Discrete Mathematics with Graph Theory (3rd Edition) 315

Discrete Mathematics with Graph Theory (3rd Edition) 315 -...

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Section 11.5 313 (b) S(-,O) B(S,10) D(A,14) 12 ® ~~1,;.-5 ~!r----=. .,50_A_~ T(E, 31) @ E(D,26) The ship can be assembled in 31 units of time along SADET, that is, by first detaching and sorting the pieces, then gluing, painting and applying the decals. 7. [BB] Since the time required for a task does not depend on which other tasks have been completed and since some tasks can occur simultaneously, this a Type II scheduling problem. Po(G,12) 4 A(Sh,20) 4 R(A,24) (a) S(-,O) 7 T(Pa,27) 0 Sh(G,16) 5 H(Sh,21) 6 Pa(H,27) (b) The only critical path is SGShH PaT, taking a total of 27 months. (c) The slack of Po is 4. This job could take as much as 9 units of time without affecting the time (21) by which the task H, subsequent to Po and on the critical path, would be accomplished. There is no slack in Sh. It's on the critical path. The slack in
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Unformatted text preview: A is 3. If this task took 7 units of time, its label would be (Sh, 23) and the label on R would become (A, 27). There would be another critical path, SGShART, but the time for the job would be unaffected. The slack in Tw is 4. Twisting could take as long as 6 units of time and the project would still be completed in 27 units. The slack in R is 3. (d) No, the project will not be delayed. Delaying Po by three months changes Po's label to (G, 15), but this does not affect any other labels on the digraph. Delaying A by three months changes A's label to (Sh, 23), but does not affect the critical path, or its length. 8. (a) Now the critical path is SGShAHPaT, taking 31 months. Note that the arcs PoH and ATw are no longer necessary since the corresponding precedences in tasks can be inferred from other arcs....
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