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Tutorial 12 - Project Management (Extra) Original - Revised

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Unformatted text preview: t 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 Number of Activities Minimize total crash cost, Z= 600YA + 700YB + 0YC + 75YD + 50YE + 1000YF + 250YG (Used when crashing problem) (c) Define the constraints Subject to: Precedence relationship (Number of Arcs) XA Xstart + 0 ‐> XA – Xstart 0 (Start ‐> A) ‐> XB – Xstart 0 (Start ‐> B) XB Xstart + 0 ‐> XC – Xstart 0 (Start ‐> C) XC Xstart + 0 ‐> XD – XA + YA 3 (A ‐> D) XD XA + (3 ‐ YA) ‐> XE – XB + YB 2 (B ‐> E) XE XB + (2 ‐ YB) ‐> XF – XC + Yc XF XC + (1 ‐ YC) 1 (C ‐> F) XG XD + (7 – YD) ‐> XG – XD + YD 7 (D ‐> G) XG XE + (6 – YE) ‐> XG – XE + YE 6 (E ‐> G) Xfinish XG + (4 – YG) ‐> Xfinish – XG +YG 4 (G‐>Finish) Xfinish XF + (2 – YF) ‐> Xfinish – XF + YF 2 (F‐>Finish) Activity Crash Time Limit: YA 1; YB 1; YC 0; YD 4; YE 3; YF 1; YG 2 (Maximum time reduced for each activity) (Our objective) Project Completion: Xfinish 10 weeks 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 (\$) Crash Cost (\$) 1000 1600 2000 2700 300 300 1300 1600 850 1000 4000 5000 1500 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+...
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