rccoleman-MBA课程作业答案.docVIP

1. R.C. Colemans Project Network Activity Expected Time Variance A 6 0.44 B 9 2.78 C 4 0.44 D 12 7.11 E 10 1.00 F 6 0.44 G 8 7.11 H 6 0.44 I 7 2.78 J 4 0.11 K 4 0.44 Activity Earliest Start Latest Start Earliest Finish Latest Finish Slack Critical Activity A 0 3 6 9 3 B 0 0 9 9 0 Yes C 9 9 13 13 0 Yes D 13 17 25 29 4 E 13 13 23 23 0 Yes F 23 23 29 29 0 Yes G 13 21 21 29 8 H 29 29 35 35 0 Yes I 29 32 36 39 3 J 35 35 39 39 0 Yes K 39 39 43 43 0 Yes The expected project completion time is 43 weeks. The critical path activities are B-C-E-F-H-J-K. The variance of the critical path is 5.67. Area = 0.3962 P(T ≤ 40) = 0.5000 - 0.3962 = 0.1038 Given the above calculations, we can conclude that there is about a 10% chance that the project can be completed in 40 weeks or less. Coleman should consider crashing project activities. 2. For 80% chance, z = +0.84 Thus Solve for E(T) = 38 weeks. R.C. Coleman should crash activities to reduce the expected project completion time to 38 weeks. 3. In this section, we will use expected activity times as normal times and use a linear programming model based on expected times to make the crashing decisions. Let xi = the completion time for activity i yi = the amount of crash time for activity i Min 450yA + 400yB + 600yC + 300yD + 1000yE + 550yF + 750yG + 700yH + 800yI + 400yJ + 500yK s.t. xA + yA ≥ 6 xB + yB ≥ 9 xC + yC – xA ≥ 4 xC + yC – xB ≥ 4 xD + yD – xC ≥ 12 xE + yE – xC ≥ 10 xF + yF – xE ≥ 6 xG + yG – xC ≥ 8 xH + yH – xF ≥ 6 xH + yH – xG ≥ 6 xI + yI – xD ≥ 7 xI + yI – xF ≥ 7 xJ + yJ – xH ≥ 4 xK + yK – xI ≥ 4 xK + yK – xJ ≥ 4 xK ≤ 38 yA ≤ 2 yB ≤ 2 yC ≤ 2 yD ≤ 4 yE ≤ 3 yF ≤ 2 yG ≤ 3 yH ≤ 2 yI ≤ 3 yJ ≤ 1 yK ≤ 1 All xi,yi ≥ 0 The