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Chapter 5

CGMS450- Chapter 5- Scheduling the Project.docx

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Department
Global Management Studies
Course Code
GMS 450
Professor
Stan Katz

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CGMS450- Chapter 5- Scheduling the Project  Project schedule is simply the project plan in an altered format  Convenient form for monitoring and controlling project activities  Take on several forms o Gantt charts o PERT/ CPM networks o Convert a project plan or WBS into these formats 5.1 PERT And CPM Networks  PERT developed by US Navy, Booz-Allen Hamilton and Lockheed Aircraft  CPM developed by Dupont De Nemours Inc.  When developed there were significant differences o PERT used probabilistic estimates of activity durations o CPM used deterministic estimates but included both time and cost estimates to allow time/cost trade offs to be used o Both employed networks to schedule and display task sequences  Identified a critical path of tasks that could not be delayed without delaying the project  Identified activities with slack that could be somewhat delayed without extending the time required to complete project  Anything one can do with PERT, they could do with CPM  Traditional PERT is used less often than CPM  CPM can be used with 3 time estimates  We can do things with PERT that were restricted to CPM in “olden times” The Language Of PERT/ CPM  Terms used in discussing PERT/ CPM o Activity—task or set of tasks required by the project  Use resources and time o Event—an identifiable state resulting from the completion of one or more activities  Consume no resources or time  Before event is achieved—all predecessor activities must be complete o Milestones—identifiable and noteworthy events marking significant progress on the project o Network—A diagram of nodes connected by directional arcs that defines the project and illustrates the technological relationships of all activities  Drawn with a start node on the left an a finish mode on the right o Path—series of connected activities between any 2 events in a network o Critical path—set of activities on a oath from the projects start event to its finish event that, of delayed, will delay the competition date of the project o Critical time—time required to complete all activities on the critical path Building The Network  2 ways displaying the project network o Depicts the activities as arrows and events in nodes  Activity-on-arrow (AOA) network—usually associated with PERT o Create an activity-on-nodes (AON) network by showing each task as a node and linking the nodes to arrows that show their technological relationship  Usually associated with CPM  Easy to draw—more then 15-20 are more difficult to draw by hand  Often do not show events but it is simple enough to add them by showing the event exactly as if it were an activity but with zero time duration and no resources o Avoids lines crossing each other o Dummy activity—used in situations where 2 activities have the same starting and finishing nodes or where a single activity connects 2 or more nodes  Require no time or resources  Problem: difficult to distinguish the tasks form one another 1 CGMS450- Chapter 5- Scheduling the Project  Solution: add an extra ending node for one of the tasks and then draw a dummy task from the new node to the previously shared node—ensures that the tasks have unique identifies while at the same time maintaining the correct technological precedence relationship Finding The Critical Path And Critical Time  We can add information to the nodes in the networks o Above each node—earliest start time (ES) and earliest finish time (EF) o Below each node—latest start time (LS) and latest finish time (LF)  All activities and thus all paths must be completed to finish the project  Shortest time for completion of the network is equal to the longest path through the network  Forward pass ES ad EF is found for each activity by beginning at the start node and moving from left to right through the network calculating as we go from node to node  Backward pass to calculate LS and LF—we begin by assuming that we would like to complete the project within the critical time identified in the forward pass Calculating Activity Slack  Within limits—if activities on the critical path cannot be delayed without causing the entire project to be delayed, it follows that activities not on the critical path can be delayed without delaying the project  Slack or float- the amount of time a noncritical task can be delayed without delaying the project o Slack= LS-ES=LF-EF  Any task on the critical path—LS must be the same is EF therefore 0 slack  If it finishes later than EF, the activity will be late, causing the project to delay in the project o Equally true for its LS and ES  Assumptions o When calculating slack for a set of activities on a noncritical path, the calculation for any given activity assumes that no other activity on the same path uses any of the slack  Once activity s underway, if a predecessor activity uses come if its slack, its EF is adjusted accordingly and the ES of successor activities must be corrected o Critical time for the project is also the projects due date—it is not common for a project to have “project slack”  Milestones may be added to the display quite easily: add desired milestone event as a node with zero duration o ES=EF, LF=LS o Immediate successors of the activities that result in results o Common to show actual dates for EF, ES, LS, LF  PM primary attention must be paid to activities on the critical path Doing It The Easy Way—Microsoft Project (MSP)  See pages 158-160 for steps in creating networks with MSP  Free slack—the activity can be delayed without affecting the start time of any successor activity  Total slack= LF-EF or LS-ES 2 CGMS450- Chapter 5- Scheduling the Project 5.2 Project Uncertainties And Risk Management Calculating Probabilistic Activity Times  All possible durations for some tasks can be represented by a statistical distribution  Optimistic (a) estimates for a task duration, a, such that the actual duration of the task will be a or lower less than 1% of the time  Pessimistic (b) estimation duration for the same task such that the actual finish time will be b or greater less than 1% of the time  Most likely or “normal duration” (m)  Mean of distribution- expected time o TE=(a+4m+b)/ 6 o Approximation of the mean of a beta distribution  Beta distribution far more flexible than the more common normal distribution o More accurately reflects actual time and cost outcome o Calculation—weighted average of 3 time estimate, a,m,b, using weights of 1-4-1 o Standard deviation σ=(b-a)/6  6 is not a weighted average but rather an assumption that the range of the distribution covers 6 standard deviations (6σ) o Variance of this distribution is estimated as  Var=σ =((b-a)/6) 2  Range of distribution, b-a, covers 6 standard deviations is important  Assumes that the estimate actually attempted to judge a and b so that 99.7$ of all cases were greater than a and less than b o Less then 1% lay outside of these estimates  Estimators are not so uncomfortable making estimates at the 90-95% levels o a is estimated so that 5-10% of all cases are less than a and 5-10% are greater than b o These levels do not cover 6σ instead we use  95% level σ=(b-a)/3.3  90% level σ=(b-a)/2.6 The Probabilistic Network, An Example  Look at page 162-164 for further explanation of the probabilistic network Once More The Easy Way  MSP can easily handle the probabilistic network—does not do some calculations that we demonstrated  Calculations can be easily done by excel  The stochastic (synonym for probabilistic) network used for the preceding discussion is shown as a product of MSP The Probability Of Completing The Project On Time  E.g. what is the probability that a project will be completed 50 days or less o Answered with the information available concerning the level of uncertainty for the various project activities  There is an assumption that should be noted o Individual variances of the activities in a series of activities may be summed to find the variance of the set of activities on the path itself—if the various activities in the set are statistically independent o E.g. if a is a predecessor of b and if a is early or late, it will not effect the duration of b  Times when assumption of statistical independence is not met o Re-estimating the duration of tasks o This should be done anytime the resources supplied to a project are different from those presumed then he duration of a project activities was originally estimated 3 CGMS450- Chapter 5- Scheduling the Project  To complete a project by a specific time requires that all the paths in the projects network by completed by a specified time o Determining the probability tat a project is completed by a specific time requires calculating the probability that all paths are finished by a specific time o o D= the desired project completion time o μ= the sum of the E activities on the path being investigated o σ μ the variance of the path being considered (the sum of the variances of the activities on the path  Simplify the task calculating the probability that a project is completed by a specific time— practical purposes it is reasonable to consider only those paths whose expected completion time have a reasonable chance of being greater than the specified time  Calculate the probability that a project will take longer than any specified t
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