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### Lecture8_Nov07_2005

Course: EMP 5100, Winter 2011
School: University of Ottawa
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Word Count: 644

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- EMP5100 Introduction to Engineering Management Lecture 8 7. Methods to Manage Engineering Projects (cont.) The lowest time, a, is called the optimistic time; the highest one, b, is pessimistic; and m the one in between is called the most likely. The expected time te is then given by a weighted average. te = (a + 4*m + b)/6 Beta distribution 1. C.E. Clark, The PERT Model for... Example: An optimistic estimate =...

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- EMP5100 Introduction to Engineering Management Lecture 8 7. Methods to Manage Engineering Projects (cont.) The lowest time, a, is called the optimistic time; the highest one, b, is pessimistic; and m the one in between is called the most likely. The expected time te is then given by a weighted average. te = (a + 4*m + b)/6 Beta distribution 1. C.E. Clark, The PERT Model for... Example: An optimistic estimate = 0.5 hours A most likely estimate = 1.5 hours A pessimistic estimate = 6.5 hours te = 1/6(0.5 + 4*1.5 + 6.5) ~= 2.2 hours The essential terms associated with the PERT and CPM techniques are: a) Event or node: an unambiguous point in time in the life of a project. (circle) b) Activity: technological operation which consumes time, money and manpower. Each activity is characterized by a specific initial event and terminal event (arrow) c) Network: A visual presentation of events and activities which depict interdependencies d) Dummy Activity: (dotted arrow) It represents a restraint. It should be considered as an imaginary activity which can be accomplished in 0 (zero) time. Used only to show the proper relationships between activities. Example: A C X B D EMP5100 1 November 07, 2005 EMP5100 - Introduction to Engineering Management Lecture 8 Activities A and B must be completed before C can start. However, only activity B must be completed before activity D can start. Example: Budgeting Project XYZ Company Activity Id A B C D E F Activity Description Forecasting unit sales Survey competitive pricing Pricing Preparing production schedules Costing the production Preparing the budget Immediate Predecessors A, B A D C,E Time to perform activity - days 14 3 3 7 4 10 3 B/3 1 A/14 2 C/3 5 F/10 6 E/4 D/7 4 A-D-E-F (14+7+4+10=35) longest path = critical path A-C-F (14+0+3+10=27) B-C-F (3+3+10=16) shortest path Critical Path is the longest path through the network. Its length determines the duration of a project. The word "critical" is used because any delay in the completion of activities along the critical path can delay the completion of the entire 07, project. EMP5100 2 November 2005 EMP5100 - Introduction to Engineering Management Lecture 8 Critical Path Determination Definitions: Earliest event time (EET) the earliest time at which an event occurs. If all activities before the event of interest have been carries out without any delay, within their prescribed duration times, then the event will be reached at its EET. Latest Event Time (LET) the latest time an event may be reached without delaying the completion of the project. Event Number LET EET i D(i,j) LET (i) EET (i) LET (j) j EET (j) Steps for CPM determination: 1. Construct CPM network 2. Calculate EET: Make a forward pass of the network using: For any event `j', EET(j) = max. for preceding `i' of [EET(i)+D(i,j)] EET(first event) = 0 3. Calculate LET: Make a backward pass of the network using: For any event `i': LET(i) = min of succeeding `j' of [LET(j)-D(i,j)] check: LET(last event) = EET(last event) check: LET(first event) = 0 4. Critical Path Criteria a. Select events with EET = LET (necessary but not sufficient condition for path to be critical). If this results in only one path from beginning to end then this path is critical. If it results in two or more paths then (b) EMP5100 3 November 07, 2005 EMP5100 - Introduction to Engineering Management Lecture 8 b. Calculate the total float for each activity on each of the paths satisfying (a). The path which results in the least sum of the total floats is the critical path 3 7 7 1 0 0 3 2 3 3 1 4 3 6 4 4 13 13 6 17 17 4 7 21 21 5 14 9 3 2 We have 3 paths with EET = LET. The longest is the critical path. 3 3 1 0 0 3 22 14 5 25 25 6 35 35 10 4 14 2 14 14 7 4 21 21 In the example above we have a single path the critical path. Additional Formulas: Interfering float for activity (i, j) = LET(j) EET(j) Free float = EET(j) EET(i) D(i, j) EMP5100 4 November 07, 2005 EMP5100 - Introduction to Engineering Management Total float = LET(j) EET(i) D(i, j) Lecture 8 i LET (i)25 EET (i)25 D(i,j) =10 LET (j)35 j EET (j)35 Total float = 35-25-10 = 0 EMP5100 5 November 07, 2005
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