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PROJECT MANAGEMENT Prof. Dr. Ahmed Farouk Abdul Moneim

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DEFINITIONS A Project is a non repetitive achievement. It differs clearly from the other two major modes of production: Batch production and Mass production BATCH Production MASS Production Batch Size Small Medium Large Volume of Work and Resources Involved SmallMedium Large Examples of PROJECTS Constructions Research & Development Exploration Promotion Campaigns Conferences …………… PROJECTS

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COURSE CONTENTS 1)PROJECT SCREENING AND SELECTION Scoring Method Benefit/Cost Analysis Integer Programming Decision Analyses and Utility Theory 2) PROJECT SCHEDULING Under Uncertainty Random Durations and Cost of Activities Fuzzy Durations and Cost of Activities Generalized Project Scheduling Problem Handling of problems of Change orders and delayed execution 3) TIME-COST OPTIMIZATION (TCO) Single Objective Optimization Pareto Front and Convex Hull Optimization 4) RISK IN PROJECTS MAMAGEMENT Risk of Time Overrun and project delay Risk of Cost Overrun and Budget Uncertainty 5) RESOURCE MANAGEMENT Resource Leveling Limited Resource Allocations

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PROJECTS SCREENING 5) UTILITY THEORY 4) DECISION ANALYSIS 3) INTEGER PROGRAMMING 2) BENEFIT/COST ANLYSIS 1) SCORING METHOD

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SCORING METHOD CRITERIA ProfitabilityTime To MarketDevelopment RiskCommercial Success Total Wt of Importance 12345123451234512345 Project A Project B Project C 3.09 2.14 3.96 0.466 0.277 0.161 0.096 Applying AHP to define weights of importance of Criteria Applying Linear Scoring Rule to evaluate a score for each project in each criterion

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Analytical Hierarchy Process (AHP) PTRS P1.0002.0003.0004.000 T0.5001.0002.0003.000 R0.3330.5001.0002.000 S0.2500.3330.5001.000 SUM2.0833.8336.50010.000 PTRS P0.4800.5220.4620.4000.466 T0.2400.2610.3080.3000.277 R0.1600.1300.1540.2000.161 S0.1200.0870.0770.1000.096 98765432123456789 PXT PXR PXS TXR TXS RXS

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Linear Scoring Rule Conversion Rule Current, Maximum and Minimum values of Criteria measured in Natural units Current, Maximum and Minimum Corresponding SCORES In NINE point scale In FIVE point scale The GREATER The BETTER The SMALLER The BETTER

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Example on The Linear Scoring Rule ALTERNATIVES CriterionWeight ABCMaxMin Optimality Direction Price0.4100200150200100 Fuel Consump tion 0.150.250.10.150.250.1 Speed0.1110150130150110 Salvage Value 0.354060306030 Data in Natural Units Corresponding Scores ABC Price0.4 915 FC0.15 196.333333 Speed0.1 195 Salvage Value0.35 3.66666791 Sum 5.1333335.83.8 RANK213 Using 9 point Scale

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Time Value of the money Single-payment compound amount factor Single-payment present worth factor (Salvage value ) Uniform series Capital Recovery factor F P F P P AAAA

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Uniform series sinking fund factor (Salvage value) Time Value of the money F AAAA

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BENEFIT/COST ANALYSIS 1. Deterministic Approach 1.1 Single Project An individual investment opportunity is deemed to be worthwhile if its B/C is greater than one. Consider the project of developing a new inventory control system with the following data: Initial cost $20 000 Project Life 5 years Salvage value $5000 Annual savings $10 000 O&M annual cost $2000 MARR 15% Uniform series Capital Recovery factor Uniform series sinking fund factor (Salvage value)

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BENEFIT/COST ANALYSIS 1. Deterministic Approach 2.1 Project Portfolio A governmental agency is considering four independent projects. Each has 30 years life time. The current budget allows not more than $35 millions. The interest rate is 10% per annum ABCD Initial Cost12000000200000001000000014000000 Annual Expenditure125000045000007500001850000 Annual Benefits3250000800000012500004050000 What is the optimum feasible portfolio of projects? Step 1 Evaluate B/C for each project and discard projects with B/C < 1

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ABCD Initial Cost 12 000 00020 000 00010 000 00014 000 000 Annual Expenditure 1 250 0004 500 000750 0001 850 000 Annual Benefits 3 250 0008 000 0001 250 0004 050 000 CR cost (annual) 1 272 9512 121 5841 060 7921 485 109 Total annual Cost 2 522 9516 621 5851 810 7923 335 109 B/C1.2881.2080.6901.214 Discarded B/C <1 ABDABADBDABD Initial Cost 12 000 000 20 000 00014 000 00032 000 0002600000034000000 46 000 000 An.Expenditure1 250 0004 500 0001 850 0005 750 00031000006350000 An. Benefits3 250 0008 000 0004 050 00011 250 000730000012050000 CR cost1 272 9512 121 5841 485 109 3394536 27580603606694 Total annual Cost2 522 9516 621 5853 335 109 9144536 58580609956694 B/C1.2881.2081.214 1.230 1.2461.210 Discarded Budget =35 m. Forming Projects Portfolio

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Step 2 Apply INCREMENTAL Analysis to accepted project portfolio Rank as regards total cost ADADBABBD Initial Cost120000001400000026000000200000003200000034000000 Total annualCost252295133351095858060662158591445369956694 Benefits32500004050000730000080000001125000012050000 B/C1.2881741.2143531.2461461.208171.2302431.210241 A is the baseline A is still the baseline Discard D Д C 3335109 Д B 4050000 Д B / Д C 1.214353 AD is the New baseline Discard A Д C 812158.5 Д B 800000 Д B / Д C 0.985029 Д C 763524.5 Д B 700000 Д B / Д C 0.916801 Discard B AD is still the baseline Д C 3286475 Д B 3950000 Д B / Д C 1.201895 AB is the New baseline Discard AD Д C 812158.5 Д B 800000 Д B / Д C 0.985029 Discard BD AB is the OPTIMUM PORTFOLIO

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The problem can be modeled in the form of A LINEAR INTEGER PROGRAM as follows: ABCD Initial Cost 12 000 00020 000 00010 000 00014 000 000 Annual Expenditure 1 250 0004 500 000750 0001 850 000 Annual Benefits 3 250 0008 000 0001 250 0004 050 000 CR cost (annual) 1 272 9512 121 5841 060 7921 485 109 Total annual Cost 2 522 9516 621 5851 810 7923 335 109 Benefits – Total annual cost7270491378415- 560792714891 Decision Variables Xi is a binary variable Xi = 1 if project i is selected and Xi = 0 otherwise Objective Function Subject to: Solution by SOLVER Projects A and B are selected Portfolio AB is selected

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BAYSEAN DECISION MODELS

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Example # 1 A company has developed a new product. It considers Two options: a)Sell the rights for $800 000 or b) Start production. The market could be high with the possibility of Selling10 000 units with probability of 20% or Could be low with possibility of selling only 1000 units with probability of 80%.The profit per unit is $550. The cost of establishing a production line is $600 000. A decision should be taken impersonally based on the EMV and personally having a risk avoider or risk seeker decision takers. Prof. Ahmed Farouk Abdul Moneim

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Decision Tree Method Expected Monetary Value (Impersonal decision) Decision Node Uncertainty Node High Market Low Market 0.2 0.8 10000*550 – 600 000= 4 900 000 1000*550 – 600 000= - 50 000 800 000 4 900 000 * 0.2 – 50 000 * 0.8 =940 000 940 000 SELL the rights Start Production The Best Option is to Start production with Expected Monetary Value (EMV) = 940 000 Prof. Ahmed Farouk Abdul Moneim

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UTILITY is a PREFERENCE Measure that is accounting for the psychological aspect of the decision maker. In this respect, decision makers could be categorized in three categories: Risk Seekers looking for Maximum Monetary outcomes even if it is associated with low probability Risk Avoiders looking for outcomes associated with highest probability or sure occurrence Indifferent decision makers for whom the utility is linearly changing with monetary outcomes Performing Decision Analyses Based on Utility Theory requires Expressing the Utility mathematically A mathematical expression is proposed to express the Utility U as a function of the monetary outcome ξ and a parameter characterizing the decision maker. Is the maximum monetary outcome Is the minimum monetary outcome Is a current monetary outcome Consider the Simplest second order equation: Constants are to be determined by considering the following boundary conditions: Therefore,Then, Finding b,This is the MARGINAL UTILITY, The Marginal Utility at is known as the Initial Marginal Utility Therefore,

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Since for Indifferent decision makers, the Marginal Utility is CONSTSNT for all values of ξ, then On the other hand, for RISK SEEKERS, as monetary outcomes ξ increases, the rate of change of utility increases. Therefore, In a similar manner, for RISK AVOIDERS, as monetary outcomes increases, the rate of change of utility decreases, therefore, For Indifferent Decision Makers For Risk SEEKERS Risk AVOIDERS Indifferent Risk Seekers Risk Avoiders Therefore Then the Marginal Utility Therefore,For all values of ξ and hence, The Marginal Utility is assumed a NON-NEGATIVE quantity

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Expected UTILITY Value UTILITY EventMonetary outcomeRisk SeekersRisk Avoider Producing in High Market4900 000111 Producing in Low Market- 50 000000 Selling the Rights800 0000.17180.10.243

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Decision Tree Method Expected UTILITY (Risk Seeker) Decision Node High Market Low Market 0.2 0.8 U=1 1* 0.2 + 0* 0.8= 0.2 0.2 SELL the rights Start Production The Best Option for a RISK SEEKER is to Start production with Expected Utility Value (EUV) = 0.2 Prof. Ahmed Farouk Abdul Moneim U=0 0.1

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Decision Tree Method Expected UTILITY (Risk Avoider) Decision Node High Market Low Market 0.2 0.8 U=1 1* 0.2 + 0* 0.8= 0.2 0.234 SELL the rights Start Production The Best Option for a RISK AVOIDER is Sell the Rights with Expected Utility Value (EUV) = 0.234 Prof. Ahmed Farouk Abdul Moneim U=0 0.234

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Example #4 A supermarket wants to determine the optimum quantity to be ordered from one type of vegetables weekly. The vegetable is sold during the week at a price per kg of $4. After a week passed the remaining vegetables is sold as animal feed for $0.5 per kg. The super market purchases the vegetable at a cost of $2.5. The demand on the this type of vegetables is random and distributed as follows: 050100150200250300 0.050.150.20.250.150.150.05 Evaluate EVPI Prof. Ahmed Farouk Abdul Moneim Evaluate the optimum size of weekly order

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DECISION TABLE METHOD Weekly Demand Probability0.050.150.20.250.150.150.05 Quantity in kg 050100150200250300 50 100 150 200 250 300 Quantity Purchased EMV -100 375 300 225 150 75 -25 125 200 450 -200 -125 -50 25 100 -300 -75 -225 -150 -400 -325 -250 -500 -425-600 66.25 106.25 83.75 7.5 111.25 72.5 150 75 225 300 375 In case of Having Demand < Qty purchased Net profit/loss = Demand *1.5 - (quantity purchased – Demand ) *(2.5 -0.5) Otherwise, Profit = quantity purchased * 1.5 50 275 In case of having purchased 50 kg, EMV= -100*0.05+75*.95=66.25 Similarly The optimum solution is to purchase 150 kg weekly

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MUo1-Muo Seeker0.5 Avoider1.5--0.5 ξ 500.4760.643 1000.3810.5480.714 1500.2860.4520.6190.786 2000.1900.3570.5240.6900.857 2500.0950.2620.4290.5950.7620.929 3000.0000.1670.3330.5000.6670.8331.000 Utility for Risk SeekerExpected 0.0500.1500.2000.2500.150 0.050Utility 500.3510.528 0.519 1000.2630.4240.612 0.567 1500.1840.3290.5010.702 0.580 2000.1130.2420.3990.5840.796 0.546 2500.0520.1650.3060.4750.6710.895 0.487 3000.0000.0970.2220.3750.5560.7641.0000.401 Utility for Risk AvoiderExpected 0.0500.1500.2000.2500.150 0.050Utility 500.6010.758 0.750 1000.4990.6710.816 0.779 1500.3880.5760.7370.870 0.775 2000.2680.4720.6490.7970.918 0.735 2500.1380.3590.5510.7160.8530.962 0.670 3000.0000.2360.4440.6250.7780.9031.0000.583

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BENEFIT/COST ANALYSIS 2. Probabilistic Approach RANDOM VARIATES GENERATION 1) Truncated Normal 3) Truncated Weibull 2) Truncated Exponential 4) Triangular X X X X Rand R R

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1) Truncated Normal a bX 2) Truncated Exponential R

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