PROJECT MANAGEMENT Prof. Dr. Ahmed Farouk Abdul Moneim

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

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

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

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

Analytical Hierarchy Process (AHP) PTRS P T R S SUM PTRS P T R S PXT PXR PXS TXR TXS RXS

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

Example on The Linear Scoring Rule ALTERNATIVES CriterionWeight ABCMaxMin Optimality Direction Price Fuel Consump tion Speed Salvage Value Data in Natural Units Corresponding Scores ABC Price FC Speed Salvage Value Sum RANK213 Using 9 point Scale

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

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

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 $ Project Life 5 years Salvage value $5000 Annual savings $ O&M annual cost $2000 MARR 15% Uniform series Capital Recovery factor Uniform series sinking fund factor (Salvage value)

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 Cost Annual Expenditure Annual Benefits What is the optimum feasible portfolio of projects? Step 1 Evaluate B/C for each project and discard projects with B/C < 1

ABCD Initial Cost Annual Expenditure Annual Benefits CR cost (annual) Total annual Cost B/C Discarded B/C <1 ABDABADBDABD Initial Cost An.Expenditure An. Benefits CR cost Total annual Cost B/C Discarded Budget =35 m. Forming Projects Portfolio

Step 2 Apply INCREMENTAL Analysis to accepted project portfolio Rank as regards total cost ADADBABBD Initial Cost Total annualCost Benefits B/C A is the baseline A is still the baseline Discard D Д C Д B Д B / Д C AD is the New baseline Discard A Д C Д B Д B / Д C Д C Д B Д B / Д C Discard B AD is still the baseline Д C Д B Д B / Д C AB is the New baseline Discard AD Д C Д B Д B / Д C Discard BD AB is the OPTIMUM PORTFOLIO

The problem can be modeled in the form of A LINEAR INTEGER PROGRAM as follows: ABCD Initial Cost Annual Expenditure Annual Benefits CR cost (annual) Total annual Cost Benefits – Total annual cost 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

BAYSEAN DECISION MODELS

Example # 1 A company has developed a new product. It considers Two options: a)Sell the rights for $ or b) Start production. The market could be high with the possibility of Selling 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 $ 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

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

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,

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

Expected UTILITY Value UTILITY EventMonetary outcomeRisk SeekersRisk Avoider Producing in High Market Producing in Low Market Selling the Rights

Decision Tree Method Expected UTILITY (Risk Seeker) Decision Node High Market Low Market U=1 1* * 0.8= 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

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

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: Evaluate EVPI Prof. Ahmed Farouk Abdul Moneim Evaluate the optimum size of weekly order

DECISION TABLE METHOD Weekly Demand Probability Quantity in kg Quantity Purchased EMV In case of Having Demand < Qty purchased Net profit/loss = Demand *1.5 - (quantity purchased – Demand ) *( ) Otherwise, Profit = quantity purchased * In case of having purchased 50 kg, EMV= -100* *.95=66.25 Similarly The optimum solution is to purchase 150 kg weekly

MUo1-Muo Seeker0.5 Avoider ξ Utility for Risk SeekerExpected Utility Utility for Risk AvoiderExpected Utility

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

1) Truncated Normal a bX 2) Truncated Exponential R