Warehousing Sample Problem

8/13/2019 Warehousing Sample Problem

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Questions Transportation cost = 0.5 / km (linear)

Demand is divisible

Loc 1 2 3 4 5 6 7

1 24 16 35 20 31 40 492 50 30 27 12 11 34 46

3 67 38 25 26 7 16 18

4 74 63 45 41 25 7 9

Location

1 2 3 4 5 6 7

1 0 0 0 0 0 0 0

2 11 0 12 9 0 13 0

3 0 0 0 0 0 0 0

4 0 6 0 0 12 18 8

11 6 12 9 12 31 8

Demand Dj 11 6 12 9 12 31 8

1 2 3 4 5 6 7

1 0 0 0 0 0 0 0

2 0 6 6 7 4 18 2

3 0 0 0 0 0 0 0

4 11 0 6 2 8 13 6

Customer No

Customer (distance from location) km


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8 Loc 1 2 3 4 5 6

61 1 12.0 8.0 17.5 10.0 15.5 20.055 2 25.0 15.0 13.5 6.0 5.5 17.0

25 3 33.5 19.0 12.5 13.0 3.5 8.0

13 4 37.0 31.5 22.5 20.5 12.5 3.5

8 NeededCap

acity

MaxCapacity

Facilityopen

(Yi)

FixedCost(f

i)

Costperunit

Capacity

0 0 55 0 250 2.3

0 45 45 1 220 1.7

0 0 40 0 200 2.2

8 52 60 1 180 1.9

8

8

8 1 2 3

0 214.5 1 0 0 0

2 400 2 11 0 12

0 175.3 3 0 0 0

6 789.8 4 0 6 0

Transportation cost (Cij)


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7 8 1 2 3 4 5

24.5 30.5 1 0 0 0 0 023.0 27.5 2 1 0 1 1 0

9.0 12.5 3 0 0 0 0 0

4.5 6.5 4 0 1 0 0 1

Transportation cost 120

Fixed Cost 400

Variable Cost 175.3

Objective function 695.3

4 5 6 7 8

0 0 0 0 0 120

9 0 13 0 0 400

0 0 0 0 0 175.3

0 12 18 8 8 695.3

Binary function (is any shipment from I t


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Ny 1 2 3 4 51 68 68 56 56 44

2 64 64 52 52 40

3 60 60 48 48 36

52 40 28

4 60 60 48 48 36

5 64 64 52 52 40

6 68 68 56 56 44

Nx Ny Distance(reach

andgoout

Timetoreach

andgoout

Timetopick

placeatlevel

0andgoout

Timetopick

placeatlevel

1andgoout

Timetopick

placeatlevel

2andgoout

1 1 68 24.48 29.48 39.48 49.481 2 64 23.04 28.04 38.04 48.04

1 3 60 21.6 26.6 36.6 46.6

1 4 60 21.6 26.6 36.6 46.6

1 5 64 23.04 28.04 38.04 48.04

1 6 68 24.48 29.48 39.48 49.48

2 1 68 24.48 29.48 39.48 49.48

2 2 64 23.04 28.04 38.04 48.04

2 3 60 21.6 26.6 36.6 46.6

2 4 60 21.6 26.6 36.6 46.6

2 5 64 23.04 28.04 38.04 48.04

2 6 68 24.48 29.48 39.48 49.48

3 1 56 20.16 25.16 35.16 45.16

3 2 52 18.72 23.72 33.72 43.72

3 3 48 17.28 22.28 32.28 42.28

3 4 48 17.28 22.28 32.28 42.28

3 5 52 18.72 23.72 33.72 43.72

3 6 56 20.16 25.16 35.16 45.16

4 1 56 20.16 25.16 35.16 45.16

4 2 52 18.72 23.72 33.72 43.72

4 3 48 17.28 22.28 32.28 42.28

4 4 48 17.28 22.28 32.28 42.284 5 52 18.72 23.72 33.72 43.72

4 6 56 20.16 25.16 35.16 45.16

5 1 44 15.84 20.84 30.84 40.84

5 2 40 14.4 19.4 29.4 39.4

5 3 36 12.96 17.96 27.96 37.96

5 4 36 12.96 17.96 27.96 37.96

5 5 40 14.4 19.4 29.4 39.4

5 6 44 15.84 20.84 30.84 40.84

Nx


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6 1 44 15.84 20.84 30.84 40.84

6 2 40 14.4 19.4 29.4 39.4

6 3 36 12.96 17.96 27.96 37.96

6 4 36 12.96 17.96 27.96 37.96

6 5 40 14.4 19.4 29.4 39.4

6 6 44 15.84 20.84 30.84 40.84

7 1 22 7.92 12.92 22.92 32.927 2 18 6.48 11.48 21.48 31.48

7 3 18 6.48 11.48 21.48 31.48

7 4 18 6.48 11.48 21.48 31.48

7 5 18 6.48 11.48 21.48 31.48

7 6 22 7.92 12.92 22.92 32.92


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6 7

44 22 Speed =

40 18 In =

36 18 Prod mj

1 10

14 2 25

36 18 3 15

40 18 Out 4 5

44 22 5 20

Nx Ny Nz Distance(reach

andgoout

7 2 0 187 3 0 18

7 4 0 18

7 5 0 18

7 1 0 22

7 6 0 22

5 3 0 36

5 4 0 36

6 3 0 36

6 4 0 36

5 2 0 40

5 5 0 40

6 2 0 40

6 5 0 40

5 1 0 44

5 6 0 44

6 1 0 44

6 6 0 44

7 2 1 18

7 3 1 18

7 4 1 18

7 5 1 183 3 0 48

3 4 0 48

4 3 0 48

4 4 0 48

7 1 1 22

7 6 1 22

3 2 0 52

3 5 0 52


10/40

4 2 0 52

4 5 0 52

3 1 0 56

3 6 0 56

4 1 0 56

4 6 0 56

1 3 0 601 4 0 60

2 3 0 60

2 4 0 60

5 3 1 36

5 4 1 36

6 3 1 36

6 4 1 36

1 2 0 64

1 5 0 64

2 2 0 64

2 5 0 64

5 2 1 40

5 5 1 40

6 2 1 40

6 5 1 40

1 1 0 68

1 6 0 68

2 1 0 68

2 6 0 68

5 1 1 44

5 6 1 446 1 1 44

6 6 1 44

7 2 2 18

7 3 2 18

7 4 2 18

7 5 2 18

3 3 1 48

3 4 1 48

4 3 1 48

4 4 1 48

7 1 2 22

7 6 2 22

3 2 1 52

3 5 1 52

4 2 1 52

4 5 1 52

3 1 1 56

3 6 1 56

4 1 1 56


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4 6 1 56

1 3 1 60

1 4 1 60

2 3 1 60

2 4 1 60

5 3 2 36

5 4 2 366 3 2 36

6 4 2 36

1 2 1 64

1 5 1 64

2 2 1 64

2 5 1 64

5 2 2 40

5 5 2 40

6 2 2 40

6 5 2 40

1 1 1 68

1 6 1 68

2 1 1 68

2 6 1 68

5 1 2 44

5 6 2 44

6 1 2 44

6 6 2 44

3 3 2 48

3 4 2 48

4 3 2 484 4 2 48

3 2 2 52

3 5 2 52

4 2 2 52

4 5 2 52

3 1 2 56

3 6 2 56

4 1 2 56

4 6 2 56

1 3 2 60

1 4 2 60

2 3 2 60

2 4 2 60

1 2 2 64

1 5 2 64

2 2 2 64

2 5 2 64

1 1 2 68

1 6 2 68


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2 1 2 68

2 6 2 68


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23.72 2 853.92

23.72 2 853.92

25.16 2 905.76

25.16 2 905.76

25.16 2 905.76

25.16 2 905.76

26.6 2 957.626.6 2 957.6

26.6 2 957.6

26.6 2 957.6

27.96 2 1006.56

27.96 2 1006.56

27.96 2 1006.56

27.96 2 1006.56

28.04 2 1009.44

28.04 2 1009.44

28.04 2 1009.44

28.04 2 1009.44

29.4 2 1058.4

29.4 2 1058.4

29.4 2 1058.4

29.4 2 1058.4

29.48 2 1061.28

29.48 2 1061.28

29.48 2 1061.28

29.48 5 707.52

30.84 5 740.16

30.84 5 740.1630.84 5 740.16

30.84 5 740.16

31.48 5 755.52

31.48 5 755.52

31.48 5 755.52

31.48 5 755.52

32.28 5 774.72

32.28 5 774.72

32.28 5 774.72

32.28 5 774.72

32.92 5 790.08

32.92 5 790.08

33.72 5 809.28

33.72 5 809.28

33.72 5 809.28

33.72 5 809.28

35.16 5 843.84

35.16 D

35.16 D


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35.16 D

36.6 D

36.6 D

36.6 D

36.6 D

37.96 D

37.96 D37.96 D

37.96 D

38.04 D

38.04 D

38.04 D

38.04 D

39.4 D

39.4 D

39.4 D

39.4 D

39.48 D

39.48 D

39.48 D

39.48 D

40.84 D

40.84 D

40.84 D

40.84 D

42.28 D

42.28 D

42.28 D42.28 D

43.72 D

43.72 D

43.72 D

43.72 D

45.16 D

45.16 D

45.16 D

45.16 D

46.6 D

46.6 D

46.6 D

46.6 D

48.04 D

48.04 D

48.04 D

48.04 D

49.48 D

49.48 D


16/40

49.48 D

49.48 D


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0.5

0

1.0

0

1.5

0

2.0

0

2.5

0

3.0

0

0 1 2.15

P1

01.5

P2

2

P3


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3.5

0

4.0

0

4.5

0

5.0

0

5.5

0

6.0

0

6.5

0

7.0

0

7.5

0

6.9

3.5

7

3.6

9


20/40

8.0

0

8.5

0

9.0

0

9.5

0

10.0

0

10.5

0

11.0

0

11.5

0

12.0

0


21/40


22/40

17.0

0

17.5

0

18.0

0

18.5

0

19.0

0

19.5

0

20.0

0

20.5

0

21.0

0


23/40

21.5

0

22.0

0

22.5

0

23.0

0

23.5

0

24.0

0

24.5

0

25.0

0

25.5

0

25.4


24/40

26.0

0

26.5

0

27.0

0

27.5

0

28.0

0

28.5

0

29.0

0

29.5

0

30.0

0


25/40

30.5

0

31.0

0

31.5

0

32.0

0

32.5

0

33.0

0

33.5

0

34.0

0

34.5

0

33.2


26/40


27/40

39.5

0

40.0

0

40.5

0

41.0

0

41.5

0

42.0

0

42.5

0

43.0

0

43.5

0


28/40

44.0

0

44.5

0

45.0

0

45.5

0

46.0

0

46.5

0

47.0

0

47.5

0

48.0

0


29/40


30/40

53.0

0

53.5

0

54.0

0

54.5

0

55.0

0

55.5

0

56.0

0

56.5

0

57.0

0


31/40

57.5

0

58.0

0

58.5

0

59.0

0

59.5

0

60.0

0

60.5

0

61.0

0

61.5

0


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8 9 10 11 12 13 14 Dep

5.25

6.39

2.42

3.44

3.33

4.76

4.84

0.75

4.77 4.04

5.72 1.65 4.97

4.36 7.27 8.77 4.75

3.96 8.63 9.67 3.97 4.71

2.80 6.22 7.60 1.57 3.27 3.24

4.54 1.37 3.01 6.23 8.12 5.37 3.90

0.75 4.04 4.97 4.75 4.71 3.24 3.90

8 9 10 11 12 13 14 Dep

5.25

6.39

2.42

3.44

3.33

4.76

e Matrix

Matrix


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Distance Load

11.89 2012.82 27

12.83 28

14.4 17

1.5 16

SUM LOAD 108

Distance Load Constraint violated, if add next cus

15.45 29 capacity, distance

16.46 12 distance

6.89 23 capacity

12.82 27 capacity

13.86 17 no more customers

SUM LOAD 108

9.7

Clarke-Wright saving

Route

D-1-7-14-9-D

Route

D-12-2-D

D-7-1-11-13-D

D-6-4-3-5-D

Sweep heuristics

D-10-9-14-D

D-8-D

D-10-5-3-D

D-4-8-D

D-2-12-D

D-6-13-11-D


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40/40

omer

Warehousing Sample Problem

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