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Project Scheduling (2) Tran Van Hoai Faculty of Computer Science & Engineering HCMC University of Technology 2010-20111Tran Van Hoai

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LP model 2010-2011Tran Van Hoai2 EF(X) = ES(X) + Weight(X) LF(X) = LS(X) + Weight(X) ES(X) = MAX Y=immediate predecessor of X {EF(Y)} EF(X) = ES(X) + Weight(X) LF(X) = LS(X) + Weight(X) ES(X) = MAX Y=immediate predecessor of X {EF(Y)} ES(X) = ES(Y) + Weight(Y) (Y is immediate predecessor) ES(X) = ES(Y) + Weight(Y) (Y is immediate predecessor)

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Klonepalm 2000 LP model 2010-2011Tran Van Hoai3 A 90 A 90 B 15 B 15 F 25 F 25 I 30 I 30 G 14 G 14 D 20 D 20 H 28 H 28 E 21 E 21 J 45 J 45 C5C5 C5C5 X G ≥ X F + 25 X G ≥ X C + 5 X G ≥ X F + 25 X G ≥ X C + 5

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Objective function Required objective function – MIN MAX i=A,B,…,J {X i } Need an additional variable X, which is X ≥ X i, for all i=A,B,…, J Revised objective function is MIN X A meaningless objective provide same result – MIN ∑ i=A,B,…,J X i 2010-2011Tran Van Hoai4

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Practical modeling issues Other time constraints – Initial production run (E) must be started in Q3. Assume project started in 1/1/xxxx – Purchase of materials (B) and Preproduction advertising campaign (I) must be started at least 10 days away from the other – Initial production run (E) must be after Preproduction advertising campaign (I) at most 45 days 2010-2011Tran Van Hoai5

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ES/EF Sequence 2010-2011Tran Van Hoai6 A 90 A 90 B 15 B 15 F 25 F 25 I 30 I 30 G 14 G 14 D 20 D 20 H 28 H 28 E 21 E 21 J 45 J 45 C5C5 C5C5 0,90 90,105 90,115 104,134 110,115 115,129 129,149 149,170 149,177 149,194

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Practical modeling issues Resource constraints – Only 2 persons (groups) executing the project. Assume Non-preemptive execution One person is possible to execute all activities 2010-2011Tran Van Hoai7

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No communication cost 2010-2011Tran Van Hoai8 A2A2 A2A2 B4B4 B4B4 D5D5 D5D5 E4E4 E4E4 G6G6 G6G6 F3F3 F3F3 H5H5 H5H5 I4I4 I4I4 J3J3 J3J3 C4C4 C4C4 K2K2 K2K2

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Scheduling on 3 persons 2010-2011Tran Van Hoai9 Time P1P1 P2P2 P3P3 AB C D E G FJ H I K 24

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Scheduling on 4 persons 2010-2011Tran Van Hoai10 Time P1P1 P2P2 P3P3 AB C D E G FJ H I K 14 P4P4

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Arc weight 2010-2011Tran Van Hoai11 A2A2 A2A2 B4B4 B4B4 D5D5 D5D5 E4E4 E4E4 G6G6 G6G6 F3F3 F3F3 H5H5 H5H5 I4I4 I4I4 J3J3 J3J3 C4C4 C4C4 K2K2 K2K2 6 2 3 4 4 2 4 2 3 4 2 3 6

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Scheduling on 3 persons 2010-2011Tran Van Hoai12 Time P1P1 P2P2 P3P3 AB C D E G FJ H I K 24

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Homework, homework, homework Read 5.6 – Gantt charts Read 5.7 – Resource leveling 2010-2011Tran Van Hoai13

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√ ⅔ ½ ¼ ⅓ ½ ⅓ ¼ BracketsFactorise Complete square Volume 1 F01 2 3 4 5 6 7 8 9 10 F01 11 F01 12 F01 13 F01 14 F01 15 F01 16 F01 2/4 +- 3/12 2 3/4 + 3 1/12.

√ ⅔ ½ ¼ ⅓ ½ ⅓ ¼ BracketsFactorise Complete square Volume 1 F01 2 3 4 5 6 7 8 9 10 F01 11 F01 12 F01 13 F01 14 F01 15 F01 16 F01 2/4 +- 3/12 2 3/4 + 3 1/12.

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