Quantitives methods for decision markers 6en wisniewski

giáo trình Quantitives methods for decision markers 6en wisniewski giáo trình Quantitives methods for decision markers 6en wisniewski giáo trình Quantitives methods for decision markers 6en wisniewski giáo trình Quantitives methods for decision markers 6en wisniewski giáo trình Quantitives methods for decision markers 6en wisniewski giáo trình Quantitives methods for decision markers 6en wisniewski

Sixth Edition Quantitative Methods for Decision Makers Mik Wisniewski Freelance Consultant and Business Analyst Pearson Education Limited Edinburgh Gate Harlow CM20 2JE United Kingdom Tel: +44 (0)1279 623623 Web: www.pearson.com/uk First published 1994 (print) Second edition published under the Financial Times/Pitman Publishing imprint 1997 (print) Third edition 2002 (print) Fourth edition 2006 (print) Fifth edition 2009 (print) Sixth edition published 2016 (print and electronic) © Mik Wisniewski 1994, 2016 The right of Mik Wisniewski to be identified as author of this work has been asserted by him in accordance with the Copyright, Designs and Patents Act 1988 The print publication is protected by copyright Prior to any prohibited reproduction, storage in a retrieval system, distribution or transmission in any form or by any means, electronic, mechanical, recording or otherwise, permission should be obtained from the publisher or, where applicable, a licence permitting restricted copying in the United Kingdom should be obtained from the Copyright Licensing Agency Ltd, Barnard’s Inn, 86 Fetter Lane, London EC4A 1EN The ePublication is protected by copyright and must not be copied, reproduced, t­ransferred, distributed, leased, licensed or publicly performed or used in any way except as s­ pecifically permitted in writing by the publishers, as allowed under the terms and conditions under which it was purchased, or as strictly permitted by applicable copyright law Any ­unauthorised distribution or use of this text may be a direct infringement of the author’s and the ­publisher’s rights and those responsible may be liable in law accordingly All trademarks used herein are the property of their respective owners The use of any trademark in this text does not vest in the author or publisher any trademark ownership rights in such trademarks, nor does the use of such trademarks imply any affiliation with or endorsement of this book by such owners Contains public sector information licensed under the Open Government Licence (OGL) v3.0 http://www.nationalarchives.gov.uk/doc/open-government-licence/version/3/ The screenshots in this book are reprinted by permission of Microsoft Corporation Pearson Education is not responsible for the content of third-party internet sites The Financial Times With a worldwide network of highly respected journalists, The Financial Times provides global business news, insightful opinion and expert analysis of business, finance and politics With over 500 journalists reporting from ­50 countries worldwide, our in-depth coverage of international news is objectively reported and analysed from an independent, global perspective To find out more, visit www.ft.com/pearsonoffer ISBN: 978-0-273-77068-8 (print) 978-1-292-11271-8 (PDF) 978-1-292-12577-0 (ePub) British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congres 10 20 19 18 17 16 Front cover image: © Swardraws-Drawsward/Getty Images Print edition typset in 9.5/12.5 Stone Serif by Lumina Datamatics Printed in Slovakia by Neografia NOTE THAT ANY PAGE CROSS REFERENCES REFER TO THE PRINT EDITION Still dedicated to Hazel – to whom I promised after the last book that I’d never write another This page intentionally left blank Contents List of ‘QMDM in Action’ case studies xii Prefacexiii Acknowledgementsxv Introduction The Use of Quantitative Techniques by Business The Role of Quantitative Techniques in Business Models in Quantitative Decision Making 10 Use of Computers 15 Using the Text 15 Summary 16 Tools of the Trade 19 Learning objectives 19 Some Basic Terminology 20 Fractions, Proportions, Percentages 21 Rounding and Significant Figures 24 Common Notation 26 Powers and Roots 28 Logarithms 30 Summation and Factorials 34 Equations and Mathematical Models 35 Graphs 38 Real and Money Terms 44 Worked Example 45 Summary 49 Exercises 49 vi contents Presenting Management Information 51 Learning objectives 51 A Business Example 52 Bar Charts 56 Pie Charts 65 Frequency Distributions 66 Percentage and Cumulative Frequencies 69 Histograms 71 Frequency Polygons 74 Ogives 75 Lorenz Curves 76 Time-Series Graphs 79 Z Charts 82 Scatter Diagrams 87 General Principles of Graphical Presentation 90 Worked Example 91 Summary 95 Exercises 99 Management Statistics 105 Learning objectives 105 A Business Example 106 Why Are Statistics Needed? 107 Measures of Average 108 Measures of Variability 112 Using the Statistics 124 Calculating Statistics for Aggregated Data 125 Index Numbers 129 Worked Example 139 Summary 140 Exercises 140 Probability and Probability Distributions 145 Learning objectives 145 Terminology 147 The Multiplication Rule 151 The Addition Rule 152 A Business Application 155 Probability Distributions 159 The Binomial Distribution 162 contents vii The Normal Distribution 172 Worked Example 181 Summary 184 Exercises 184 Decision Making Under Uncertainty 187 Learning objectives 187 The Decision Problem 188 The Maximax Criterion 191 The Maximin Criterion 191 The Minimax Regret Criterion 192 Decision Making Using Probability Information 193 Risk 195 Decision Trees 195 The Value of Perfect Information 201 Worked Example 203 Summary 205 Exercises 208 Market Research and Statistical Inference 211 Learning objectives 211 Populations and Samples 212 Sampling Distributions 214 The Central Limit Theorem 216 Characteristics of the Sampling Distribution 217 Confidence Intervals 218 Other Confidence Intervals 222 Confidence Intervals for Proportions 222 Interpreting Confidence Intervals 224 Hypothesis Tests 227 Tests on a Sample Mean 235 Tests on the Difference Between Two Means 237 Tests on Two Proportions or Percentages 239 Tests on Small Samples 240 Inferential Statistics Using a Computer Package 243 p Values in Hypothesis Tests 245 x Tests 245 Worked Example 252 Summary 258 Exercises 258 viii contents Quality Control and Quality Management 262 Learning objectives 262 The Importance of Quality 263 Techniques in Quality Management 264 Statistical Process Control 265 Control Charts 267 Control Charts for Attribute Variables 274 Pareto Charts 275 Ishikawa Diagrams 276 Six Sigma 279 Worked Example 279 Summary 281 Exercises 284 Forecasting I: Moving Averages and Time Series 286 Learning objectives 286 The Need for Forecasting 287 Approaches to Forecasting 290 Trend Projections 293 Time-Series Models 308 Worked Example 325 Summary 328 Exercises 331 10 Forecasting II: Regression 339 Learning objectives 339 The Principles of Simple Linear Regression 340 The Correlation Coefficient 344 The Line of Best Fit 347 Using the Regression Equation 349 Further Statistical Evaluation of the Regression Equation 352 Non-linear Regression 363 Multiple Regression 365 The Forecasting Process 378 Worked Example 381 Summary 387 Exercises 393 contents 11 Linear Programming ix 399 Learning objectives 399 The Business Problem 400 Formulating the Problem 403 Graphical Solution to the LP Formulation 406 Sensitivity Analysis 412 Computer Solutions 416 Assumptions of the Basic Model 417 Dealing with More than Two Variables 417 Extensions to the Basic LP Model 420 Worked Example 421 Summary 423 Exercises 426 Appendix: Solving LP Problems with Excel 428 12 Stock Control 431 Learning objectives 431 The Stock-Control Problem 432 Costs Involved in Stock Control 434 The Stock-Control Decision 437 The Economic Order Quantity Model 439 The Reorder Cycle 440 Assumptions of the EOQ Model 441 Incorporating Lead Time 441 Classification of Stock Items 442 MRP and JIT 446 Worked Example 448 Summary 450 Exercises 450 13 Project Management 453 Learning objectives Characteristics of a Project Project Management Business Example Network Diagrams Developing the Network Diagram Using the Network Diagram Precedence Diagrams Gantt Charts 453 454 455 456 460 464 468 469 470 www.downloadslide.net APPENDIX F: SOLUTIONS TO CHAPTER PROGRESS CHECK QUESTIONS 565 giving: Q3 = 10 000 + 84.75 - 702 10 000 = £16 705 22 Progress Check 5.1 ‘Common sense’ would tell us that there is a one in six chance of throwing the die and showing a six This would be a theoretical probability since we know that there are six possible outcomes (the numbers to 6) but only one of them can occur, and that each of them has the same chance of occurring (1/6) However, consider the scenario that we have been throwing the die and noting which numbers are shown We have done this 100 times and, as yet, have never thrown a six We pick up the die one more time to throw What would you say the probability is of throwing a six next time (assuming the die has not been tampered with in any way)? The answer will depend on which of the three approaches to probability you adopt On a strictly theoretical basis the answer must still be 1/6 On an empirical basis you might say the answer is since a six has never appeared On a subjective basis you might say the answer is (or close to it) – that is, you’re certain a six will appear because it hasn’t been thrown for such a long time and has to appear sooner or later Progress Check 5.11 The mean and standard deviation are easily calculated: Mean = np = 50 0001 0.122 = 6000 Standard deviation = 2npq = 21 50 0002 0.122 0.882 = 72.7 Potentially, these results and the principles of the Binomial could be used in a number of ways First, by estimating the likely number of returns we can determine what these returns will cost us in postage, handling, etc We also know that this cost has to be recouped from somewhere, so we can build this likely cost into the calculations for the profit margins we need to realise on the sales we achieve (estimated at 44 000) Equally, we can use this information for production and ordering If we anticipate sales of 44 000 from orders of 50 000, there is clearly no point producing 50 000 items, as we will at some time have 6000 unsold items on our hands We could also some ‘what-if’ analysis around the problem Clearly, the orders of 50 000 and the return rate of 12 per cent are not guaranteed outcomes – they are based on empirical observations We could readily use the Binomial to determine the consequences of the number of orders differing from 50 000, and equally for the return rate to differ from 12 per cent to assess the consequences on our production decision and our profit Progress Check 5.13 Using the Z score formula we have: Machine X = 475, Z = - 2.5 X = 505, Z = 0.5 X = 518, Z = 1.8 www.downloadslide.net 566 APPENDIX F: SOLUTIONS TO CHAPTER PROGRESS CHECK QUESTIONS Machine X = 745, Z = - 0.33 X = 725, Z = - 1.67 X = 759, Z = 0.60 Progress Check 7.17 We can treat the age distribution from government statistics as our expected (E) distribution If our sample were representative then we should have a distribution by age group like the one in the government statistics The sample we have obtained is clearly the observed (O) distribution As with all these types of test, the null hypothesis is that O = E (that is, that our sample distribution is representative, based on the government statistics) Presumably, it is important for the market research company to know whether or not the sample is representative so let us choose a = 0.01 The calculations are then: Observed 54 Expected (O - E) (O - E)2 -11 121 65 (O - E)2/E 1.86 63 60 0.15 167 190 -23 529 2.78 85 75 10 100 1.33 131 110 21 441 4.01 500 500 – – 10.14 Notice that the expected frequencies total to 500 (the sample size) We have obtained a calculated x2 of 10.14 We have degrees of freedom and from Appendix D we obtain a critical statistic of 13.28 Given the calculated statistic is less than the critical we have no reason to reject the null hypothesis Remember that this is that O = E, so we cannot reject the hypothesis that the sample is representative compared with the government statistics Progress Check 8.3 The relevant information for the construction of a control chart is that we anticipate an average of 12 customer complaints per day averaged over 14 days (the sample period of two weeks) This would give warning limits of: 12 { 1.96 5> 2142 = 12 { 2.62 and action limits of: 12 { 3.09 5> 2142 = 12 { 4.13 One of the implications of these calculations, amongst others, is that a reduction in the mean number of customer complaints is not necessarily an indication that the number of complaints is falling A reduction in one two-week period, for example, to 11 complaints would still be within the warning limits and could not be taken to indicate that the mean number of www.downloadslide.net APPENDIX F: SOLUTIONS TO CHAPTER PROGRESS CHECK QUESTIONS 567 17 AL 16 15 WL Mean number of complaints 14 13 12 11 10 WL AL Period Figure A.9 Complaints control chart complaints had actually fallen (we would explain the reduction through the concept of sampling variation) The relevant control chart, with the first seven sets of results also plotted, is shown in Figure A.9 Our commentary on these results might be as follows We observe that in period the result of 14.8 exceeds the upper warning limit We would take this as evidence that the process might be out of control and we should obtain another sample as soon as is practical We also observe that from period onwards a clear downward trend is evident and although this is, by period 7, still within the warning limit we might anticipate period being below the lower warning limit In one sense this is not a problem for the supermarket since it implies a declining mean number of complaints However, the store manager would still be advised to try to assess why this trend was occurring Is it linked to some management initiative intended to improve customer satisfaction? Is it linked to a customer care training programme introduced by the store? Is it linked to a change in the way customers are encouraged to complain (perhaps deliberately or accidentally the store has made it more difficult for customers to make complaints)? Progress Check 10.2 Graphical solutions to Activity 10.2 are shown in Figure A.10 www.downloadslide.net 568 APPENDIX F: SOLUTIONS TO CHAPTER PROGRESS CHECK QUESTIONS (a) y 100 X y (b) 100 ]100 Figure A.10 Graphical solutions to Activity 10.2 X www.downloadslide.net APPENDIX F: SOLUTIONS TO CHAPTER PROGRESS CHECK QUESTIONS 569 Progress Check 10.9 The regression results using T = to are: SUMMARY OUTPUT Regression Statistics Multiple R 0.99167303 R Square 0.983415398 Adjusted R Square 0.977887197 Standard Error 0.10764138 Observations ANOVA df SS Regression 2.06116 2.06116 Residual 0.03476 0.011586667 Total 2.09592 Coeffi­ Standard cients Error t Stat Intercept MS P-value Lower 95% F 177.8906789 Upper 95% Significance F 0.000911006 Lower 95.0% Upper 95.0% 29.206 0.112895232 258.7000316 1.27367E-07 28.84671699 29.56528301 28.84671699 29.56528301 X Variable -0.454 0.034039193 -13.33756645 0.000911006 -0.562327904 -0.345672096 -0.562327904 -0.345672096 This confirms a forecast for the trend in 2015 IV T = 122 of 23.76 We also see that R2 at 0.99 is higher than that for the model for Scenario A, implying a better fit of the regression line to the data This would also be confirmed by comparing the two prediction intervals for Scenarios A and B The trend forecast for Scenario B is statistically ‘better’, although whether it provides a better forecast in a business context is another matter, since both forecasts imply that the respective trend will remain unchanged Progress Check 11.2 We have a formulation: Minimise 0.85H + 1.1C such that 4H + 2C … 20 000 1H + 3C … 15 000 1H … 4000 1C … 4500 1H Ú 2000 1C Ú 2500 H, C Ú Solutions and feedback on Progress Checks for Chapters 12–15 are contained in the chapter text www.downloadslide.net 570 INDEX Index ABC classification system 443–6 accuracy and rounding 24–5 action limits 268 activities in project planning 456–7, 458 activity dependencies 457–60 project management and 457–60 see also network diagrams activity duration 457 addition rule mutually exclusive events 152–3 non-mutually exclusive events 152–3 additive model in time-series analysis 324 adjusted frequency in histogram 73 AER see EAR 524 aggregate index numbers 133–8 aggregated data 125–6 accuracy 125 arithmetic mean for 126 median 128–9 quartiles 128–9 standard deviation 127–8 alternative hypothesis 228–30 analysis of variance (ANOVA) 368–9 annual equivalent rate 524 annual percentage rate (APR) 524 ANOVA see analysis of variane antilogarithms 31 anti-speeding campaign, vehicle 143–4 APR see annual percentage rate arithmetic mean 108–10 see also mean arithmetic operators 26–7 assessment, personal 290–1 assignable variation 267–8 association, tests of 249–52 attributable variable 20 autocorrelation 375 automobile business 85 averages 108–11 arithmetic mean 108–10 ideals and 487 median 110–11 moving 284–97 purchase value in constant prices 94 weighted 134–8 see also mean; median Bank of England 180, 288 bar charts 56–65, 92 component 58 constructing 64–5 histograms and 71, 73 multiple 57 percentage component 59 simple 57 base period 129 base-date weighted index 134–8 bell-shaped curve 172, 226 best fit 355 bias 254, 256, 307 big data 3, social media and 267 Big Mac index 138 binding constraints 411–12 Binomial distribution 162–72, 544–8 in Excel 171–2 formula 165–7 mean and standard deviation 170–1 tables 168–70, 544–8 Binomial experiment 165 break-even analysis 36 broadcasters fear 63–4 budgeting decisions see financial decision making Bureau of Economic Analysis (BEA) 213–14 Bureau of Labor Statistics (BLS) 213 Business analytics application 155–7 automobile 85 decision-making process 10 example 52–3, 55–6, 106, 456–7, 459–60, 489–90 mathematics offers 7–8 www.downloadslide.net INDEX problems see management quantitative techniques in 8–10 risk for 293 uncertainty and risk 509–12 use of quantitative techniques by 2–3, 5–7 buying power 132, 520 Capgemini consulting 215, 223, 273–4 contingency planning in project management 471–2 controlling staff costs through regression analysis 364 cost–benefit analysis 527 estimating energy consumption 223 forecasting retail sales 312 improving forecasting accuracy 302 improving stock management 436 optimisation model 42–3 optimising supply chain 420 risk management modelling 197 sampling for perfect modelling 215 simulating airport management 493–4 cash flow 528–9 see also present value causal and non-causal forecasting see forecasting causal relationship 341 cause-effect diagrams (Ishikawa diagrams) 276–9 census data 401 Central Limit Theorem 216–17 chi-square (x2) distributions 245–7, 551 chi-square (x2) test 245–52 class widths, in frequency table 69 classification of stock items 442–6 coefficient of correlation (r) 344–6 of determination (R2) 353 of skewness 120, 123 of variation 118–19 collectively exhaustive events 149–50 common logarithms 32 complement of an event 150 component bar chart 58 components of a time series 310–11 composite index 133–7 compound interest 520–1 computers and computer programs 15, 117, 243–5 checking output against personal assessment 291 interpreting output 15, 499–500 and LP 416–19 and regression 354–8, 375 and simulation 499–500, 506, 510 and time-series decomposition 324 conditional events 149 confidence interval 218–26, 256–7 interpreting 224–6 for a mean 219 misinterpret 225 other 222 for a proportion or percentage 222–4 for a regression equation 358–60 and sample size 222, 225–6 sampling variation 225, 227 confidence level 257 constrained optimisation 400 constraints 403–4, 413–15 binding 411–12 graphing 406–7 non-binding 411–12 non-negativity 405 slack 416, 418 consumer price index 133, 137 contingency/dependence 149, 250 contingency table test 249–52 continuous variable 20 control charts 267–73 for attributable variables 274–5 co-ordinates of a graph 39–40 correlation coefficient (r) 344–6 correlation matrix 375 cost benefit analysis 527 costs and crashing of projects 475–6 for health care provision 99 holding 434, 438, 439–40 involved in stock control 434–5 order 434, 438, 439 purchase 434 resale value and running 533 and savings of projects 542 stockout 434–5 CPM see critical path crash costs 475–6 crash times 475–6 critical activity 466–8 critical path 467–8, 479 critical statistic in hypothesis test 233 current date weighted index 136–7 customer service strategy 502–5 computer simulation for 2500 days 504 inter-arrival time 502 pay-in facility layout 502 simulation of 504 time taken to serve 503 data aggregated see aggregated data manipulating 67 mining 351 population 117 primary 21 sample 117–18 secondary 21 571 www.downloadslide.net 572 INDEX data presentation 51–2 bar charts 56–65 frequency distributions 66–9 histograms 71–4 importance of 51–2 pie charts 65–6 see also graphical presentation DEC see Digital Equipment Corporation deciles 122 decision analysis 510 decision making criteria and attitudes 190–3 financial 519–36 hypothesis tests and 235 probability and 193–4 quantitative techniques and 8–11 risk analysis 509–12 software 488–9 simulation and 486–502, 509–12 decision node 196 decision trees 195–200, 510 expected value 198, 200, 202 value of perfect information 201–2 decreases and increases 24 deflating 45, 130–2 degrees of freedom chi-square (x2) test 247, 249, 251 t test 240–3 Delphi method 291 dependence/independence 149, 249–50 dependencies of activities see activity dependencies dependent variable 341 depreciation 532 descriptive statistics 107 deviation 112 per quarter 314, 319 standard see standard deviation from trend 317–18 Digital Equipment Corporation (DEC) digits, significant 24–5 Dimson, Elroy 53 direct mail 12–14 discount factor 525, 534 discount rate 525, 529–31 discounted cash flow 520, 538 discrete variable 20 dishonesty 213 dispersion see variation distortions 311–12 distribution age 141 chi-square (x2) 245–6, 551 F distribution 552–3 frequency 66–71 line of equal 78 sampling 214–22 symmetrical 123 t distribution 550 see also Binomial distribution; Normal ­distribution; probability distribution doctor’s orders 111 dummy activity 463 Durbin–Watson test 375 E terms 357 EAR see equivalent annual rate 524 earliest finish time (EFT) 464–8 earliest start time (EST) 468 economic growth 37, 122, 323 economic order quantity (EOQ) 437–40 assumptions of 441 and lead time 441–2 effective interest rate 523 EFT see earliest finish time EOQ see economic order quantity equations 35–8 graphical representation 38–42 linear 38 non-linear 38, 40–2 equipment, purchasing/replacing 526–36 equivalent annual rate (EAR) 524 error types in hypothesis testing 230, 257, 266–7 errors in forecasts 297–302, 365 EST see earliest start time EV see expected value events 148–50 collectively exhaustive 149–50 conditional 149 independent 149 mutually exclusive 149 Excel Binomial probabilities in 171–2 Normal probabilities in 180 simulation with 517–18 solving LP problems with 428–30 expected duration 473 expected frequency, in chi-square (x2) test 246 expected value (EV) 193, 198, 202 experimentation, simulation and 487 experiments 148 explained variation in regression 352, 369 explanatory variable 341 exponent 28 exponential smoothing 303–7 exponential weights 303–4 extrapolation 350 F test / F distribution 369, 552–3 factorials 34, 166 failure, possibilities 189–90 Fanikiwa Microfinance 37 feasible area 407 figures, significant 24–5 financial decision making 519–36 fishbone diagrams (Ishikawa diagrams) 276–9 www.downloadslide.net INDEX float time 467 flow charts 491–3 football’s global transfer system 84 forecasting 286–324, 378–81 accuracy 289, 381 approaches to 290–3 causal/non-causal methods 380 choice of technique 379 Delphi method 291 errors 297–302, 365 evaluation and monitoring of 380–1 exponential smoothing 303–7 historical comparison 291–2 non-linear regression 363–4 panel methods 291 personal assessment 290–1 prediction intervals 358–60 process 378–81 qualitative 290–2 quantitative 290, 293 with a regression equation 349–62 fractions 21–4 frequency cumulative 69–71 distribution 66–9 histogram 71 percentage 69, 71 polygon 74–5 table 66–9 FTSE 100 index 53–4 functions 340–4 Gantt charts 470–1 global risks report 293 goal programming 421 goldbuggers 116 goodness of fit test 249 ‘goodwill’ costs 435 government spending 323 gradient 342–4 graphical presentation 52–95, 508 limitations 95 graphical solution to the LP formulation 406–12 graphs 38–42 computer-generated 97, 98 constraints 406–8 co-ordinates 39–40 linear 39–40 non-linear 40–2 objective function 408–9 profit and sales 38, 39 time series 52–6, 79–82 2Y 82, 92 gravity modelling 401–2 group dynamics 291 growth, economic 37, 122, 323 Gulf Oil 205–8 Halliburton 200–1 Hayward, Tony 201 health care provision, costs 99 health clinic 279–81 healthy-living guide 421–3 hedge funds 505 histograms 71–4 open-ended intervals 73 in percentage form 74 unequal intervals 73 historical comparison 291–2 holding costs 434, 438, 439 honesty 213 household disposable income 382, 385 hypothesis alternative 228–30 null 228–30, 234 hypothesis tests 227–52, 257 ANOVA 368–9 of association 249–52 chi-square (x2) 245–52 choosing 234–5 critical statistical value 233 decision making and 235 error types 230, 257, 266–7 F test 369–70 goodness of fit 249 limitations 235 on a mean 235–7 on a percentage 224–5 p values in 245 on regression equation 355 rejection area 232–3 significance level 230–2 small sample 240–3 stages of 227–8 statistic value calculation 234 t test 240–3 on two means 237–9 on two proportions or percentages 239–40 ICT see computers and computer programs increases and decreases 24 independence/dependence 149, 249–50 independent variable 341 index 45, 129 aggregate 133–7 alternative 137 deflating a series using 130–2 Laspeyres 134–7 Paasche 136–7 simple 129 tracking 122 weights 134–7 inequalities 26 infeasible area 407 573 www.downloadslide.net 574 INDEX inferential statistics 212–13 computers and 243, 245 see also hypothesis tests inflation 23, 44–5, 131–3, 135, 288–9, 525–7 and financial decision making 520–1, 523, 526 measure 135 information, value of perfect 201–2 information technology see computers and ­computer programs insurance 189–90, 194–5, 210, 433 integer programming 420–1 inter-arrival time 502 intercept of a linear equation 341–2 interest 520–2 annual percentage rate 523 compound 524 effective rate of 523 nominal rate of 523 real rate of 525–6 internal rate of return (IRR) 529–31 International Monetary Fund (IMF), eurozone recession 149 internet and spam 157–9 interpolation 350 interpretation 15, 106, 224–6, 500 see also judgment, personal interquartile range (IQR) 120 intervals adjusting in histograms 73 confidence see confidence interval in frequency tables 68–9 open-ended 69, 73 prediction see forecasting inventory problems 432 investment 194–5 investment appraisal 526–31 net present value method 528–9 payback method 528 rate of return method 528 Investment Property Databank (IPD) 122 IQR see interquartile range IRR see internal rate of return Ishikawa diagrams 276–9 IT see computers and computer programs joint probabilities 156 judgment, personal 290–1 see also interpretation just-in-time management (JIT) 446, 448 labour market statistics 100, 101, 102 Laspeyres index 134–7 latest finish time (LFT)466–7 latest start time (LST) 469–72 lead time 441–2 least squares method 347–9 LED see line of equal distribution leisure centres 203–5 LFT see latest finish time life-cycle process 291 line of best fit 347–9 line of equal distribution (LED) 78 linear equations 38 graphical form 38–40 intercept of 341–2 parameters of 341 slope of 342–4 linear programming 399–430 assumptions 417 constraints see constraints feasible area 407 formulation 405 graphical solution 406–12 infeasible area 407 maximisation problems 405, 411–12 minimisation problems 405, 411 objective function 405 sensitivity analysis 412–15 simultaneous equations 412 solution method 406–12 solving problems with Excel 428–30 linear regression 339–64 logarithms 30–2 calculations using 32 common 32 division of numbers 31–2 and Google 33 multiplication of numbers 31 natural 32 powers 32 roots 32 working with 30 Lorenz curves 76–9 see also Pareto charts lotteries 153–4, 402 lower quartile 119 LP see linear programming LST see latest start time MAD see mean absolute deviation management 453, 479 interdependence of problems 15–16 pressures on 8–9 see also financial decision making; project management margin of error (MoE) 220, 227 market research 146, 402 mathematics 7–8 Mathematics Knowledge Transfer Network 7–8 mathematical notation 26–38, 117, 355, 357 matrix, correlation 375–6 maximax criterion 191, 192–3 maximin criterion 191 www.downloadslide.net INDEX maximisation problems in LP 405, 411 McKinsey Global Institute mean 108–10, 126 absolute deviation (MAD) 298–300 for aggregated data 126 arithmetic 108–9 for Binomial distribution 170–1 for Normal distribution 172–4 population 117–18 for raw data 109–10 sample 117–18 squared error (MSE) 300–2 tests on 235–7 measures of average see averages measures of variability 112–23 IQR 120 range 112 standard deviation 112–13 media campaign 101, 103, 104 median 110–11 from aggregated data 128–9 from raw data 110–11 minimax regret criterion 192–3 minimisation problems in LP 405, 411 monetary policy committee (MPC) 288–9 money terms and real terms 44–5, 130–2 Monte Carlo simulation 511 most likely duration 473 motor vehicle production 100, 101 moving average methods of trend projection 290–308 exponential 303–7 simple 294 MPC see monetary policy committee MRP 446–8 MSE see mean squared error multicollinearity 375 multiple bar chart 56–7 multiple regression 365–78 assumptions 365, 373–8 multiplication rule conditional events 151–2 independent events 151–2 multiplicative model in time-series analysis 324–8 mutually exclusive events 149 naïve Bayes method 158 national income and production accounting (NIPA) system 213 National Lottery 153–4, 402 Natixis 530 natural logarithms 32 negative skew 123 net present value (NPV) 528–30 and internal rate of return 529–31 use in project appraisal 529 network diagrams 460–9 completed 463 developing 464–8 simple 460 stages 461–2 survey project 464 using 468–9 networked computer system, WWE 536–7 new vehicle registrations 79–82 Nielsen 23 nodes in decision trees 195–6 in network diagrams 460 nominal interest rate 523 non-binding constraints 411–12 non-linear equations 38, 40–2 non-linear programming 420–1 non-linear regression 363–4 non-negativity condition 405 non-response 254 Normal distribution 172–7, 180, 549 and Central Limit Theorem 216–17 and control charts 268–70 in project planning 473–5 standardising 174–5 and statistical inference 216–17 and the t distribution 240–3 tables 172–80, 549 Z score 175 notation see mathematical notation; symbols NPV see net present value null hypothesis 228–30, 234 objective function 405, 415 graphing 408–9 observed frequency 249–50 Office for National Statistics (ONS) 135, 213–14, 297 ogives 75–6 see also Lorenz curves on-demand services 64 one-tail test 229–30 ONS see Office of National Statistics open-ended intervals 69–71, 73 opinion polls 212, 254–7 opinions, personal see judgment, personal opportunity cost 192, 414, 520 optimistic duration 472 optimum solution in LP 410, 418 order costs 434, 438, 439 outcome node 196 outcomes 148 p values in hypothesis tests 245 Paasche index 136–7 Pamplin, Ryan 60 panel consensus 291 575 www.downloadslide.net 576 INDEX parameters of an equation 341 parametric/non-parametric tests 245 Pareto charts 275–6 Pareto diagrams (Lorenz curves) 76–9 Pareto system 79, 443–6 pay-offs decision trees 195–6 tables 190, 192 payback method 528 Pearson’s coefficient of skewness 120–3 pensions 121 percentage(s) 21–4, 130 component bar chart 59 cumulative 69–71 gas sales 559 histograms 74 standard error of 274 tests on two 239–40 percentiles 119 perfect information, value of 201–2 performance evaluation 350–1 performance-related pay 67 personal assessment see judgment, personal personal tax statements, Osborne 66 PERT see project evaluation and review technique pessimistic duration 473 pie charts 65 polygons 74–5 populations 117 by age group 99 mailing 14 mean 117 and samples 117, 212–13, 254 standard deviation 117–18, 217–18 positive skew 123 powers logarithms and 30–2 and roots 28–9 working with 28 precedence diagrams 469–70 prediction see forecasting predictive modelling 12–14 present value 523–6, 534–6 net see net present value primary data 21 principal amount 521 probability 148–9 addition rule 152–3 Binomial 168, 171–2 birthdays calculation 146–7 collectively exhaustive events 149–50 conditional events 149 decision making and 193–4 distribution see probability distribution empirical 148 events 155 failure 150–1 independent events 149 insurance 194–5 measuring 148–9 and Monty Hall problem 150–1 multiplication rule 151–2 mutually exclusive events 149 Normal 176–80 outcome 161 polygon 162 subjective 148 sum of 193 tables 172–9, 544–53 terminology 147–50 theoretical 148–9 probability distribution 159–62 chi squared (x2) 245, 551 t test 240–3, 550 see also Binomial distribution; Normal ­distribution process design/redesign, Six Sigma 279 process improvement, Six Sigma 279 process management, Six Sigma 279 process variation 267–8 product life cycle 291–2 profit centres 67 fall of Toyota 22 and sales, graphs 38, 39 for stores 124–5, 126 project evaluation and review technique (PERT) 472–5, 479 project management 453–76, 479 activities 457–60 conflicts in 454 crashing 475–7 dependencies 457–60 network diagrams 460–9 training course on 477–9 uncertainty, dealing with 472–5 projects 453–4 activities and duration of 483 appraisal 526–31 ATM 481 Cafeteria 481 characteristics of 454 costs and crashing 475–6 costs and savings 542 information 484 network diagram 456, 466, 468 precedence diagram 470 programme 483 proportions 21–4 of bottles 177 confidence intervals for 222–4 standard error 223 tests on two 239–40 www.downloadslide.net INDEX purchase cost 434 purchasing supplies of education authority 448–50 purchasing/replacing equipment 526–36 PV see present value PwC 23 qualitative approaches 290–2 Delphi method 291 historical comparison 291–2 market research 292 panel consensus 291 personal assessment 290–1 quality management techniques 262–79 control charts 267–73 Ishikawa diagrams 276–9 Pareto charts 275–6 Six Sigma 279 statistical process control 265–73 quantitative techniques 20 by business 2–3, 5–7 decision making models 10–11 to forecasting 293 role in business 8–10 use of computers 15 using text 15–16 quartiles 119–20 for aggregated data 128–9 calculating 120 queueing problems 486–7 r 344–6 R2 353 random elements of a time series 310–11 random numbers 255–6, 495–6 random samples 147–8, 255–6 range 112 rate of return 528 real rate of interest 525–6 real terms and money terms 44–5, 130–1 regression 339–81 multiple 365–78 non-linear 363–4 results 362, 383, 386 statistical evaluation of equation 352–62 variation in 352–3 regret 192–3 rejection area in hypothesis test 232–3 reliability 355 reorder cycle 440 reorder level 437–40 replacing/purchasing equipment 526–36 residuals and residual analysis 373–8 response rates 256 retail price index (RPI) 130–2 inflating cost of living 133 retail supermarket chain application 329–30 577 revenues broadcasters falling 63–4 Twitter’s growth 108 risk 195 analysis 509–12 for business 293 of eurozone recession in IMF 149 and financial decision making 523–5 out of uncertainty 509–12 tail 180–1 Risk Savvy: How to Make Good Decisions ­(Gigerenzer) 196 road projects 456 Rogers, Richard 189 Rolls-Royce sports utility vehicle 62 roots logarithms and 32 powers and 28–9 rounding 24–5 sales electricity 52–3, 308, 309, 310–11, 332–3, 361 forecasting retail 312 seasonally adjusted 320, 321 sports utility vehicle in Europe 62–3 trend 52–3 samples/sampling 117, 216, 254–7 cluster 256 convenience 256 distribution 214–22 error 228 mean 117 methodology 213 and populations 117–18, 212–13, 254 quota 256 random 148, 256 selection processes 151 standard deviation 117, 217–18 stratified 256 variation 228 scatter diagrams 87–90, 340–1 scenario analysis 510 seasonal components of a time series 310–11, 314–19 seasonality 52 seasonally adjusted series 311–12, 319–22 secondary data 21 sensitivity analysis 412–15, 510 shadow price 414 see also opportunity cost share prices 130 shopping basket to measure inflation 135 shortage costs 434–5 Significance F 370–1 significance level in hypothesis tests 230–2 significant figures 24–5 simple index 129–30 www.downloadslide.net 578 INDEX simplex method 418 simulation 485–502, 506 airport management in Capgemini 493–4 bank 514 beginning 496–502 of customers 504 evaluation 512 with Excel 517–18 flowcharts 491–3 gas 515, 516 model 490–1 Monte Carlo 511–12 principles of 486–7 simultaneous equations 412 Six Sigma 279, 281–2 skewness 120–3 slack 416, 418 slope of a linear function 342–4 smoothing methods see moving average methods of trend projection social media 60–1, 64, 108 and big data 267 social spending 121 spam 157–9 spider plots 510 spreadsheet programs see computers and ­computer programs squares, method of least 347–9 stacked bar charts 57 staffing levels 18, 112 standard deviation for aggregated data 127 for Binomial distribution 170–1 formulae for calculating 115, 117 for Normal distribution 172–4 of a population 117–18, 217–18 for raw data 112–15 of a sample 117, 217–18 of the sampling distribution 217–18 standard error 218 of a mean 219–20 of a percentage or proportion 223–4 Standardised Normal distribution 174–5 states of nature 188–93 statistical evaluation of the regression equation 352–62 statistical inference 212–13 statistical packages for computers see computers and computer programs statistical process control 265–73 statistics about spam 157 for aggregated data 125–9 distortions 311–12 inferential 243–5 labour market 101, 102 management 107 modern cult of 213–14 using 124–5 stock categories 442–5 stock control 431–48 ABC 443–5 decision 437–9 costs 434–5 economic order quantity 437–40 fraud losses 435 JIT 446, 448 MRP 446–8 problems 432–3 stockout costs 434–5 summation 34, 109 supermarket pricing 23 surveys 212–13 symbols 26–38, 117, 214, 217–18, 352 symmetry 120, 123 t distribution/t test 240–3, 550 tables pay-off 190, 192 probability 172–80, 544–53 tail risks 180–1 taxation 121–2 technical analysis 307–8 tests of association/contingency table 249–52 on the difference between two means 237–9 Durbin–Watson 375 goodness of fit 249 one-tail 229, 233 parametric/non-parametric 245–6 on a percentage or proportion 224–5 on regression equation 368–73 on a sample mean 235–7 on small samples 240–3 statistic value 234 statistical 354–5 on two proportions or percentages 239–40 two-tail 229–30, 233 x2 245–52 see also hypothesis tests time preference 520 time series components 310–11 deflating 131 graphs 52–6, 79–82 time-series data, autocorrelation and 375 time-series decomposition 293, 313–22, 324 time-series methods of trend projection 308–24 toolbox approach 15 tornado diagrams 510 trade-offs 487, 501–2 transportation 6–7 transportation model 421 trendline 308 www.downloadslide.net INDEX trends 52–6, 293–324, 360–2 calculations 314, 315–16 centring 313 deviations from 314–19 technical analysis 307–8 two-tail test 229–30 2Y graphs 81–2, 92 Type I/Type II errors 230–2, 257, 266–7 UK (United Kingdom) age distribution 141 council tax 252–4 expenditure on bilateral aid 100 increase in winter deaths 297–8 marriages in 334–5 new vehicle registrations 79–82 per capita income in 104, 393 popular world foods 62 retail supermarkets in 329–30 trends in air passenger 325–8 unemployment benefit 142 weekly earnings and RPI 46, 132, 142 welfare measures 44 uncertainty 145–7, 286 and financial decision making 520–1 in project planning 472–5 see also risk, analysis unexplained variation in regression 352, 369 upper quartile 119 validity 213 value, present see present value variability 107 measures of see measures of variability see also standard deviation variables 20 dependent 341 equations and 35–7 independent 341 variance 114–15, 473–4 variation coefficient of 118 explained and unexplained, in regression 352–3 vehicle registrations 79–82 vehicle speed survey 144 visual interactive simulation 506 voting 29–30, 212 warning limits 268 weighted average 134–7 weights in index numbers 134–7 what-if-analysis 18, 510 see also linear programming; simulation worst-case scenarios 189–90 x 115, 117 x2 (chi-square) distributions 245–6, 551 x2 (chi-square) test 245–52 Xerox 281–2 Yates’ correction 252 Z charts 82–7, 97–9 Z score 175 and confidence interval 218–20 zero sum 113 579 ... vehicle’s performance with other vehicles, forecasting the likely demand for refuse collection over the life of the vehicle and so on However, before reaching a decision, other factors and information... analysis Decision Figure 1.2 The decision- making process into account by the manager before reaching a decision Clearly, techniques have a potentially important role to play in helping reach a decision. .. managers Accountants will make decisions based on the information relating to the financial state of the organisation Economists will make decisions based on the information relating to the economic