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9/22: Transportation: review Initial allocation –NorthWest corner method –Least Cost method –Remember: this is for the INITIAL LAYOUT ONLY -- this is NOT.

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Presentation on theme: "9/22: Transportation: review Initial allocation –NorthWest corner method –Least Cost method –Remember: this is for the INITIAL LAYOUT ONLY -- this is NOT."— Presentation transcript:

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 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 15 20 30 20 10 30 45 20 30 30 +

5 SS Method - find the path 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 15 20 30 20 10 30 45 20 30 30 -++--++-

6 SS Method - add it up 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 15 20 30 20 10 30 45 20 30 30 -++--++- 10-8+9-13

7 SS Method - record index value 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 15 20 30 20 10 30 45 20 30 30 -2

8 SS Method - find the path 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 15 20 30 20 10 30 45 20 30 30 -2 + + +- - -

9 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 15 20 30 20 10 30 45 20 30 30 -2 +8 +9 -8 +9 -13 +16 -5

10 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 15 20 30 20 10 30 45 20 30 30 -2 +8 +

11 SS Method - find the path 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 15 20 30 20 10 30 45 20 30 30 -2 + +8 +- -

12 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 15 20 30 20 10 30 45 20 30 30 -2 + +8 +- - +7 -13 +16 -5 +5

13 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 15 20 30 20 10 30 45 20 30 30 -2 + +8 +5

14 SS Method - find the path, add it up 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 15 20 30 20 10 30 45 20 30 30 -2 + +8 +5 +- - +12 -9 +8 -6 +5

15 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 15 20 30 20 10 30 45 20 30 30 -2 + +8 +5

16 SS Method - find the path, add it up 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 15 20 30 20 10 30 45 20 30 30 -2 + +8 +5 + - - +14 -9 +13 -16 +5 +2

17 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 15 20 30 20 10 30 45 20 30 30 -2 +8 +5 +2 +

18 SS Method - find the path, add it up 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 15 20 30 20 10 30 45 20 30 30 -2 + +8 +5 + - - +9 -6 +8 -9 +13 -16 +5 +2 - +

19 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 15 20 30 20 10 30 45 20 30 30 -2 +8 +5 +2 Choose the MOST NEGATIVE cell. Stepping Stone Method

20 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 15 20 30 20 10 30 45 20 30 30 -2 +8 +5 +2 Move as many units as possible into this cell. Stepping Stone Method

21 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 15 20 30 20 10 30 45 20 30 30 -2 +8 +5 +2 Find the path you used to evaluate this cell. Move units around that path.

22 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 15 20 30 20 10 30 45 20 30 30 -2 +8 +5 +2 Move as many units as possible into this cell. + -+ -

23 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 15 20 30 20 10 30 45 20 30 30 -2 +8 +5 +2 Move as many units as possible into this cell, and rebalance the tableau. +15 -+ - -15 +15

24 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 2015 45 5 10 30 45 20 30 30

25 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 2015 45 5 10 30 45 20 30 30 Repeat evaluation of empty cells to see if the tableau is optimized.

26 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 2015 45 5 10 30 45 20 30 30 +

27 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 2015 45 5 10 30 45 20 30 30 + +2 - + -

28 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 2015 45 5 10 30 45 20 30 30 + +2

29 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 2015 45 5 10 30 45 20 30 30 + +2 - +-

30 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 2015 45 5 10 30 45 20 30 30 + +2

31 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 2015 45 5 10 30 45 20 30 30 +2 -5 - +- +

32 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 2015 45 5 10 30 45 20 30 30 +2 + -5

33 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 2015 45 5 10 30 45 20 30 30 +2 -5 +3 - +- +

34 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 2015 45 5 10 30 45 20 30 30 +2 -5 +3 +

35 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 2015 45 5 10 30 45 20 30 30 +2 -5 +10 - +- + +3

36 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 2015 45 5 10 30 45 20 30 30 +2 -5 +10 + +3

37 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 2015 45 5 10 30 45 20 30 30 +2 -5 +10 - +- + +3 +5

38 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 2015 45 5 10 30 45 20 30 30 +2 -5 +10 +3+5 Choose the MOST NEGATIVE cell.

39 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 2015 45 5 10 30 45 20 30 30 +2 -5 +10 +3+5 Move as many units as possible into this cell, and rebalance the tableau. -10 +10 -10

40 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 1025 45 5 10 30 45 20 30 30 Repeat evaluation of empty cells to see if the tableau is optimized.

41 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 1025 45 5 10 30 45 20 30 30 +

42 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 1025 45 5 10 30 45 20 30 30 + +2 - + -

43 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 1025 45 5 10 30 45 20 30 30 + +2

44 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 1025 45 5 10 30 45 20 30 30 + +5 - + - +2 - +

45 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 1025 45 5 10 30 45 20 30 30 + +5 +2

46 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 1025 45 5 10 30 45 20 30 30 + +5 - +2 - + +3

47 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 1025 45 5 10 30 45 20 30 30 + +5 +2 +3

48 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 1025 45 5 10 30 45 20 30 30 + +5 - +2 - +3 +

49 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 1025 45 5 10 30 45 20 30 30 + +5 - +2 - +3 +

50 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 1025 45 5 10 30 45 20 30 30 +5 +2 +3 +

51 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 1025 45 5 10 30 45 20 30 30 + +5 - +2 - +3 + + - +2

52 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 1025 45 5 10 30 45 20 30 30 +5 +2 +3 + +2

53 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 1025 45 5 10 30 45 20 30 30 +5 - +2 +3 + + - +2 +7

54 Stepping Stone Method 8 6 10 9 35 9 12 13 7 50 14 9 16 5 40 Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #4 1025 45 5 10 30 45 20 30 30 +5 +2 +3 +2 +7 OPTIMIZED -- TOTAL COST $ 1020

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