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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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Presentation on theme: "Project Scheduling (2) Tran Van Hoai Faculty of Computer Science & Engineering HCMC University of Technology 2010-20111Tran Van Hoai."— Presentation transcript:

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

2 LP model Tran 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)

3 Klonepalm 2000 LP model Tran 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

4 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 Tran Van Hoai4

5 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 Tran Van Hoai5

6 ES/EF Sequence Tran 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, , , , , , , ,194

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

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

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

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

11 Arc weight Tran Van Hoai11 A2A2 A2A2 B4B4 B4B4 D5D5 D5D5 E4E4 E4E4 G6G6 G6G6 F3F3 F3F3 H5H5 H5H5 I4I4 I4I4 J3J3 J3J3 C4C4 C4C4 K2K2 K2K

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

13 Homework, homework, homework Read 5.6 – Gantt charts Read 5.7 – Resource leveling Tran Van Hoai13


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