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 transcript:

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.

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.

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.

SS Method - empty cell Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

SS Method - find the path Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

SS Method - add it up Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

SS Method - record index value Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

SS Method - find the path Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

SS Method - find the path Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

SS Method - find the path, add it up Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

SS Method - find the path, add it up Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

SS Method - find the path, add it up Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. # Choose the MOST NEGATIVE cell. Stepping Stone Method

Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. # Move as many units as possible into this cell. Stepping Stone Method

Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. # Find the path you used to evaluate this cell. Move units around that path.

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. # Move as many units as possible into this cell

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. # Move as many units as possible into this cell, and rebalance the tableau

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. # Repeat evaluation of empty cells to see if the tableau is optimized.

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. # Choose the MOST NEGATIVE cell.

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. # Move as many units as possible into this cell, and rebalance the tableau

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. # Repeat evaluation of empty cells to see if the tableau is optimized.

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. #

Stepping Stone Method Supply #1 Supply #2 Supply #3 Cust. #1 Cust. #2 Cust. #3 Cust. # OPTIMIZED -- TOTAL COST $ 1020