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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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  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. Evaluating Alternatives List the Benefits in Numerical Terms Select a Mathematical Decision Making Model List the Possible Alternatives Identify the Possible Outcomes Apply the Mathematical Model Define the Problem 13 • Decision Trees and Risk • Expected Monetary Value • Value of Perfect Information • Uncertainty • Time Value of Money 1301

  3. Example 13 1. Define the Problem. A student is considering moving out of rented accommodation and taking on a mortgage. 2. List the Possible Alternatives. The alternatives are:- Buy a house. Buy a flat. Remain in rented accommodation. 3. Identify the Possible Outcomes. Conditions could be favourable or otherwise. 4. List the Benefits in Numerical Terms Favourable Unfavourable House £10,000 -£2,000 Flat £6,000 -£1,000 Rent £0 £0 5/6. Select a Mathematical Decision Making Model and Apply. • Do not ignore any alternatives, including doing nothing. • Do not ignore possible outcomes (positive or negative). Outcomes over which you have no control are called “states of nature”. 1302

  4. Decision Making Situations 13 • Decision Making Under Certainty • Decision Making Under Uncertainty • Decision Making Under Risk 1303

  5. Decision Trees and Risk 13 State of Nature Node £10,000 £7,500 Favourable (0.75) Decision Node Unfavourable (0.25) -£2,000 -£500 Buy a House £6,000 £4,500 Favourable (0.75) Buy a Flat Unfavourable (0.25) -£1,000 -£250 Do Nothing £0 -£0 *EMV = Expected Monetary Value • Multi-Stage Decisions Can be Analysed 1304

  6. Value of Perfect Information 13 Should the Student Take Professional Advice? This is the Value Where Bad Decisions Have Been Avoided. This is the Value that Would be Obtained Under Conditions of Risk. This is the Most that the Advice would be Worth - An Offer of Advice at £1000 should be declined. EVOPI = Expected Value of Perfect Information, EVWPI = Expected Value with Perfect Information. How Would You Make the Decision? 1305

  7. Uncertainty 13 House Flat Do Nothing • Maximax (Optimistic) - House • Maximin (Pessimistic) - Nothing • Equally Likely (Balanced) - House 1306

  8. 13 Decision Making Example – Question Two sisters plan to go to a party. A lift is available to get to the party, but there is no guarantee this will be available for the return journey. It may be necessary to use a taxi therefore, and this will cost £7.50. Taking the car will cost £2.00. • Produce a decision table for this case • What is the best decision based on the Maximax, Maximin and Equally Likely criteria? • The probability of obtaining a lift is 0.4. Draw a decision tree for this case • Should the sisters take the car based on the probability information given? 1307

  9. 13 Decision Making Example – Answer States of Nature No Lift Row Max Row Min Row Average Alternatives Lift £-2.00 £-2.00 £-2.00 £-2.00 £-2.00 Take Car Leave Car £0.00 £-7.50 £0.00 £-7.50 £-3.75 Maximax = Leave CarMaximin = Take CarEqually Likely = Take Car -£0.00 Lift (0.4) -£7.50 Leave Car No Lift (0.6) Take Car But are There Any Other Factors? -£2.00 1308

  10. 13 Summary • Evaluating Alternatives is a Common Management Task • There are Three Conditions for Evaluating Alternatives • Decision Making Under Certainty • Decision Making Under Uncertainty • Decision Making Under Risk • Analytical Approaches Can Support Decision Making • Ultimately, Decisions Must be Taken by Managers 1309

  11. Overview 14 • Definition The Imitation of a Real World System • Examples Flow of People Through an Airport • Nuclear War • Traffic Flow in a Large City • Behaviour of a Suspension System • World Economy • Temperature/Stress in a Piston • Forces in a Metal Cutting Process • Queues within a Manufacturing System 1401

  12. Reasons for Simulation 14 • Practicality • Safety • What-if Analysis • Understanding Large Systems Extreme of Systems Cost Time Repeatability Visualisation (VR) Verification of Analytical Solutions Simulation is Becoming an Increasingly Common Engineering Technique 1402

  13. Terminology 14 1403

  14. Simulation Model 14 Simulation Methodology Step 1. Build Conceptual Model Step 2. Covert the Conceptual Model Inputs (Procedures) Outputs (Responses) Step 3. Verify the Model Step 4. Model Experimentation Experimentation Step 5. Draw Conclusions 1404

  15. Hierarchy of Simulation Techniques 14 1405

  16. Continuous Simulation m (Kg) 14 x Linear Second Order Differential Equation k (N/m) c (Ns/m) Analytical Solution 1406

  17. Kinematic Simulation 14 1407

  18. Static Simulation 14 1408

  19. Simple Example 14 1409

  20. Simple Example - 10 Coins 9 8 7 6 Frequency 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 Score 14 1410

  21. Probability Distribution Function 14 PDF CDF DiscreteDistribution ContinuousDistribution Mapping Random Number to PDF: 1411

  22. PDF/CDF Example (1) 13 1412

  23. Random Numbers 13 1413

  24. PDF/CDF Example (2) 13 0.785 0.744 0.119 5.78 2.65 5.55 1414

  25. PDF/CDF Example (3) 9 8 7 6 Frequency 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 Score 13 An Accurate Picture Takes Many Iterations – This is Called “Warm-Up” 1415

  26. Dynamic Discrete Event Simulation 13 • Behaviour of a System Over Time • Concerned with Discrete Variables • Applied in a Variety of Fields • Useful for Examining Material Flow • Two forms: Deterministic and Stochastic • Originally Used Standard Languages (Fortran, Pascal) • Specialised Systems Now Exist (HOCUS, ProModel) 1416

  27. Dynamic Simulation - Example – 1 Start-up 15 End of 1st Hour 15 End of 2nd Hour 8 7 Units Used End of 3rd Hour 8 End of 4th Hour 8 End of 5th Hour 11 7 Units Used, 10 Units Arrive End of 6th Hour 11 End of 7th Hour 11 End of 8th Hour 4 7 Units Used End of 9th Hour 4 End of 10th Hour 14 10 Units Arrive End of 11th Hour 7 7 Units Used End of 12th Hour 7 End of 13th Hour 7 End of 14th Hour 0 7 Units Used End of 15th Hour 10 10 Units Arrive End of 16th Hour 10 End of 17th Hour 3 7 Units Used End of 18th Hour 3 End of 19th Hour 3 End of 20th Hour 10 3 Units Used, 10 Units Arrive End of 21st Hour 10 End of 22nd Hour 10 13 Time Period Q Event(s) Initial Queue = 15 10 Every 5 Hours Starting 5th Hr Queue (Q) Process Output 1417

  28. Dynamic Simulation - Example - 2 Quantity Queue Process Arrivals 14 Initial Queue = 15 10 Every 5 Hours Starting 5th Hr Queue (Q) 7 Every 3 Hours (Max) Starting 2nd Hr Process Output 1418

  29. Simulation Method - Time Slicing Initial Model Definition Re-define Entity States Display Model Status End ti = ti + t 14 ti t0 Time is incremented by “t” Statistics 1419

  30. Simulation Method – Advanced Initial Model Definition Calculate Next Event Re-Define Entity Status Display Model Status End 14 t0 Next ti Future Event List Statistics Update ti 1420

  31. 14 Stochastic Simulation • Stochastic Processes are Uncertain • Many Processes are Stochastic • Stochastic Variation can be Modelled • General Conclusions • CDFs Model Stochastic Variation 1421

  32. 14 Example - Waiting Line Model 1422

  33. 14 Simulation – Limitations • Simulations Themselves Can be Costly • Base Data can be Difficult to Collect • Simulations are Not Reality • A False Sense of Security 1423

  34. 14 Simulation - Summary • It Uses Models of Real-World Situations • It Can be Applied to Many Different Problems • It is a Powerful Tool • Standard Packages are Now Available 1424

  35. 15 Project Management • Common Activity for Engineers • Essential for Any Complex Task • Allows Tasks to be Divided • Allows Progress Monitoring • Provides a Critical Path • Formal Methods Available • Techniques and Good Practice 1501

  36. 04 Activities and Events Event Activity Event Building Site Construct Frame Completed Frame Activity Activity on Node (AON) AON Event Event Event Event AOA Activity on Arrow (AOA) Activity 1502

  37. 04 Modelling Projects – Example (1) • Boil Water • Locate Coffee • Locate Sugar • Locate Milk • Add Coffee and Sugar • Add Boiling Water • Add Milk • Serve Coffee • Drink Coffee 1503

  38. 15 Modelling Projects – Example (2) Locate Milk 4 Add Milk Drink Coffee • Activity Precedence is Critical Boil Water 6 8 7 9 1 Add Boiling Water Serve Coffee AON Locate Coffee 2 5 Add Coffee And Sugar Locate Sugar 3 Add Milk Serve Coffee Drink Coffee Locate Milk 6 5 7 8 1 Boil Water Add Boiling Water 4 Locate Coffee 2 Dummy Activity Add Coffee And Sugar Locate Sugar AOA 3 1504

  39. 15 Modelling Projects – Example (3) Locate Milk 4 7 Add Milk Drink Coffee • Activity Precedence is Critical Boil Water 6 8 9 1 Add Boiling Water Serve Coffee AON Locate Coffee 2 5 Add Coffee And Sugar Locate Sugar Note Change in Diagrams 3 Add Milk Serve Coffee Drink Coffee Locate Milk 6 5 7 8 1 Boil Water Add Boiling Water 4 Locate Coffee 2 Dummy Activity Add Coffee And Sugar Locate Sugar AOA 3 1505

  40. 15 Modelling Projects – Example (4) • CPM – AON • PERT – AOA • AOA – Easy to Visualise • AOA – Needs Dummy Activities • Infinite Resources Assumed 1506

  41. Add Coff. + Sug. 5 15 Secs 61 75 15 AON Diagram (MS Project Format) Locate Milk 60 secs 4 60 0 Boil Water Add Boiling Water Add Milk Serve Coffee Drink Coffee 1 300 secs 6 15 Secs 7 15 Secs 8 120 Secs 9 540 Secs 0 300 301 315 316 330 331 450 451 990 Add Coff. + Sug. Locate Coffee 2 60 Secs 5 15 Secs 60 61 0 75 Locate Sugar Activity Name 3 60 Secs 0 60 Activity Number Duration Earliest Start Time Earliest Finish Time Note: MS Project Does Not Handle Seconds 1507

  42. 15 Use of a Gantt Chart Time (in Seconds) 100 200 300 400 500 600 700 800 900 Locate Milk Locate Coffee Locate Sugar Boil Water Add Coffee +Sugar Add Boiling Wat. Add Milk Serve Coffee Drink Coffee Critical Path 1508

  43. 15 Activity Scheduling - Definitions • Critical Path – Longest Path Through a Network • Critical Activity – Activity on the Critical Path • Slack – Length of Time Available Before an Activity Needs to Start • ESD – Earliest Date that an Activity Could Start • EFD - Earliest Date that an Activity Could Finish • LSD – Latest Date that an Activity Could Start Without Extending Project • LFD – Latest Date that an Activity Could Finish Without Extending Project ESD = LSD, EFD = LFD, Slack = 0 for Critical Activities 1509

  44. 15 Activity Scheduling – Principles Forward Pass Backward Pass • ESD = LSD, EFD = LFD, Slack = 0 for Critical Activities • ESD for an Activity is the Largest EFD of Immediate Predecessors • LFD for an Activity is the Smallest LSD of Immediate Successors 1510

  45. 0 0 300 300 Yes 0 225 60 285 225 0 225 60 285 225 ESD EFD X 0 255 60 315 255 60 285 75 300 225 Dur. LSD LFD 300 300 315 315 Yes 315 315 330 330 Yes 330 330 450 450 Yes 450 450 990 990 Yes 15 Activity Scheduling – Standard Form • Boil Water • Locate Coffee • Locate Sugar • Locate Milk • Add Coffee and Sugar • Add Boiling Water • Add Milk • Serve Coffee • Drink Coffee D Activity 60 Duration A 300 S B E F G H I F 60 15 15 15 120 540 C Imm. Pred. 60 Activity Dur. ESD LSD EFD LFD Slack Crit. A 300 B 60 C 60 • Note the Slight Difference to MS Project • Slack Cannot be Used Twice in All Cases D 60 E B, C 15 A, E F 15 15 G D, F H G 120 H I 540 1511

  46. S 15 Activity Scheduling – Logic Summary Greater of Two EFDs 0 20 30 40 A E 20 0 20 10 40 50 20 30 C F 10 20 30 0 10 30 50 B E 10 10 20 20 30 50 Greater of Two EFDs Smaller of Two LSDs 1512

  47. 15 Stochastic Activity Times • Activity Times Generally Stochastic • This Implies Project Times are Stochastic • What are the Chances of Success? • Need to Use Probability Distributions • Traditional to Use a Beta Distribution • Only Provides an Estimate Where:- a = Pessimistic Estimate b = Optimistic Estimate m = Most Probable Time t = Expected Time Sigma = Standard Dev. P(x) m,t m t t m P(x) P(x) a b a b b a x x x 1513

  48. 15 Project Uncertainty – Example - 1 What are the Chances of this Project Being Completed in Less than 17 Minutes (1020 Seconds)? D 0 60 60 255 315 Slack =255 A 0 300 300 0 300 S B 0 60 E 60 75 F 300 315 G 315 330 H 330 450 I 450 990 F 60 225 285 15 285 300 15 300 315 15 315 330 120 330 450 540 450 990 Slack =225 Slack =225 C 0 60 60 225 285 Slack =225 Project Deadline = 1020 Project Time = 990 Project Slack = 30 Slack as = 30 42 = 0.715 1514

  49. 15 Normal Distributions x1 x2 1515

  50. 15 Project Uncertainty – Example - 2 By Linear Interpolation: y (x2, y2) More Accurate Tables for Standard Deviation Yield a Probability of 0.7625 (xv, yv) (x1, y1) x 1516

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