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OPERATIONS RESEARCH

OPERATIONS RESEARCH. MANAGEMENT SCIENCE. Part I. Prof. Dr. Ahmed Farouk Abdul Moneim. PROBLEMS ADDRESSED. Optimum Product Mix. Portfolio Management. Investment Planning. Resource Allocations. Transportation Problems. Selecting Optimum Maintenance Policy.

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OPERATIONS RESEARCH

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  1. OPERATIONS RESEARCH MANAGEMENT SCIENCE Part I Prof. Dr. Ahmed Farouk Abdul Moneim

  2. PROBLEMS ADDRESSED Optimum Product Mix Portfolio Management Investment Planning Resource Allocations Transportation Problems Selecting Optimum Maintenance Policy Prof. Dr. Ahmed Farouk Abdul Moneim

  3. PROBLEMS ADDRESSED • Travelling Salesman • Job and Personnel Scheduling • Selecting A Service Facility Location • Size and Capacity of Service facilities • Optimum Promotional Mix • Inventory Problems Prof. Dr. Ahmed Farouk Abdul Moneim

  4. SOLUTIONS METHODOLOGY 1- Define the problem concretely 2- Build a Relevant Model 3- Validate the Model 4- Sensitivity Analyses 5- Implementation Prof. Dr. Ahmed Farouk Abdul Moneim

  5. TYPES OF MODELS IN MANAGEMENT SCIENCE 1- Mathematical Models 2- Computational Models Prof. Dr. Ahmed Farouk Abdul Moneim

  6. MATHEMATICAL MODELS IN MANAGEMENT SCIENCE 1- Linear Programming 2- Non Linear Programming 3- Integer Programming 4- Binary Programming 5- Goal Programming 6- Dynamic Programming 7- Markovian Analyses 8- Bayesian Decision Analysis Prof. Dr. Ahmed Farouk Abdul Moneim

  7. COMPUTATIONAL MODELS IN MANAGEMENT SCIENCE 1- Simulation Models 2- Genetic Algorithms 3- Other Meta Heuristic Models Prof. Dr. Ahmed Farouk Abdul Moneim

  8. Course Contents 1- Project Planning Under Uncertainty PERT 2- Project Planning By Monte Carlo Simulation 3-Markovian Analyses 4- Queuing Models 5- Dynamic Programming 6- Markovian Decision Analysis Prof. Dr. Ahmed Farouk Abdul Moneim

  9. 1- Project Planning Under Uncertainty 1.1- Project Evaluation & Review Technique (PERT) FF=MinES of Suc-EC TF=LC -EC 0 0 12.33 D,G 12.33 12.33 0 5.67 E 16.67 16.67 0 22.33 22.33 7.67 F 22.33 22.33 0 30.50 30.5 22.33 E 0 0 12.33 22.33 22.33 30.50 F 0 0 22.33 30.5 30.50 40.00 H 30.50 0 0 40 40 22.33 12.33 H 40 17.67 17.67 40 40 48 0 0 No 48 48 Prof. Dr. Ahmed Farouk Abdul Moneim

  10. C B A D E F H If TC = 51 month Evaluate probability of Delay G Probability of DELAY Probability of Delay = TE TC Prof. Dr. Ahmed Farouk Abdul Moneim

  11. 1.2- DELAY in Completing Projects Given: TE Project Completion Average Time TC Project Completion CONTRACT Time σP Standard Deviation of Project Completion Time ZC ZED Therefore, Prof. Dr. Ahmed Farouk Abdul Moneim

  12. TED TE TC Prof. Dr. Ahmed Farouk Abdul Moneim

  13. SDF table

  14. Example • The contract time is 51 days. Evaluate the probability of delay • Find the expected delay time • It is required to reduce the delay by 50% . • What is the optimum policy, whether to reduce the variance or to reduce • the expected project time. The cost of reducing the variance by 1% is $ 500 • whereas the cost reducing the mean project time by 1% is $ 3000. SOLUTION From table of SDF, we get at Z c = 0.8165 SDF= 0.594 Prof. Dr. Ahmed Farouk Abdul Moneim

  15. Optimum Strategy of Reducing Project Delay Strategy 1: Reducing Expected Project Time (Keeping Variance Constant) Resource Quantity Strategy From SDF table we get New Z c Therefore New Expected Project Time will be found TE TC TENew Percentage Decrease of Expected Project Time=100* (TE old – TE new )/TE old = 100*(48 –38.75)/48 = 19.267% Cost of compressing Project Time = 19.267 * 3000 = $ 57803 Prof. Dr. Ahmed Farouk Abdul Moneim

  16. Strategy 2: Reducing Variance of Project Time (Keeping Expected Project Time Constant) Resource Quality Strategy σP New Target =0.5*2.59= 1.295days σP old = 4.359 days σP TE T c Percentage Decrease of Variance= Cost of compressing Project Time Variance = 94.74*500= $ 47368 Decision: Implement Strategy 2 Prof. Dr. Ahmed Farouk Abdul Moneim

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