Tutorial 12 - Project Management (Extra) Student - Revised

Nonnegativity

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Unformatted text preview: ≥ 0 Start ‐ > B ‐1 1 0 ≥ 0 X____ ≥ X__ + __ => ‐X__ + X__ ≥ __ (B ‐> C) Start ‐ > E ‐1 1 0 ≥ 0 A ‐ > C ‐1 1 4 ≥ 2 ‐X__ + X__ ≥ __ (B ‐> D) X____ ≥ X__ + __ B ‐ > C ‐1 1 4 ≥ 4 B ‐ > D ‐1 1 4 ≥ 4 ‐X__ + X__ ≥ 3 (C ‐> F) X____ ≥ X__ + 3 C ‐ > F ‐1 1 4 ≥ 3 X____ ≥ X__ + 8 ‐X__ + X__ ≥ 8 (E ‐> F) E ‐> F ‐1 1 8 ≥ 8 D ‐ > Finish ‐1 1 6 ≥ 4 ‐X__ + XFinish ≥ 4 (D ‐> Finish) F ‐> Finish XFinish ≥ X__ + 4 ‐1 1 2 ≥ 2 LHS Sign RHS ‐X__ + XFinish ≥ 2 (F ‐> Finish) XFinish ≥ X__ + 2 All X ≥ 0 All X ≥ 0 (Non‐Negativity) Conclusion: The total project time is ______ days and the ES for A, B, C, D, E, F are ____________________ respectively. CB2201 Sem B in 2012/2013 – TA1, TA3, TA4, TB5, TC4, TF4, TE3, TE4, TE5, TF1, and TF3 Q13.24 (Project Crashing) (a) What is the project completion date? M1) List all possible paths M2) Use the Earliest and Latest times Possible Paths Time (Weeks) A-D-G 3+7+4=14* B-E-G 2+6+4=12 C-F 1+2=3 Conclusion: The critical path is A‐D‐G and the project completion time is 14 weeks. (b) Formulate an LP problem to crash this project to 10 weeks. Crash: Reduce the total project time to below its normal completion time Crash Time: The new time (t) for the specified activity Crash Cost: The cost we have to pay for to get the new time (t) for the specified activity Step1: Construct the project network by using the AON network Step2: Calculate the “Time Reduced” and “Crash Cost per week” for each activity Activity A B C D E F G Immediate Predecessors A B C D,E Activity A B C D E F G Normal Time 3 2 1 7 6 2 4 Immediate Predecessors A B C D,E Normal Time 3 2 1 7 6 2 4 Crash Time 2 1 1 3 3 1 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 Step3: Formulate an LP problem to crash this project to 10 weeks Objective: Use the minimum total crash cost to reduce the project to 10 weeks Decision: Which activities should we crash and How many weeks should we reduce for that activity? (a) Define the de...
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This document was uploaded on 04/05/2014.

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