1 1120

  33. 11 Multiple Regression Analysis Multiple Regression y=a+b1x1+b2x2 New Mark Attendance Old Mark 1121

  34. Improving Forecast Accuracy - 1 11 • Reduce Lead Time • Aggregate Forecast 1122

  35. Improving Forecast Accuracy - 2 11 1123

  36. Forecasting Summary 11 • Essential for all Businesses • Three Approaches • Uncertainty is Inherent • Uncertainty Must be Anticipated • Forecast Accuracy can be Improved If We Make this Man Accountable for the Weather, Will it make the Sun Shine? 1124

  37. Optimisation 12 The most favourable conditions; the best compromise between opposing tendencies; the best or most favourable. • Objective Functions • Basic Optimisation • Linear Programming • Sensitivity Analysis 1201

  38. Objective Functions 12 • Different Objectives e.g.: Profit • Cashflow • Sales • Strategic and Judgmental • Basis for Optimisation 1202

  39. Simple Optimisation (1) 12 6.38 1203

  40. Simple Optimisation (2) 12 Medium Resolution Low Resolution High Resolution 1204

  41. Optimisation - 2 Variables (7.1, 6.7) 12 1205

  42. 12 Linear Programming (1) • Linear Objective Function • A Set of Linear Constraints • Non-Negativity 1206

  43. Linear Programming (2) Power 1. Power Limitation: 160 = 1.34X + Y 112 = 1.6X + 1. 4Y Objective Function - Sales Machining Capacity 2. Machining Capacity: 150 = X + 1.25Y 3. Objective Function: Sales = 1.6X + 1.4Y 12 160 Optimum Point 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 X 160 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 1207

  44. Linear Programming (3) Lab Capacity 3. Labour Capacity: 130 = X + Y 12 Y 160 150 140 Power 130 120 110 1. Power Limitation: 160 = 1.34X + Y 2. Machining Capacity: 150 = X + 1.25Y 100 90 80 70 60 50 40 30 Machining Capacity 20 10 X 160 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 1208

  45. Linear Programming (4) 224 = 1.6X + 1. 4Y 196 = 1.6X + 1. 4Y Objective Function: Sales = 1.6X + 1.4Y Optimum: X= 50, Y = 80 Optimum Point 12 Y 160 150 140 130 1. Power Limitation: 160 = 1.34X + Y 2. Machining Capacity: 150 = X + 1.25Y 3. Labour Capacity: 130 = X + Y 120 110 100 90 80 70 60 50 40 30 20 10 X 160 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 1209

  46. Multiple Variables 12 Y Material Total Capacity Y Z Objective Function Z Material X Material X 1210

  47. Sensitivity Analysis - 1 12 • Problems So Far Assume Perfect Information • Sensitivity Analysis Determines Criticality of Base Data 6.38 5.95 f(x) g(x) 1211

  48. Sensitivity Analysis - 2 12 Profit Different Variables May Have Different Effects Sales Cost Costs = £1000K 1212

  49. Sensitivity Analysis – 3 12 1213

  50. 12 Sensitivity Analysis – 4 • Test the Sensitivity of the Model Itself • Test the Sensitivity of the Model to Input Variables • Can be Used for a Variety of Problems 1214

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