Chapter 11 Monte Carlo Simulation

Size: px
Start display at page:

Download "Chapter 11 Monte Carlo Simulation"

Transcription

1 Chapter 11 Monte Carlo Simulation 11.1 Introduction The basic idea of simulation is to build an experimental device, or simulator, that will act like (simulate) the system of interest in certain important aspects in a quick, cost-effective manner. Simulation versus optimization - In an optimization model the values of the decision variables are outputs. That is, the model provides a set of values for the decision variables that maximizes (or minimizes ) the value of the objective function. - In a simulation model the values of the decision variables are inputs. The model evaluates the objective function for a particular set of values the quality of the suggested solution as well as how much variability there might be in the various performance measures due to randomness in the inputs. When should simulation be used? - analytical models yield the best answer, but they may be difficult/impossible to obtain depending on complicating factors - analytical models typically predict only average or steady-state (long run) behavior - simulation can be performed with a great variety of software Simulation and random variables - Simulation models are often used to analyze a decision under risk the factor that is not know with certainty is though of as a random variable (behavior is described by a probability distribution)! sometimes called Monte Carlo method - Used e.g. for queuing models when it is difficult or impossible to obtain analytic results, or for multi-item, multi-location inventory models which are very difficult to analyze using an analytical model 11.2 Generating random variables Discrete random variables = can assume only certain, specific values (e.g. integers) - Discrete uniform distribution = each value is equally likely can be generated from a continuous uniform distribution by INT(x+(y-x+1)*RAND()) x being the lower, y being the upper bound Continuous random variables = may take on any fractional value (an infinite number of possible outcomes! probability of a specific value is zero) - Cumulative distribution function (CDF) e.g. f(x) = Prob{D <= x} - As the probability that any specific value occurs is strictly zero, continuous random variables do not have probability distributions; the density function and the CDF are the 2 functions used to define a continuous random variable - Exponentially distributed random variable with a mean of x: -x*ln(1-rand()) - Normal distributed random variable with a mean of x and standard dev. of y: NORMINV(RAND(),x,y) Random number generators (RNG) are built in into spreadsheet software 11.4 Simulating with spreadsheet add-ins Don t fall into the expected value trap! There are cases where the true mean of a variable can be calculated by setting all the random values to their means, but it does not always work! True mean of a sample normal distribution is contained in an interval of ± 1.96 standard deviations about the estimated mean divided by the square root of the number of samples Poisson distribution = is good description when demand is relatively small, is a one-parameter distribution, as only the mean value needs to be known (is ad discrete distribution only nonnegative integer values) About simulations: - Increasing the number of trials gives a better estimate, but even with large numbers, the can be a difference between the simulated averaged and the true expected return - Simulations provides useful information on the distribution of results, but is sensitive to assumptions affecting the input parameters by Boris Nissen Page 1

2 Chapter 10 Decision Analysis 10.1 Introduction Decision analysis provides a framework that establishes (1) a system of classifying decision models based on the amount of information about the model that is available and (2) a decision criterion decision theory treats decisions against nature the result (return) from an individual decision depends on the action of another player (nature), over which you have no control (in game theory both players have an economic interest) payoff table = lists alternative decisions along the side of the table, the possible states of nature on top and gives the payoffs for all possible combinations! the decision is always made first 10.2 Tree classes of decision models decision under certainty = you know which state of nature will occur (or there is just one single state) - to solve such a decision model, you just select the decision that yields the highest return decisions under risk = lack of certainty about future events is a characteristic of most management decision models - definition of risk in the decision under risk: There is more than one state of nature and for which we make the assumption that the decision maker can arrive at a probability estimate for the occurrence for each of the various states of nature (generally by using historical frequencies) "# expected value of any random variable is the weighted average of all possible values of it! management should make the decision that maximizes the expected return "# risk profile = shows all the possible outcomes with their associated probabilities for a given decision "# a sensitivity analysis can be made using the data table command decisions under uncertainty = more than one possible state of nature, but decision maker is unwilling or unable to specify the probabilities - Laplace Criterion = approaches the condition of uncertainty as equivalent to assuming that all states of nature are equally likely! transforms problem into a decision under risk - Maximin criterion = evaluates each decision by the worst thing that can happen if you make that decision! decision that yields the maximum value of the minimum returns is then selected (but does not necessarily give the best result often used if planner feels he cannot afford to go wrong - Maximax criterion = evaluates each decision by the best thing that can happen! decision that yields the maximum values of the maximum returns is then selected (same flaw as maximin) - Regret and Minimax Regret = new payoff table is made, where each current entry is subtracted from the maximum in its column (opportunity costs)! the typical suggestion then is to use the conservative minimax criterion, by which the smallest maximum regret is chosen 10.3 The expected value of perfect information Expected value of perfect information = expected return with perfect information expected return with current sequence of events - Can be easily calculated using Excels MAX() function 10.6 Decision Trees decision tree = graphical device for analyzing decisions under risk square node (or decision node) = represents a point at which a decision must be made each line leading from a square represents a possible decision circular nodes = represent sitatuations when the outcome is not certain each line is a possible outcome terminal positions = end of a branch terminal nodes = nodes not followed by others terminal value = return associated with each terminal position 10.8 Decision trees: incorporating new information a market research study can increase the expected return, even if it is not perfectly reliable conditional probability = P(A B), probability that the event A occurs given that the event B occurs by Boris Nissen Page 2

3 prior probabilities = initial estimates posterior probabilities = conditional probabilities! key to obtain them is Bayes Theorem (see Statistics book W&W) when incorporating posterior probabilities in the decision tree, the tree has to be created in the chronological order in which information becomes available and decisions are required expected value of sample information - EVSI (expected value of sample information) = maximum possible expected return with sample information maximum possible expected return without sample information - EVPI (expected value of perfect information) = maximum outcomes times the prior probabilities - when P(E S) = 1.0 and P (D W) = 1.0 then EVSI = EVPI, the better the sample information, the close gets EVSI to EVPI 10.9 Sequential decisions: To test or not to test sequential decision model = value of an initial decision depends on a sequence of decisions and uncertain events that will follow the initial decision optimal strategy = a complete plan for the entire tree, it specifies what action to take no matter which of the uncertain events occurs to incorporate utilities into the decision tree, all you need to do is replace the payoffs with their utilities - treeplan has a built-in exponential utility function, which assumes a risk-averse utility function and calculates the utilities for the given cash flows already on the tree Management and decision theory typical management decision has the following characteristics: - is made once and only once - return depends on an uncertain event that will occur in the future we know about related event that may tell us something about the likelihood of the various outcomes! for each decision, determine the utility of each possible outcome! determine the probability of each possible outcome! calculate the expected utility of each decision! select the decision with the largest expected utility how do we know about the utilities and probabilities! they are subjective and represent the best judgment and taste of the manager Assessing subjective probabilities: - structure is provided by equivalent lottery! it allows one to quantify both subjective probability and utility through a process of personal judgment - what we gain form assessing probability and utility separately manager can concentrate attention on each of the entities one at a time - Separating the assessments of probabilities and utilities forces a manager to give appropriate and separate consideration to each before combining the 2 to determine the final decision Notes on implementation - decision analysis involves assigning probabilities and utilities to possible outcomes and maximizing expected utility in a 4 step process: (1) structuring the model, (2) assessing the probability of the possible outcomes, (3) determining the utility of the possible outcomes, and (4) evaluating alternatives and selecting a strategy - important: decision analysis does not provide a completely objective analysis, but its important role is to make it consistent (the subjective component does not depend on how you feel at the moment - continuous outcomes: - approximate the continuous outcomes with a Pearson-Tukey approach (3 branches (representing the 0.05 fractile, the 0.5 fractile and the 0.95 fractile with optimal weights of 0.185, 0.63, 0.185) - or use the Monte Carlo simulation Chapter 14 Project Management: PERT and CPM 14.1 Introduction - managing major projects involves complicated problems of scheduling, as they are often structured by the interdependence of activities by Boris Nissen Page 3

4 - PERT (Program Evaluation Review Technique, 1950s) and CPM (Critical Path Method, 1957) are approaches to scheduling events of a project, that see the project as a network! they allow for management by exception by reducing the number of activities that have to be closely monitored 14.2 A typical project: The global oil credit card operation - first step: activity list = defines the activities in the project and establishes the immediate predecessors in the same line - immediate predecessor = an activity that must be completed prior to the start of the activity in question - Gantt chart simple graphical representation of earliest possible starting time for each activity and each earliest possible completion time! fails to show the necessary information of predecessors, as it automatically stamps each activity not completed on the earliest possible time as behind schedule and does not show the relation of the earliest possible starting times of other activities! one cannot see whether or not the entire project is delayed - PERT network diagram = each activity is represented by an arrow that is called a branch or an arc. The beginning and end of each activity is indicated by a circle that is called a node. The term event is also used in connection with the nodes. An event represents the completion of the activities that lead into a node (when an activity is completed, the event occurs.). - each activity must start at the node in which its immediate predecessors ended "# Dummy activity (dashed line) = fictitious activity in the sense that it requires no time or resources, is just a device to enable us to draw a network representation and maintain the correct precedence relationships "# Dummy variables can be avoided by associating activities with nodes instead of arcs (activity-on-the-node-approach) 14.3 The critical path - second step: come up with time estimates for completion of each activity and do the critical path calculation - path = a sequence of connected activities that leads form starting to end node - critical path = path that takes the longest time to complete, thus as all paths have to be completed successfully, it determines the overall project duration! longest route problem - critical activities = activities on the critical path have to be kept on schedule - earliest start and earliest finish times: - earliest starting time rule: The ES time for an activity leafing a particular node is the largest of the EF times for all activities entering the node - EF = ES + t (earliest finishing time = earliest starting time + expected activity time - continuing to each node in a forward pass through the entire network, the values [ES,EF] are computed - latest start and latest finish times: - in order to determine the latest date each activity can finish without delaying the entire project, we work backward form the target completion date determined with the earliest finish times - LS = LF t (latest starting time = latest finishing time expected activity time) - Latest finish time rule = the LF time for an activity entering a particular node is the smallest of the LS times for all activities leaving that node - Slack = the amount of time an activity can be delayed without affecting the completion date for the overall project! critical path activities are those with zero slack - ways of reducing project duration: - strategic analysis! make arrangements to accomplish some activities in a different way to exclude them from the critical way! what if question - tactical approach: reduce the time of certain activities on the critical path 14.4 Variability in activity times - estimating he expected activity time requires 3 inputs for each project: - optimistic time [a] (the minimum, if everything goes perfectly); most probable time [m] (the most likely outcome); pessimistic time [b] (the maximum time, if everything goes wrong) - activity time is thus a random variable with the beta probability distribution - beta distribution = has a finite range of values and is capable of assuming a wide variety of shapes - estimate of expected activity time = (a + 4m + b)/6 - standard deviation of activity time = (b-a)/6 (assumption that there are 6 standard deviations between optimistic and pessimistic times) - variance of activity time = [(b-a)/6]² - but it is possible to use any procedure that seems appropriate to estimate the expected value and standard deviation by Boris Nissen Page 4

5 - probability of completing the project in time: - T = total time that will be taken by the activities on the critical path - Var (T) = sum of the variances of the activities on the critical path - if we assume the activity times to be independent random variables and T to have an approximately normal distribution, we can calculate the probability of completing the project in time by the formula using the standard normal distribution (Z = (T-µ)/σ)) - the result though has to be treated with care, as due to the randomness, some other path might become the critical path and thus what we observe with the critical path we observe is irrelevant Using Crystal Ball - by making the activity times random with Crystal Ball we can get a feel for the variability of both the project length and the critical path - the forecasts can give us the expected project length and we can get the probability of completing in a certain time by using the cumulative chart - for determining whether an activity might be a critical activity, we just have to look at the frequency distribution of the activity, if there is a peak at zero, it may be a critical activity (an insight that the PERT analysis might obscure) 14.5 CPM and time-cost trade-offs - PERT is a useful approach when there is little previous time and cost experience to draw upon - CPM is useful, if good estimates of time and resource requirements can be made on the basis of historical data, as then the trade-off between time for completion and cost of resources devoted to the activity may be very interesting - CPM assumes costs to be a linear function of time - Question: What activity times should be selected to yield the desired project completion time at minimum cost? Required date for the CPM! 4 pieces of input for each activity - normal time: maximum time for the activity a known quantity - normal cost: cost required to achieve the normal time - crash time: minimum time for the activity - crash cost: cost required to achieve the crash time - with this data, the max crash hours (normal time crash time) and the cost of one hour of crash time can be computed - crashing = process of reducing an activity time Crashing a project - using the normal time for each activity the earliest completion time incurring only normal costs can be calculated, then we are in a position to determine the minimum cost method of reducing this time to a specified level, by the use of a linear programming model (SOLVER!) - objective function: minimize total cost of crashing the network for a specified completion time - constraints: - crash time per activity <= max crash time for activity - earliest start time for an activity => normal earliest start time hours crashed - earliest finish time for an activity = earliest start time + normal time crashed time - earliest finish of terminal activities <= required finishing time - interpreting the sensitivity report the solver can provide we get insight in the cost structure of further reductions in the required finishing time Chapter 7 Integer optimization 7.1 Introduction to integer optimization - integer linear programming (ILP) model = model that could be formulated and solved as linear programming model except that some or all variables are required to assume integer values by Boris Nissen Page 5

6 - rounded solution = in a LP model, a noninteger solution is often adapted to the integer requirement by simply rounding, this leads to acceptable answers, the larger the LP solution decision variable value is, but cannot be generalized - integer solutions matter: for small scale variables, for variables indicating logical decisions (1=Yes) and others - many models that can be easily solved as LP formulations become unsolvable for practical reasons as ILPs; usually it takes 10 times longer, but frequently hundreds or thousands of times 7.2 Types of integer linear programming models - all-integer linear program = all decision variables are required to be integers - mixed integer linear program (MILP) = only some of the variables are restricted to integer values - binary integer linear program (0-1 integer linear program) = integer variables are restricted to 0 and 1, representing dichotomous decisions (yes/no)! can be found in all-integer and MILPs - LP relexation = LP model that results if we start with an ILP and ignore the integer restrictions 7.3 Graphical interpretations of ILP models - to sole an ILP graphically we follow 3 steps: - find the feasible set for the LP relaxation of the ILP model - identify the integer points inside the set - find among those points the one that optimizes the objective function - optimal value (OV) = the highest value the objective function can reach (LP) always occurs at the intersection of 2 constraint lines - In a MAX model the OV of the LP relaxation always provides an upper bound on the OV of the original ILP, adding the integer constraint can only lower the OV or leave it the same - In a MIN model the OV of the LP relaxation always provides a lower bound on the OV of the original ILP, addint the integer constraint can only raise the OV or leave it the same - rounded solutions! with n decisions there are 2 n points that can be rounded to, but: - Non of the neighboring integer points may be feasible - Even if one or more of the neighboring integer points is feasible, (a) such a point need not be optimal for the ILP, (b) nor does it need to be even near the optimal ILP solution - Complete enumeration = list all feasible points and evaluate the objective function at each of them! due to the complexity, this is usually not a feasible solution 7.4 Applications of binary variables logical conditions - 1 = yes, 0 = no - no more than k of n alternatives! x 1 + x x n <= k - dependent decisions: - not select k unless first m is selected! x k <= x m - if either k or m is selected, the other also has to be selected! x k = x m - lot size constraints: if we make the decision, then the lot size has a minimum (and a maximum)! has to be modeled with 2 variables, a binary variable for the decision (y), a continuous variable (or integer variable) for the size (x)! x >= min*y (and x <= max*y) - k of m constraints 7.5 An ILP Vignette: A fixed charge model - fixed charge models: lot size models incorporating a cost behavior in which if a facility is used a fixed amount has to be paid - if in a warehousing model, supply variables at the points are decided upon with a binary variable and the demand at other points are integers, also the optimal solution for number of transportation units will be an integer, without the requirement of an integer output by Boris Nissen Page 6

Operational Research. Project Menagement Method by CPM/ PERT

Operational Research. Project Menagement Method by CPM/ PERT Operational Research Project Menagement Method by CPM/ PERT Project definition A project is a series of activities directed to accomplishment of a desired objective. Plan your work first..then work your

More information

Project Scheduling: PERT/CPM

Project Scheduling: PERT/CPM Project Scheduling: PERT/CPM Project Scheduling with Known Activity Times (as in exercises 1, 2, 3 and 5 in the handout) and considering Time-Cost Trade-Offs (as in exercises 4 and 6 in the handout). This

More information

Project Planning and Scheduling

Project Planning and Scheduling Project Planning and Scheduling MFS606 Project Planning Preliminary Coordination Detailed Task Description Objectives Budgeting Scheduling Project Status Monitoring When, What, Who Project Termination

More information

Project Scheduling: PERT/CPM

Project Scheduling: PERT/CPM Project Scheduling: PERT/CPM CHAPTER 8 LEARNING OBJECTIVES After completing this chapter, you should be able to: 1. Describe the role and application of PERT/CPM for project scheduling. 2. Define a project

More information

Network Calculations

Network Calculations Network Calculations The concepts and graphical techniques described in this week s readings form the basis of the tools widely used today to manage large projects. There is no way of simplifying the tasks

More information

Scheduling Resources and Costs

Scheduling Resources and Costs Student Version CHAPTER EIGHT Scheduling Resources and Costs McGraw-Hill/Irwin Copyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved. Gannt Chart Developed by Henry Gannt in 1916 is used

More information

DECISION MAKING UNDER UNCERTAINTY:

DECISION MAKING UNDER UNCERTAINTY: DECISION MAKING UNDER UNCERTAINTY: Models and Choices Charles A. Holloway Stanford University TECHNISCHE HOCHSCHULE DARMSTADT Fachbereich 1 Gesamtbibliothek Betrtebswirtscrtaftslehre tnventar-nr. :...2>2&,...S'.?S7.

More information

PROJECT EVALUATION REVIEW TECHNIQUE (PERT) AND CRITICAL PATH METHOD (CPM)

PROJECT EVALUATION REVIEW TECHNIQUE (PERT) AND CRITICAL PATH METHOD (CPM) PROJECT EVALUATION REVIEW TECHNIQUE (PERT) AND CRITICAL PATH METHOD (CPM) Project Evaluation Review Technique (PERT) and Critical Path Method (CPM) are scheduling techniques used to plan, schedule, budget

More information

Network Diagram Critical Path Method Programme Evaluation and Review Technique and Reducing Project Duration

Network Diagram Critical Path Method Programme Evaluation and Review Technique and Reducing Project Duration Network Diagram Critical Path Method Programme Evaluation and Review Technique and Reducing Project Duration Prof. M. Rammohan Rao Former Dean Professor Emeritus Executive Director, Centre for Analytical

More information

Project Management Chapter 3

Project Management Chapter 3 Project Management Chapter 3 How Project Management fits the Operations Management Philosophy Operations As a Competitive Weapon Operations Strategy Project Management Process Strategy Process Analysis

More information

Scheduling Glossary Activity. A component of work performed during the course of a project.

Scheduling Glossary Activity. A component of work performed during the course of a project. Scheduling Glossary Activity. A component of work performed during the course of a project. Activity Attributes. Multiple attributes associated with each schedule activity that can be included within the

More information

Project and Production Management Prof. Arun Kanda Department of Mechanical Engineering Indian Institute of Technology, Delhi

Project and Production Management Prof. Arun Kanda Department of Mechanical Engineering Indian Institute of Technology, Delhi Project and Production Management Prof. Arun Kanda Department of Mechanical Engineering Indian Institute of Technology, Delhi Lecture - 9 Basic Scheduling with A-O-A Networks Today we are going to be talking

More information

8. Project Time Management

8. Project Time Management 8. Project Time Management Project Time Management closely coordinated Two basic approaches -bottom-up (analytical) -top-down (expert judgement) Processes required to ensure timely completion of the project

More information

Project management: a simulation-based optimization method for dynamic time-cost tradeoff decisions

Project management: a simulation-based optimization method for dynamic time-cost tradeoff decisions Rochester Institute of Technology RIT Scholar Works Theses Thesis/Dissertation Collections 2009 Project management: a simulation-based optimization method for dynamic time-cost tradeoff decisions Radhamés

More information

Chapter 4 DECISION ANALYSIS

Chapter 4 DECISION ANALYSIS ASW/QMB-Ch.04 3/8/01 10:35 AM Page 96 Chapter 4 DECISION ANALYSIS CONTENTS 4.1 PROBLEM FORMULATION Influence Diagrams Payoff Tables Decision Trees 4.2 DECISION MAKING WITHOUT PROBABILITIES Optimistic Approach

More information

Project Time Management

Project Time Management Project Time Management Plan Schedule Management is the process of establishing the policies, procedures, and documentation for planning, developing, managing, executing, and controlling the project schedule.

More information

A Generalized PERT/CPM Implementation in a Spreadsheet

A Generalized PERT/CPM Implementation in a Spreadsheet A Generalized PERT/CPM Implementation in a Spreadsheet Abstract Kala C. Seal College of Business Administration Loyola Marymount University Los Angles, CA 90045, USA kseal@lmumail.lmu.edu This paper describes

More information

10 Project Management with PERT/CPM

10 Project Management with PERT/CPM 10 Project Management with PERT/CPM 468 One of the most challenging jobs that any manager can take on is the management of a large-scale project that requires coordinating numerous activities throughout

More information

PROJECT RISK MANAGEMENT

PROJECT RISK MANAGEMENT 11 PROJECT RISK MANAGEMENT Project Risk Management includes the processes concerned with identifying, analyzing, and responding to project risk. It includes maximizing the results of positive events and

More information

ME 407 Mechanical Engineering Design Spring 2016

ME 407 Mechanical Engineering Design Spring 2016 ME 407 Mechanical Engineering Design Spring 2016 Project Planning & Management Asst. Prof. Dr. Ulaş Yaman Acknowledgements to Dieter, Engineering Design, 4 th edition Ullman, The Mechanical Design Process,

More information

The work breakdown structure can be illustrated in a block diagram:

The work breakdown structure can be illustrated in a block diagram: 1 Project Management Tools for Project Management Work Breakdown Structure A complex project is made manageable by first breaking it down into individual components in a hierarchical structure, known as

More information

Application Survey Paper

Application Survey Paper Application Survey Paper Project Planning with PERT/CPM LINDO Systems 2003 Program Evaluation and Review Technique (PERT) and Critical Path Method (CPM) are two closely related techniques for monitoring

More information

Chapter 4: Project Time Management

Chapter 4: Project Time Management Chapter 4: Project Time Management Importance of Project Schedules Managers often cite delivering projects on time as one of their biggest challenges Time has the least amount of flexibility; it passes

More information

Scheduling. Anne Banks Pidduck Adapted from John Musser

Scheduling. Anne Banks Pidduck Adapted from John Musser Scheduling Anne Banks Pidduck Adapted from John Musser 1 Today Network Fundamentals Gantt Charts PERT/CPM Techniques 2 WBS Types: Process, product, hybrid Formats: Outline or graphical organization chart

More information

Project Management SCM 352. 2011 Pearson Education, Inc. publishing as Prentice Hall

Project Management SCM 352. 2011 Pearson Education, Inc. publishing as Prentice Hall 3 Project Management 3 SCM 35 11 Pearson Education, Inc. publishing as Prentice Hall Boeing 787 Dreamliner Delays are a natural part of the airplane supply business. They promise an unreasonable delivery

More information

Project Time Management

Project Time Management Project Time Management Study Notes PMI, PMP, CAPM, PMBOK, PM Network and the PMI Registered Education Provider logo are registered marks of the Project Management Institute, Inc. Points to Note Please

More information

CHAPTER 1. Basic Concepts on Planning and Scheduling

CHAPTER 1. Basic Concepts on Planning and Scheduling CHAPTER 1 Basic Concepts on Planning and Scheduling Scheduling, FEUP/PRODEI /MIEIC 1 Planning and Scheduling: Processes of Decision Making regarding the selection and ordering of activities as well as

More information

MANAGEMENT SCIENCE COMPLEMENTARY COURSE. IV Semester BBA. (2011 Admission) UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION

MANAGEMENT SCIENCE COMPLEMENTARY COURSE. IV Semester BBA. (2011 Admission) UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION MANAGEMENT SCIENCE COMPLEMENTARY COURSE IV Semester BBA (2011 Admission) UNIVERSITY OF CALICUT SCHOOL OF DISTANCE EDUCATION Calicut University P.O. Malappuram, Kerala, India 673 635 414 School of Distance

More information

Scheduling Fundamentals, Techniques, Optimization Emanuele Della Valle, Lecturer: Dario Cerizza http://emanueledellavalle.org

Scheduling Fundamentals, Techniques, Optimization Emanuele Della Valle, Lecturer: Dario Cerizza http://emanueledellavalle.org Planning and Managing Software Projects 2011-12 Class 9 Scheduling Fundamentals, Techniques, Optimization Emanuele Della Valle, Lecturer: Dario Cerizza http://emanueledellavalle.org Credits 2 This slides

More information

22 Project Management with PERT/CPM

22 Project Management with PERT/CPM hil61217_ch22.qxd /29/0 05:58 PM Page 22-1 22 C H A P T E R Project Management with PERT/CPM One of the most challenging jobs that any manager can take on is the management of a large-scale project that

More information

A Robustness Simulation Method of Project Schedule based on the Monte Carlo Method

A Robustness Simulation Method of Project Schedule based on the Monte Carlo Method Send Orders for Reprints to reprints@benthamscience.ae 254 The Open Cybernetics & Systemics Journal, 2014, 8, 254-258 Open Access A Robustness Simulation Method of Project Schedule based on the Monte Carlo

More information

MECH 896 Professional Development for MEng Students. Homework Discussion. Scheduling Overview. Winter 2015: Lecture #5 Project Time Management

MECH 896 Professional Development for MEng Students. Homework Discussion. Scheduling Overview. Winter 2015: Lecture #5 Project Time Management MECH 896 Professional Development for MEng Students Mohamed Hefny and Brian Surgenor (hefny@cs.queensu.ca and surgenor@me.queensu.ca) Winter : Lecture # Project Time Management Homework Discussion Homework

More information

CISC 322 Software Architecture. Project Scheduling (PERT/CPM) Ahmed E. Hassan

CISC 322 Software Architecture. Project Scheduling (PERT/CPM) Ahmed E. Hassan CISC 322 Software Architecture Project Scheduling (PERT/CPM) Ahmed E. Hassan Project A project is a temporary endeavour undertaken to create a "unique" product or service A project is composed of a number

More information

SE351a: Software Project & Process Management

SE351a: Software Project & Process Management SE351a: Software Project & Process Management W8: Software Project Planning 22 Nov., 2005 SE351a, ECE UWO, (c) Hamada Ghenniwa SE351 Roadmap Introduction to Software Project Management Project Management

More information

Egypt Scholars Presented by Mohamed Khalifa Hassan Jan 2014

Egypt Scholars Presented by Mohamed Khalifa Hassan Jan 2014 Project Management Six Session Egypt Scholars Presented by Mohamed Khalifa Hassan Jan 2014 Mohamed Khalifa, 2014 All Rights 1 7. Scheduling 2 7. Scheduling 7.1 Scheduling techniques 7.3 Critical path method

More information

Chapter 6: Project Time Management. King Fahd University of Petroleum & Minerals SWE 417: Software Project Management Semester: 072

Chapter 6: Project Time Management. King Fahd University of Petroleum & Minerals SWE 417: Software Project Management Semester: 072 Chapter 6: Project Time Management King Fahd University of Petroleum & Minerals SWE 417: Software Project Management Semester: 072 Learning Objectives Understand the importance of project schedules Define

More information

Chapter 11: PERT for Project Planning and Scheduling

Chapter 11: PERT for Project Planning and Scheduling Chapter 11: PERT for Project Planning and Scheduling PERT, the Project Evaluation and Review Technique, is a network-based aid for planning and scheduling the many interrelated tasks in a large and complex

More information

Decision Analysis. Here is the statement of the problem:

Decision Analysis. Here is the statement of the problem: Decision Analysis Formal decision analysis is often used when a decision must be made under conditions of significant uncertainty. SmartDrill can assist management with any of a variety of decision analysis

More information

PROJECT MANAGEMENT: PERT AND CPM

PROJECT MANAGEMENT: PERT AND CPM 14 Chapter PROJECT MANAGEMENT: PERT AND CPM CHAPTER OUTLINE 14.1 Introduction 14.2 A Typical Project: The Global Oil Credit Card Operation 14.3 The Critical Path Meeting the Board s Deadline 14.4 Variability

More information

Network Planning and Analysis

Network Planning and Analysis 46 Network Planning and Analysis 1. Objective: What can you tell me about the project? When will the project finish? How long will the project take (project total duration)? 2. Why is this topic Important

More information

A spreadsheet Approach to Business Quantitative Methods

A spreadsheet Approach to Business Quantitative Methods A spreadsheet Approach to Business Quantitative Methods by John Flaherty Ric Lombardo Paul Morgan Basil desilva David Wilson with contributions by: William McCluskey Richard Borst Lloyd Williams Hugh Williams

More information

Project Planning. Lecture Objectives. Basic Reasons for Planning. Planning. Project Planning and Control System. Planning Steps

Project Planning. Lecture Objectives. Basic Reasons for Planning. Planning. Project Planning and Control System. Planning Steps Project Planning What are you going to do in the project? Lecture Objectives To discuss the tasks in planning a project To describe the tools that can be used for developing a project plan To illustrate

More information

AN INTRODUCTION TO MANAGEMENT SCIENCE QUANTITATIVE APPROACHES TO DECISION MAKING. David R. Anderson. University of Cincinnati. Dennis J.

AN INTRODUCTION TO MANAGEMENT SCIENCE QUANTITATIVE APPROACHES TO DECISION MAKING. David R. Anderson. University of Cincinnati. Dennis J. 2008 AGI-Information Management Consultants May be used for personal purporses only or by libraries associated to dandelon.com network. E L E V E N T H E D I T I O N AN INTRODUCTION TO MANAGEMENT SCIENCE

More information

Network analysis: P.E.R.T,C.P.M & Resource Allocation Some important definition:

Network analysis: P.E.R.T,C.P.M & Resource Allocation Some important definition: Network analysis: P.E.R.T,C.P.M & Resource Allocation Some important definition: 1. Activity : It is a particular work of a project which consumes some resources (in ) & time. It is shown as & represented

More information

Schedule Risk Analysis Simulator using Beta Distribution

Schedule Risk Analysis Simulator using Beta Distribution Schedule Risk Analysis Simulator using Beta Distribution Isha Sharma Department of Computer Science and Applications, Kurukshetra University, Kurukshetra, Haryana (INDIA) ishasharma211@yahoo.com Dr. P.K.

More information

Cambridge International AS and A Level Computer Science

Cambridge International AS and A Level Computer Science Topic support guide Cambridge International AS and A Level Computer Science 9608 For examination from 2017 Topic 4.4.3 Project management PERT and GANTT charts Cambridge International Examinations retains

More information

Project Scheduling and Gantt Charts

Project Scheduling and Gantt Charts Project Scheduling and Gantt Charts Siddharth Gangadhar Dr. Prasad Kulkarni Department of Electrical Engineering & Computer Science Lab Presentation siddharth@ku.edu prasadk@ku.edu 4 November 2015 2015

More information

Chapter 3 RANDOM VARIATE GENERATION

Chapter 3 RANDOM VARIATE GENERATION Chapter 3 RANDOM VARIATE GENERATION In order to do a Monte Carlo simulation either by hand or by computer, techniques must be developed for generating values of random variables having known distributions.

More information

Priori ty ... ... ...

Priori ty ... ... ... .Maintenance Scheduling Maintenance scheduling is the process by which jobs are matched with resources (crafts) and sequenced to be executed at certain points in time. The maintenance schedule can be prepared

More information

Introduction to Project Management

Introduction to Project Management L E S S O N 1 Introduction to Project Management Suggested lesson time 50-60 minutes Lesson objectives To be able to identify the steps involved in project planning, you will: a b c Plan a project. You

More information

Dynamic Programming 11.1 AN ELEMENTARY EXAMPLE

Dynamic Programming 11.1 AN ELEMENTARY EXAMPLE Dynamic Programming Dynamic programming is an optimization approach that transforms a complex problem into a sequence of simpler problems; its essential characteristic is the multistage nature of the optimization

More information

Chapter 3 Managing the Information Systems (IS) Project

Chapter 3 Managing the Information Systems (IS) Project Content Chapter 3 Managing the Information Systems (IS) Project Process of managing IS projects Skills required to be an effective project manager Skills and activities of a project manager during project

More information

Basic Concepts. Project Scheduling and Tracking. Why are Projects Late? Relationship between People and Effort

Basic Concepts. Project Scheduling and Tracking. Why are Projects Late? Relationship between People and Effort Basic s Project Scheduling and Tracking The process of building a schedule for any case study helps really understand how it s done. The basic idea is to get across to break the software project into well-defined

More information

CPM-200: Principles of Schedule Management

CPM-200: Principles of Schedule Management CPM-: Principles of Schedule Management Lesson B: Critical Path Scheduling Techniques Instructor Jim Wrisley IPM Fall Conference PMI-College of Performance Management Professional Education Program Copyright

More information

Monte Carlo analysis used for Contingency estimating.

Monte Carlo analysis used for Contingency estimating. Monte Carlo analysis used for Contingency estimating. Author s identification number: Date of authorship: July 24, 2007 Page: 1 of 15 TABLE OF CONTENTS: LIST OF TABLES:...3 LIST OF FIGURES:...3 ABSTRACT:...4

More information

Project Management DISCUSSION QUESTIONS

Project Management DISCUSSION QUESTIONS 3 C H A P T E R Project Management DISCUSSION QUESTIONS. There are many possible answers. Project management is needed in large construction jobs, in implementing new information systems, in new product

More information

TEACHING SIMULATION WITH SPREADSHEETS

TEACHING SIMULATION WITH SPREADSHEETS TEACHING SIMULATION WITH SPREADSHEETS Jelena Pecherska and Yuri Merkuryev Deptartment of Modelling and Simulation Riga Technical University 1, Kalku Street, LV-1658 Riga, Latvia E-mail: merkur@itl.rtu.lv,

More information

PROGRAM EVALUATION AND REVIEW TECHNIQUE (PERT)

PROGRAM EVALUATION AND REVIEW TECHNIQUE (PERT) PROGRAM EVALUATION AND REVIEW TECHNIQUE (PERT) ABSTRACT Category: Planning/ Monitoring - Control KEYWORDS Program (Project) Evaluation and Review Technique (PERT) (G) is a project management tool used

More information

Goals of the Unit. spm - 2014 adolfo villafiorita - introduction to software project management

Goals of the Unit. spm - 2014 adolfo villafiorita - introduction to software project management Project Scheduling Goals of the Unit Making the WBS into a schedule Understanding dependencies between activities Learning the Critical Path technique Learning how to level resources!2 Initiate Plan Execute

More information

Fundamentals of Decision Theory

Fundamentals of Decision Theory Fundamentals of Decision Theory Chapter 16 Mausam (Based on slides of someone from NPS, Maria Fasli) Decision Theory an analytic and systematic approach to the study of decision making Good decisions:

More information

PROJECT TIME MANAGEMENT. 1 www.pmtutor.org Powered by POeT Solvers Limited

PROJECT TIME MANAGEMENT. 1 www.pmtutor.org Powered by POeT Solvers Limited PROJECT TIME MANAGEMENT 1 www.pmtutor.org Powered by POeT Solvers Limited PROJECT TIME MANAGEMENT WHAT DOES THE TIME MANAGEMENT AREA ATTAIN? Manages the project schedule to ensure timely completion of

More information

Linear Programming Supplement E

Linear Programming Supplement E Linear Programming Supplement E Linear Programming Linear programming: A technique that is useful for allocating scarce resources among competing demands. Objective function: An expression in linear programming

More information

Systems Analysis and Design

Systems Analysis and Design Systems Analysis and Design Slides adapted from Jeffrey A. Hoffer, University of Dayton Joey F. George, Florida State University Joseph S. Valacich, Washington State University Modern Systems Analysis

More information

Information Technology Project Management, Sixth Edition. Note: See the text itself for full citations. More courses at cie-wc.edu

Information Technology Project Management, Sixth Edition. Note: See the text itself for full citations. More courses at cie-wc.edu Note: See the text itself for full citations. More courses at cie-wc.edu Understand the importance of project schedules and good project time management Define activities as the basis for developing project

More information

Project Time Management

Project Time Management Project Time Management Study Notes PMI, PMP, CAPM, PMBOK, PM Network and the PMI Registered Education Provider logo are registered marks of the Project Management Institute, Inc. Points to Note Please

More information

Prof. Olivier de Weck

Prof. Olivier de Weck ESD.36 System Project Management + Lecture 9 Probabilistic Scheduling Instructor(s) Prof. Olivier de Weck Dr. James Lyneis October 4, 2012 Today s Agenda Probabilistic Task Times PERT (Program Evaluation

More information

PROJECT COMPLETION PROBABILITY AFTER CRASHING PERT/CPM NETWORK

PROJECT COMPLETION PROBABILITY AFTER CRASHING PERT/CPM NETWORK PROJECT COMPLETION PROBABILITY AFTER CRASHING PERT/CPM NETWORK M Nazrul, ISLAM 1, Eugen, DRAGHICI 2 and M Sharif, UDDIN 3 1 Jahangirnagar University, Bangladesh, islam_ju@yahoo.com 2 Lucian Blaga University

More information

Collaborative Scheduling using the CPM Method

Collaborative Scheduling using the CPM Method MnDOT Project Management Office Presents: Collaborative Scheduling using the CPM Method Presenter: Jonathan McNatty, PSP Senior Schedule Consultant DRMcNatty & Associates, Inc. Housekeeping Items Lines

More information

Appendix A of Project Management. Appendix Table of Contents REFERENCES...761

Appendix A of Project Management. Appendix Table of Contents REFERENCES...761 Appendix A Glossary Terms of Project Management Appendix Table of Contents REFERENCES...761 750 Appendix A. Glossary of Project Management Terms Appendix A Glossary Terms of Project Management A Activity

More information

Module 3: The Project Planning Stage

Module 3: The Project Planning Stage Overview Once you've initiated the project and gathered all relevant information, you'll then begin planning your project. The planning stage depends on the size of your project, how much information you

More information

A SIMULATION MODEL FOR RESOURCE CONSTRAINED SCHEDULING OF MULTIPLE PROJECTS

A SIMULATION MODEL FOR RESOURCE CONSTRAINED SCHEDULING OF MULTIPLE PROJECTS A SIMULATION MODEL FOR RESOURCE CONSTRAINED SCHEDULING OF MULTIPLE PROJECTS B. Kanagasabapathi 1 and K. Ananthanarayanan 2 Building Technology and Construction Management Division, Department of Civil

More information

Chapter 1.7 Project Management. 1. Project financing is one of the step of project management- State True or False

Chapter 1.7 Project Management. 1. Project financing is one of the step of project management- State True or False Chapter 1.7 Project Management Part I: Objective type questions and answers 1. Project financing is one of the step of project management- State True or False 2. Proposed new technologies, process modifications,

More information

Unit 4 DECISION ANALYSIS. Lesson 37. Decision Theory and Decision Trees. Learning objectives:

Unit 4 DECISION ANALYSIS. Lesson 37. Decision Theory and Decision Trees. Learning objectives: Unit 4 DECISION ANALYSIS Lesson 37 Learning objectives: To learn how to use decision trees. To structure complex decision making problems. To analyze the above problems. To find out limitations & advantages

More information

Chapter 13: Binary and Mixed-Integer Programming

Chapter 13: Binary and Mixed-Integer Programming Chapter 3: Binary and Mixed-Integer Programming The general branch and bound approach described in the previous chapter can be customized for special situations. This chapter addresses two special situations:

More information

Test Fragen + Antworten. October 2004 Project Management Wilhelm F. Neuhäuser IBM Corporation 2003

Test Fragen + Antworten. October 2004 Project Management Wilhelm F. Neuhäuser IBM Corporation 2003 Test Fragen + Antworten October 2004 Project Management Wilhelm F. Neuhäuser IBM Corporation 2003 Question 1 All the following Statements about a WBS are true except that it a. Provides a framework for

More information

Managing Information Systems Project Time and Resources

Managing Information Systems Project Time and Resources 06-Avison-45664:06-Avison-45664 7/29/2008 7:18 PM Page 153 6 Managing Information Systems Project Time and Resources Themes of Chapter 6 What is project time management? What characteristics define an

More information

Module 11. Software Project Planning. Version 2 CSE IIT, Kharagpur

Module 11. Software Project Planning. Version 2 CSE IIT, Kharagpur Module 11 Software Project Planning Lesson 29 Staffing Level Estimation and Scheduling Specific Instructional Objectives At the end of this lesson the student would be able to: Identify why careful planning

More information

Decision Making under Uncertainty

Decision Making under Uncertainty 6.825 Techniques in Artificial Intelligence Decision Making under Uncertainty How to make one decision in the face of uncertainty Lecture 19 1 In the next two lectures, we ll look at the question of how

More information

PROJECT TIME MANAGEMENT

PROJECT TIME MANAGEMENT 6 PROJECT TIME MANAGEMENT Project Time Management includes the processes required to ensure timely completion of the project. Figure 6 1 provides an overview of the following major processes: 6.1 Activity

More information

Simulation and Risk Analysis

Simulation and Risk Analysis Simulation and Risk Analysis Using Analytic Solver Platform REVIEW BASED ON MANAGEMENT SCIENCE What We ll Cover Today Introduction Frontline Systems Session Ι Beta Training Program Goals Overview of Analytic

More information

Learning Objectives. Learning Objectives (continued) Importance of Project Schedules

Learning Objectives. Learning Objectives (continued) Importance of Project Schedules Chapter 6: Project Time Management Information Technology Project Management, Fifth Edition Learning Objectives Understand the importance of project schedules and good project time management Define activities

More information

Project Management 1. PROJECT MANAGEMENT...1 2. PROJECT ANALYSIS...3

Project Management 1. PROJECT MANAGEMENT...1 2. PROJECT ANALYSIS...3 Project Management What is a project? How to plan a project? How to schedule a project? How to control a project? 1. PROJECT MNGEMENT...1 2. PROJECT NLYSIS...3 3 PROJECT PLNNING...8 3.1 RESOURCE LLOCTION...8

More information

Normality Testing in Excel

Normality Testing in Excel Normality Testing in Excel By Mark Harmon Copyright 2011 Mark Harmon No part of this publication may be reproduced or distributed without the express permission of the author. mark@excelmasterseries.com

More information

Unit 1: Project Planning and Scheduling

Unit 1: Project Planning and Scheduling Unit : Project Planning and Scheduling Objective Ð To provide a brief introduction to project planning and scheduling. The critical area where project management meets system development. ackground Most

More information

PERT/CPM. Network Representation:

PERT/CPM. Network Representation: - 1 - PERT/CPM PERT Program Evaluation & Review Technique It is generally used for those projects where time required to complete various activities are not known as a priori. It is probabilistic model

More information

Use project management tools

Use project management tools Use project management tools Overview Using project management tools play a large role in all phases of a project - in planning, implementation, and evaluation. This resource will give you a basic understanding

More information

Deming s 14 Points for TQM

Deming s 14 Points for TQM 1 Deming s 14 Points for TQM 1. Constancy of purpose Create constancy of purpose for continual improvement of products and service to society, allocating resources to provide for long range needs rather

More information

ONLINE SUPPLEMENTAL BAPPENDIX PROJECT SCHEDULES WITH PERT/CPM CHARTS

ONLINE SUPPLEMENTAL BAPPENDIX PROJECT SCHEDULES WITH PERT/CPM CHARTS ONLINE SUPPLEMENTAL BAPPENDIX PROJECT SCHEDULES WITH PERT/CPM CHARTS Chapter 3 of Systems Analysis and Design in a Changing World explains the techniques and steps required to build a project schedule

More information

5 INTEGER LINEAR PROGRAMMING (ILP) E. Amaldi Fondamenti di R.O. Politecnico di Milano 1

5 INTEGER LINEAR PROGRAMMING (ILP) E. Amaldi Fondamenti di R.O. Politecnico di Milano 1 5 INTEGER LINEAR PROGRAMMING (ILP) E. Amaldi Fondamenti di R.O. Politecnico di Milano 1 General Integer Linear Program: (ILP) min c T x Ax b x 0 integer Assumption: A, b integer The integrality condition

More information

Lecture 26 CPM / PERT Network Diagram

Lecture 26 CPM / PERT Network Diagram Lecture 26 CPM / PERT Network Diagram 26.1 Introduction to CPM / PERT Techniques CPM (Critical Path Method) was developed by Walker to solve project scheduling problems. PERT (Project Evaluation and Review

More information

technical tips and tricks

technical tips and tricks technical tips and tricks Performing critical path analysis Document author: Produced by: Andy Jessop Project Learning International Limited The tips and tricks below are taken from Project Mentor, the

More information

MBA Foundation. www.excelsior.edu

MBA Foundation. www.excelsior.edu MBA Foundation Quantitative Analysis (BUSx903) www.excelsior.edu EXAM PREPARATION GUIDE Introduction The MBA Foundation Examinations measure knowledge and understanding of material covered in Excelsior

More information

15. How would you show your understanding of the term system perspective? BTL 3

15. How would you show your understanding of the term system perspective? BTL 3 Year and Semester FIRST YEAR II SEMESTER (EVEN) Subject Code and Name BA7201 OPERATIONS MANAGEMENT Faculty Name 1) Mrs.L.SUJATHA ASST.PROF (S.G) 2) Mr. K.GURU ASST.PROF (OG) Q.No Unit I Part A BT Level

More information

Notes on Continuous Random Variables

Notes on Continuous Random Variables Notes on Continuous Random Variables Continuous random variables are random quantities that are measured on a continuous scale. They can usually take on any value over some interval, which distinguishes

More information

A. O. Odior Department of Production Engineering University of Benin, Edo State. E-mail: waddnis@yahoo.com

A. O. Odior Department of Production Engineering University of Benin, Edo State. E-mail: waddnis@yahoo.com 2012 Cenresin Publications www.cenresinpub.org APPLICATION OF PROJECT MANAGEMENT TECHNIQUES IN A CONSTRUCTION FIRM Department of Production Engineering University of Benin, Edo State. E-mail: waddnis@yahoo.com

More information

Test Fragen. October 2003 Project Management Wilhelm F. Neuhäuser IBM Corporation 2003

Test Fragen. October 2003 Project Management Wilhelm F. Neuhäuser IBM Corporation 2003 Test Fragen October 2003 Project Management Wilhelm F. Neuhäuser IBM Corporation 2003 Question 7 Which term describes a modification of a logical relationship that delays a successor task? a. Lag b. Lead

More information

Linear Programming. Solving LP Models Using MS Excel, 18

Linear Programming. Solving LP Models Using MS Excel, 18 SUPPLEMENT TO CHAPTER SIX Linear Programming SUPPLEMENT OUTLINE Introduction, 2 Linear Programming Models, 2 Model Formulation, 4 Graphical Linear Programming, 5 Outline of Graphical Procedure, 5 Plotting

More information

Arena 9.0 Basic Modules based on Arena Online Help

Arena 9.0 Basic Modules based on Arena Online Help Arena 9.0 Basic Modules based on Arena Online Help Create This module is intended as the starting point for entities in a simulation model. Entities are created using a schedule or based on a time between

More information

Measuring the Performance of an Agent

Measuring the Performance of an Agent 25 Measuring the Performance of an Agent The rational agent that we are aiming at should be successful in the task it is performing To assess the success we need to have a performance measure What is rational

More information