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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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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
10 Overview • Qualitative Analysis • Quantitative Analysis • Management Science • Operations Research 1001
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
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
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
Basic Probability - Law of Addition - 2 10 Adding Mutually Exclusive Events A B Adding Non Mutually Exclusive Events A B 1005
Basic Probability - Independence 10 • Marginal or Simple Probability • Joint Probability Independent Events a b a • Conditional Probability Then b 1006
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
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
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
The Normal Distribution 10 M x1 x2 1010
Statistical Formulae 10 1011
Forecasting - Overview 11 • To Provide Information • To Anticipate Changes • Rationale Short Medium Long 1101
Forecasting Approaches 11 Forecasting Intuition Extrapolation Prediction • Judgement • Conference • Survey • Delphi • Graphical • Moving Average • Exponential Smoothing • Regression • Multiple Regression 1102
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
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
Forecasting Exercise (2) December 2002 Sales - 11 125 1105
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
11 Exponential Smoothing - 1 1107
Exponential Smoothing - 2 11 Trend 1108
Exponential Smoothing - 3 11 Seasonal 1109
Exponential Smoothing - 4 11 Combined 1110
Trend Correction 11 1st Order Smoothing 2nd Order Smoothing • Second Order Smoothing Correction “Anticipates” Changes in the Data. • Also Called Trend Correction 1111
11 Second Order Smoothing - 1 Random Random 1112
Second Order Smoothing - 2 11 Trend Trend 1113
Second Order Smoothing - 3 11 Seasonal 1114
Second Order Smoothing - 4 11 Combined Combined 1115
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
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
Regression Analysis – 3 11 1118
11 Use of Regression Analysis • Inside the company • Inside the Industry • Outside the Industry 1119
Correlation Coefficients No Correlation 11 Positive Correlation 0 < r < 1 Perfect Positive r =+1 Perfect Negative r =-1 Negative Correlation 0 > r > -1 1120
11 Multiple Regression Analysis Multiple Regression y=a+b1x1+b2x2 New Mark Attendance Old Mark 1121
Improving Forecast Accuracy - 1 11 • Reduce Lead Time • Aggregate Forecast 1122
Improving Forecast Accuracy - 2 11 1123
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
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
Objective Functions 12 • Different Objectives e.g.: Profit • Cashflow • Sales • Strategic and Judgmental • Basis for Optimisation 1202
Simple Optimisation (1) 12 6.38 1203
Simple Optimisation (2) 12 Medium Resolution Low Resolution High Resolution 1204
Optimisation - 2 Variables (7.1, 6.7) 12 1205
12 Linear Programming (1) • Linear Objective Function • A Set of Linear Constraints • Non-Negativity 1206
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
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
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
Multiple Variables 12 Y Material Total Capacity Y Z Objective Function Z Material X Material X 1210
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
Sensitivity Analysis - 2 12 Profit Different Variables May Have Different Effects Sales Cost Costs = £1000K 1212
Sensitivity Analysis – 3 12 1213
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