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Project Scheduling (2)

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

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Project Scheduling (2)

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

  2. LP model EF(X) = ES(X) + Weight(X) LF(X) = LS(X) + Weight(X) ES(X) = MAXY=immediate predecessor of X{EF(Y)} ES(X) = ES(Y) + Weight(Y) (Y is immediate predecessor) Tran Van Hoai

  3. Klonepalm 2000 LP model E 21 B 15 C 5 A 90 F 25 G 14 D 20 H 28 XG ≥ XF + 25 XG ≥ XC + 5 I 30 J 45 Tran Van Hoai

  4. Objective function • Required objective function • MIN MAXi=A,B,…,J{Xi} • Need an additional variable X, which is X ≥ Xi, for all i=A,B,…, J • Revised objective function is MIN X • A meaningless objective provide same result • MIN ∑i=A,B,…,J Xi Tran Van Hoai

  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 Hoai

  6. ES/EF Sequence 149,170 90,105 110,115 E 21 B 15 C 5 129,149 90,115 149,177 0,90 115,129 A 90 F 25 G 14 D 20 H 28 104,134 149,194 I 30 J 45 Tran Van Hoai

  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 Hoai

  8. No communication cost B 4 F 3 J 3 C 4 G 6 A 2 K 2 D 5 H 5 E 4 I 4 Tran Van Hoai

  9. Scheduling on 3 persons D I P3 C G H K P2 A B E F J P1 Time 24 Tran Van Hoai

  10. Scheduling on 4 persons E I P4 D H P3 P2 C G K A B F J P1 14 Time Tran Van Hoai

  11. Arc weight B 4 4 F 3 4 J 3 6 6 2 2 C 4 2 G 6 A 2 K 2 3 3 D 5 4 H 5 4 2 E 4 3 I 4 Tran Van Hoai

  12. Scheduling on 3 persons D I P3 C G H K P2 A B E F J P1 Time 24 Tran Van Hoai

  13. Homework, homework, homework • Read 5.6 • Gantt charts • Read 5.7 • Resource leveling Tran Van Hoai

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