Each activity is represented by one and only one arc

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Unformatted text preview: : . Each activity is represented by one, and only one, arc 1 . Each activity must be identified by two distinct end nodes 2 . To maintain the correct precedence relationships, the following questions must 3 be answered as each activity is added to the network: . What activities must immediately precede this activity? . What activities must immediately follow this activity? . What activities must occur concurrently with this activity? 3 1 2 We may need to insert “dummy edges” to make precedences sensible J. G. Carlsson, U of MN ISyE Lecture 7: PERT & CPM October 3/17, 2013 8 / 38 Dummy edges We want each activity to be identified by two distinct end nodes, so this is not allowed: A B C We can fix this by inserting a dummy edge: A 1 J. G. Carlsson, U of MN ISyE 2 B 3 Lecture 7: PERT & CPM C 4 October 3/17, 2013 9 / 38 Dummy edges Consider the following constraints “C starts immediately after A and B have been completed” “E starts only after B has been completed” The diagram at left is incorrect because it implies that A and B both must precede C; the diagram at right is correct J. G. Carlsson, U of MN ISyE Lecture 7: PERT & CPM October 3/17, 2013 10 / 38 Another example A generic construction project: Activity A: Excavate B: Lay foundation C: Put up rough wall D: Put up roof E: Install exterior plumbing F: Install interior plumbing G: Put up exterior siding H: Exterior painting I: Electrical work J: Put up wallboard K: Install flooring L: Interior painting M: Install exterior fixtures N: Install interior fixtures J. G. Carlsson, U of MN ISyE Predecessor(s) none A B C C E D E, G C F, I J J H K, L Lecture 7: PERT & CPM Duration (weeks) 2 4 10 6 4 5 7 9 7 8 4 5 2 6 October 3/17, 2013 11 / 38 Project network, activity-on-node (AoN) D (6) G (7) H (9) M (2) END START A (2) B (4) C (10) E (4) F (5) I (7) J. G. Carlsson, U of MN ISyE Lecture 7: PERT & CPM K (4) J (8) N (6) L (5) October 3/17, 2013 12 / 38 Project network, activity-on-arc (AoA) D (6) START A (2) 1 B (4) 2 C (10) 3 E (4) I (7) 4 G (7) 8 F (5) 10 J. G. Carlsson, U of MN ISyE Lecture 7: PERT & CPM 5 H (9) 6 9 J (8) M (2) L (5) 11 K (4) 7 12 N (6) END 13 October 3/17, 2013 13 / 38 AoN vs. AoA Advantages of AoN: Easy to construct Advantages of AoA: Easier to interpret “paths” Often simpler diagrams J. G. Carlsson, U of MN ISyE Lecture 7: PERT & CPM October 3/17, 2013 14 / 38 Extreme example, AoA vs. AoN Activity A B C D E F J. G. Carlsson, U of MN ISyE Predecessor(s) none none none A,B,C A,B,C A,B,C Lecture 7: PERT & CPM October 3/17, 2013 15 / 38 Time to completion If everything is completed on time, when will the project be completed? D (3) H (1) A (3) START B (2) E...
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