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Tutorial 12 - Project Management (Extra) Student - Revised

# xgxeye xg xe6ye xfinish xg4yg xfinishxgyg

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Unformatted text preview: cision variables Let Xstart be the earliest start time for a Project Number of nodes Xi be the ES for the activity i (where i = A, B, C, D, E, F, G) (Including the dummy nodes) Xfinish be the earliest finish time for a project Yi be the amount of time reduced / crashed for the activity i (where i = A, B, C, D, E, F, G) (b) Define the objective function Minimize total crash cost, Z= ____YA + ____YB + ____YC + ____YD + ____YE + ____YF + ____YG (c) Define the constraints Number of Activities Subject to: (Used when crashing problem) Precedence relationship (Format: ES for the following activity ≥ EF for the required activity) 0 (____________) XA Xstart + 0 ‐> XA – Xstart 0 (____________) ‐> XB – Xstart XB Xstart + 0 XC Xstart + 0 ‐> XC – Xstart 0 (____________) 3 (____________) XD XA + (3 ‐ YA) ‐> XD – XA + YA 2 (____________) XE XB + (2 ‐ YB) ‐> XE – XB + YB ‐> XF – XC + Yc 1 (____________) XF XC + (1 ‐ YC) 7 (____________) ‐> XG – XD + YD XG XD + (7 – YD) 6 (____________) ‐> XG – XE + YE XG XE + (6 – YE) Xfinish XG + (4 – YG) ‐> Xfinish – XG +YG 4 (____________) Xfinish XF + (2 – YF) ‐> Xfinish – XF + YF 2 (____________) Activity Crash Time Limit: YA ___; YB ___; YC ___; YD ___; YE ___; YF ___; YG ___ (Maximum time reduced for each activity) Project Completion: Xfinish ___________ (Our objective) Non‐Negativity: All X, Y ≥ 0 CB2201 Sem B in 2012/2013 – TA1, TA3, TA4, TB5, TC4, TF4, TE3, TE4, TE5, TF1, and TF3 *Reference: Crash the project manually (May be asked…I don’t know…) I. Consider the Critical Path: Possible Paths Time (Weeks) A-D-G 3+7+4=14* B-E-G 2+6+4=12 C-F 1+2=3 The Critical Path is A‐D‐G and the project completion time is 14 weeks. II. Crash the Critical Activity which has the lowest “Crash Cost per week” Activity A B C D E F G Immediate Predecessors A B C D,E Normal Time Crash Time 3 2 2 1 1 1 7 3 6 3 2 1 4 2 Normal Cost (\$) 1000 2000 300 1300 850 4000 1500 Crash Cost (\$) 1600 2700 300 1600 1000 5000 2000 Time Reduced (3-2)=1 1 0 4 3 1 2 Crash Cost per week (\$) (1600-1000)/(3-2)=600 700 0 75 50 1000 250 The Critical Activities are A, D and G. As the Crash Cost per week of D is \$75 per week, which is the lowest among A,D and G, D is crashed by 4 weeks and the crash cost is \$75*4= \$300. III. Calculate the new total time for each path and investigate the impact on the critical path and the total project time Possible Paths A-D-G B-E-G C-F IV. Time (Weeks) 3+7+4=14* 2+6+4=12 1+2=3 Crash Activity D by 4 weeks (-4) 3+7+4-4=10 12* 3 After crashing...
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