8/8/2019 Dynamic Progg

1/24

A B C D

Stage 4 Stage 3 Stage 2 Stage 3

5 5 5 5 0

4 4 4

3 3 32 2 2

1 1 1

Stage 1 Stage 2

s1 d1 r1 s0 f0 f1 s2

1 0 0 0 0 0 1

1 14 0 0 14 2

2 0 0 0 0 0

1 14 0 0 14 32 22 0 0 22

3 0 0 0 0 0

1 14 0 0 14 4

2 22 0 0 22

3 30 0 0 30

4 0 0 0 0 0

1 14 0 0 14 5

2 2 0 0 2

3 30 0 0 30

4 36 0 0 365 0 0 0 0 0

1 14 0 0 14

2 22 0 0 22

3 30 0 0 30

4 36 0 0 36

5 38 0 0 38

Optimal Solutions

A B C D

3 0 1 1

2 1 1 1

2 0 2 1

1 1 2 1

Marginal Increase Matrix

0 1 2 3 4

A

B

I have solved this problem using different approach but yoC wer

8/8/2019 Dynamic Progg

2/24

C

D

revenue for adding a new plane. Similarly if you start with 0th plane, find the

adding each plane.

8/8/2019 Dynamic Progg

3/24

Stage 3

d2 r2 s1 f1 f2 s3 d3

0 0 1 14 14 1 0

0 0 2 22 22 2 0

1 8 1 14 22 1

0 0 3 30 30 3 01 8 2 22 30 1

2 14 1 14 28 2

0 0 4 36 36 4 0

1 8 3 30 38 1

2 14 2 22 36 2

3 19 1 14 33 3

0 0 5 38 38 5 0

1 8 4 36 44 1

2 14 3 30 44 2

3 19 2 22 41 34 23 1 14 37 4

can solve this problem using method used to solve other problems. Part B andtaught in the KT session.

8/8/2019 Dynamic Progg

4/24

maximum revenues that can be generated by

8/8/2019 Dynamic Progg

5/24

Stage 4

r3 s2 f2 f3 s4 d4 r4

0 1 14 14 5 0 0

0 2 22 22 1 10

12 1 14 26 2 17

0 3 30 30 3 2412 2 22 34 4 29

20 1 14 34

0 4 38 38

12 3 30 42

20 2 22 42

26 1 14 40

0 5 44 44

12 4 38 50

20 3 30 50

26 2 22 4832 1 14 46

8/8/2019 Dynamic Progg

6/24

8/8/2019 Dynamic Progg

7/24

s3 f3 f4

5 50 50

4 42 52

3 34 51

2 26 501 14 43

8/8/2019 Dynamic Progg

8/24

8/8/2019 Dynamic Progg

9/24

Stage 1 Stage 2 Stage 3 Stage 4 Stage 5 Stage 6

A B C D E F G

Stage 6 Stage 5

s6 s5 5 4 3 2 1

5 0 5 240 160 0 320 800

4 0 4 1600 480 240 400 8003 0 3 3040 1600 560 640 960

2 320 2 4640 3120 2240 1120 1280

1 800 1 6080 6160 4000 3000 2400

8/8/2019 Dynamic Progg

10/24

Stage 4 Stage 3

s4 5 4 3 2 1 s3

5 240 400 560 1120 2400 5

4 1600 720 800 1200 2400 43 3040 1840 1120 1440 2560 3

2 4640 3360 2800 1920 2880 2

1 6080 4960 4560 3800 4000 1

8/8/2019 Dynamic Progg

11/24

Stage 2

5 4 3 2 1 s2 5 4

480 880 1120 1920 3800 5 720 1360

1840 1200 1360 2000 3800 4 2080 16803280 2320 1680 2240 3960 3 3520 2800

4880 3840 3360 2720 4280 2 5120 4320

6320 5440 5120 4600 5400 1 6560 5920

8/8/2019 Dynamic Progg

12/24

Stage 1

3 2 1 s2 5 4 3 2

1680 2720 4600 0 7440 7840 7760 8320

1920 2800 46002240 3040 4760

3920 3520 5080

5680 5400 6200

8/8/2019 Dynamic Progg

13/24

1

9400

8/8/2019 Dynamic Progg

14/24

Stage 1 Stage 2 Stage 3 Stage 4

Product A Product B Product C Product D

1 1 1 5

Stage 4 Stage 3

s4 r4 s3 5 4 3 2 1

6 15 14 12 14 14

5 -- 12 10 10 124 -- -- 8 8 8

5 14 3 -- -- -- 6 6

4 11 2 -- -- -- -- 4

3 7

2 5

1 3

8/8/2019 Dynamic Progg

15/24

Stage 2 Stage 1

s2 6 5 4 3 2 s1

7 17 15 13 14 15 8

6 -- 14 11 11 125 -- -- 10 9 9

4 -- -- 8 7

3 -- -- 6

1 2

2 3

3 5

4 85 11

8/8/2019 Dynamic Progg

16/24

7 6 5 4 3

18 16 14 15 17

8/8/2019 Dynamic Progg

17/24

Stage 1 Stage 2 Stage 3

Team 1 Team 2 Team 3

Stage 3

s3 r3

0 0.81 0.5

2 0.3

Stage 2

s2 2 1 0

2 0.18 0.2 0.16

1 0.3 0.32

0 0.48

Stage 1

s3 2 1 0

2 0.06 0.06 0.07

Stage 1 Stage 2 Stage 3

1 0 1

8/8/2019 Dynamic Progg

18/24

Diameter22" 23" 24" 25" 26" 27"

Length 0 2 4 6 8 10

Stage 3 29" - 32" Stage 2 25" - 28"

s3 s2 32" 31" 30" 29" 28"

32" 0 28" 1070 920 970 970

31" 200 27" -- 1270 1240 1250 1240

30" 520 26" -- 1590 1520 1520

29" 800 25" -- 1870 1790

Stage 4 Stage 3

s4 s3 8 6 4 2

8 950 14 1670 1720 -- --

6 650 12 1400 1370 1350 --

4 400 10 1120 1100 1050 1100

2 150 8 -- 820 800 800

6 -- -- 550 550

21" - 24" 25" - 28" 29" - 32"

2 150 170 200

4 400 450 520

6 650 720 800

8 950 1070 1200

In this I have assumed that there can be any number of logs of any silog of each specification, viz., 2', 4', 6' and 8'. In tha

Assuming that 1 log of each sizes have to be cut. This will most probway. Network map w

8/8/2019 Dynamic Progg

19/24

28" 29" 30" 31" 32"

12 14 16 18 20

Stage 1 21" - 24"

27" 26" s1 28" 27" 26" 25" 24"

24" 2020 1920 1990 2020

23" -- 2220 2240 2270 2170

1440 22" 2540 2520 2420

1720 1760

Stage 1 Stage 2 Stage 3

4" or 8' 4" or 8' 2" or 4'

Stage 2 Stage 1

s2 14 12 10 8 6 s1 18

18 2240 2120 2170 -- -- 20 2440

16 1920 1850 1820 1890 --

14 -- 1570 1550 1540 1620

12 -- -- 1270 1270 1270

Stage 1 Stage 2 Stage 3 Stage 4

8' 2' 4' 6'

8' 4' 2' 6'

8' 6' 4' 2'

8' 6' 2' 4'

zes. While in question paper, sir might give an assumption of having 1t case, solve the problem as I told in the KT session.

bly be given in the exam and hence I recommend to solve using thisas shown in the class.

8/8/2019 Dynamic Progg

20/24

23"

2420

16 14 12

2440 2420 2470

8/8/2019 Dynamic Progg

21/24

8/8/2019 Dynamic Progg

22/24

Stage 3

1 Profit s3 5 Profit 4 Profit 3

-- 5 4.8 5.28 13 14.3 17.5

-- 4 -- -- 48 52.8 52.5

12 13.2 3 -- -- -- -- 77.5

32 35.2 2 -- -- -- -- --

47 51.7 1 -- -- -- -- --

ds on previous year cash flows. This does not exhibits the Markovian Property.decision tree as shown below.

8/8/2019 Dynamic Progg

23/24

Stage 4

Profit 2 Profit 1 Profit s4 5 Profit

19.25 -- -- -- -- 5 59.25 65.18

57.75 39.5 43.45 -- -- 4 -- --

85.25 64.5 70.95 31.7 34.87 3 -- --

-- 84.5 92.95 51.7 56.87 2 -- --

-- -- -- 71.7 78.87 1 -- --

8/8/2019 Dynamic Progg

24/24