9/22: Transportation: review

1
9/22 Transportation review

• Initial allocation
• NorthWest corner method
• Least Cost method
• Remember this is for the INITIAL LAYOUT ONLY --
  this is NOT necessarily the optimal solution.

2
Stepping Stone method RULES

• 1. Select an empty cell to evaluate.
• 2. Beginning at this cell, trace a closed path
  back to the cell, turning corners only on filled
  cells. Only horizontal vertical moves are
  allowed. You may step over any cell.
• 3. Place alternating s and -s on this path,
  beginning with a on the empty cell being
  evaluated.
• 4. Calculate the change index by summing the
  unit costs, in the tagged cells, accounting for
  the - signs.

3
Stepping Stone method RULES

• 1. Select an empty cell to evaluate.
• 2. Trace a closed path, turning only on filled
  cells.
• 3. Place alternating s and -s on this path.
• 4. Calculate the change index by summing the
  unit costs in the tagged cells.
• 5. Repeat for each empty cell in the tableau.
• 6. MINIMIZATION if all change index values are
  , the problem is OPTIMIZED.
• MAXIMIZATION if all values are -, the problem
  is OPTIMIZED.

4
SS Method - empty cell

5
SS Method - find the path
- -
6
SS Method - add it up
- -
10-89-13
7
SS Method - record index value
-2
8
SS Method - find the path
-2
-

-


-
9
Stepping Stone Method
9 -8 9 -13 16 -5
8
-2
10
Stepping Stone Method
8
-2

11
SS Method - find the path
8
-2
-


-
12
Stepping Stone Method
7 -13 16 -5
8
-2
-

5

-
13
Stepping Stone Method
8
-2
5

14
SS Method - find the path, add it up
12 -9 8 -6
8
-2

-
5

-
5
15
Stepping Stone Method
8
-2
5
5

16
SS Method - find the path, add it up
14 -9 13 -16
8
-2
5
5

-

-
2
17
Stepping Stone Method
8
-2
5
5
2

18
SS Method - find the path, add it up
9 -6 8 -9 13 -16
8
-2
-

5
5

-
2
-

-1
19
Stepping Stone Method
Choose the MOST NEGATIVE cell.
8
-2
5
5
2
-1
20
Stepping Stone Method
Move as many units as possible into this cell.
8
-2
5
5
2
-1
21
Stepping Stone Method
Find the path you used to evaluate this cell.
Move units around that path.
8
-2
5
5
2
-1
22
Stepping Stone Method
Move as many units as possible into this cell.
8
-2
-

5
5
-

2
-1
23
Stepping Stone Method
Move as many units as possible into this cell,
and rebalance the tableau.
8
-2
-
-15
15
5
5
-

-15
15
2
-1
24
Stepping Stone Method
25
Stepping Stone Method
Repeat evaluation of empty cells to see if the
tableau is optimized.
26
Stepping Stone Method

27
Stepping Stone Method
-

2

-
28
Stepping Stone Method
2

29
Stepping Stone Method
2

-

-
2
30
Stepping Stone Method
2
2

31
Stepping Stone Method
2

-
2
-

-5
32
Stepping Stone Method
2

2
-5
33
Stepping Stone Method
2

-
-

3
2
-5
34
Stepping Stone Method
2

3
2
-5
35
Stepping Stone Method
2
-

10
3
2
-5

-
36
Stepping Stone Method
2
10
3

2
-5
37
Stepping Stone Method
10
2
-
3

5
2
-5

-
38
Stepping Stone Method
Choose the MOST NEGATIVE cell.
10
2
3
5
2
-5
39
Stepping Stone Method
Move as many units as possible into this cell,
and rebalance the tableau.
10
2
10
-10
3
5
2
-5
-10
10
40
Stepping Stone Method
Repeat evaluation of empty cells to see if the
tableau is optimized.
41
Stepping Stone Method

42
Stepping Stone Method
-

2

-
43
Stepping Stone Method
2

44
Stepping Stone Method
-
2


-

-
5
45
Stepping Stone Method
2
5

46
Stepping Stone Method
-
2

5

-
3
47
Stepping Stone Method
2

5
3
48
Stepping Stone Method
-
2

-

3
5
3
49
Stepping Stone Method
-
2

-

3
5
3
50
Stepping Stone Method
2
3

5
3
51
Stepping Stone Method
-
2

3
-

2
5
3
-

52
Stepping Stone Method
2

3
2
5
3
53
Stepping Stone Method
-
2

7
3
2
5
3
-

54
Stepping Stone Method
OPTIMIZED -- TOTAL COST 1020
7
2
3
2
5
3