Program dinamik jaringan

1.
Riset Operasi
Program Dinamik
endrayanto@ugm.ac.idirwanendrayanto
Irwan Endrayantoendrayanto
Network Problems

4. Network Problems
L
J
K
G
H
I
D
E
F
B
C
A

5. Network Problems
L
J
K
G
H
I
D
E
F
B
C
A

6. Network Problems
L
J
K
G
H
I
D
E
F
B
C
A
Stage 6Stage 5Stage 4Stage 3Stage 2Stage 1

7. Contoh: Shortest PathWinston, Operations Research: Applications and
Algorithms
Ch. 18. Deterministic Dynamic Programming
18.2 A Network Problem: Exampe 3

8. Network Problems
10
8
9
5
6
7
2
3
4
1
Stage 5Stage 4Stage 3Stage 2Stage 1

9. Network Problems
10
8
9
Stage 5Stage 4
1030
1390
stage 4
City 8
stage 4
City 9
Shortest path in
stage 4 to City 8
Shortest path in
stage 4 to City 9

10. Network Problems
10
8
9
5
6
7
2
3
4
1
Stage 5Stage 4Stage 3Stage 2Stage 1

11. Network Problems
10
8
9
5
6
7
2
3
4
1
Stage 5Stage 4Stage 3Stage 2Stage 1

12. Network Problems
8
9
5
6
7
Stage 4Stage 3

13. Network Problems
8
9
5
6
7
Stage 4Stage 3
610
790

14. Network Problems
8
9
5
6
7
Stage 4Stage 3
610
790

15. Network Problems
8
9
5
6
7
Stage 4Stage 3
610
790

16. Network Problems
8
9
5
6
7
Stage 4Stage 3
610
790

17. Network Problems
8
9
5
6
7
Stage 4Stage 3
540
940

18. Network Problems
8
9
5
6
7
Stage 4Stage 3
540
940

19. Network Problems
8
9
5
6
7
Stage 4Stage 3
540
940

20. Network Problems
8
9
5
6
7
Stage 4Stage 3
540
940

21. Network Problems
8
9
5
6
7
Stage 4Stage 3
790
270

22. Network Problems
8
9
5
6
7
Stage 4Stage 3
790
270

23. Network Problems
10
8
9
5
6
7
2
3
4
1
Stage 5Stage 4Stage 3Stage 2Stage 1

24. Network Problems
10
8
9
5
6
7
2
3
4
1
Stage 5Stage 4Stage 3Stage 2Stage 1

25. Network Problems
10
8
9
5
6
7
2
3
4
1
Stage 5Stage 4Stage 3Stage 2Stage 1

26. Network Problems
5
6
7
2
3
4
Stage 3Stage 2

27. Network Problems
5
6
7
2
Stage 3Stage 2

28. Network Problems
5
6
7
2
Stage 3Stage 2
680
790
1050

29. Network Problems
5
6
7
2
Stage 3Stage 2
680
790
1050

30. Network Problems
5
6
7
2
Stage 3Stage 2
680
790
1050

31. Network Problems
5
6
7
2
3
4
Stage 3Stage 2

32. Network Problems
5
6
7
3
Stage 3Stage 2

33. Network Problems
5
6
7
3
Stage 3Stage 2

34. Network Problems
5
6
7
3
Stage 3Stage 2
580
760
660

35. Network Problems
5
6
7
3
Stage 3Stage 2
580
760
660

36. Network Problems
5
6
7
2
3
4
Stage 3Stage 2

37. Network Problems
5
6
74
Stage 3Stage 2

38. Network Problems
5
6
74
Stage 3Stage 2
510
700
830

39. Network Problems
5
6
74
Stage 3Stage 2
510
700
830

40. Network Problems
5
6
74
Stage 3Stage 2
510
700
830

41. Network Problems
10
8
9
5
6
7
2
3
4
1
Stage 5Stage 4Stage 3Stage 2Stage 1

42. Network Problems
10
8
9
5
6
7
2
3
4
1
Stage 5Stage 4Stage 3Stage 2Stage 1

43. Network Problems
10
8
9
5
6
7
2
3
4
1
Stage 5Stage 4Stage 3Stage 2Stage 1

44. Network Problems
2
3
4
1
Stage 2Stage 1

45. Network Problems
2
3
4
1
Stage 2Stage 1
550
900
770

46. Network Problems
2
3
4
1
Stage 2Stage 1
550
900
770

47. Network Problems
2
3
4
1
Stage 2Stage 1
550
900
770

48. Network Problems
2
3
4
1
Stage 2Stage 1
550
900
770

49. Network Problems
2
1
Stage 2Stage 1
550

50. Network Problems
10
8
9
5
6
7
2
1
Stage 5Stage 4Stage 3Stage 2Stage 1
550

51. Network Problems
10
8
9
5
6
7
2
1
Stage 5Stage 4Stage 3Stage 2Stage 1
550
680
790
1050

52. Network Problems
10
8
9
5
6
7
2
1
Stage 5Stage 4Stage 3Stage 2Stage 1
550
680
790
1050

53. Network Problems
10
8
9
52
1
Stage 5Stage 4Stage 3Stage 2Stage 1
550
680

54. Network Problems
10
8
9
52
1
Stage 5Stage 4Stage 3Stage 2Stage 1
550
680 610
790

55. Network Problems
10
8
9
52
1
Stage 5Stage 4Stage 3Stage 2Stage 1
550
680 610
790

56. Network Problems
10
8
52
1
Stage 5Stage 4Stage 3Stage 2Stage 1
550
680 610
1030

57. Problem:
Find the shortest path from node 1 to node 10 in the network
shown in Figure 3. Also, find the shortest path from node 3 to
node 10.
Winston, Operations Research: Applications and
Algorithms
Ch. 18. Deterministic Dynamic Programming
18.2 A Network Problem

58. Problem
I must drive from Bloomington to Cleveland. Several paths are available (see Figure 4). The number on each arc is
the length of time it takes to drive between the two cities. For example, it takes 3 hours to drive from Bloomington to
Cincinnati. By working backward, determine the shortest path (in terms of time) from Bloomington to
Cleveland. [Hint: Work backward and don’t worry about stages—only about states.]

59. Selamat belajar
endrayanto@ugm.ac.id
irwanendrayanto
Irwan Endrayanto
endrayanto