Chapter 10:

Simplest Methods to Solve Transportation Problems:
1. Use Northwest Corner Rule (pages 396-398).
2. Find and compare improvement indices – see "Five Steps to Test Unused Squares with the Stepping-Stone Method" on page 400.
3. If the solution is not optimum (optimum if all indices are 0 or +), do the following:
-----a. Re-distribute units (i.e., obtain improved solution)
-----b. Return to Step 2.
4. End, if solution is optimum.
5. Calculate shipping cost based on optimum transportation table.

Further guidance:
• (see #2 above) Calculate improvement indices as shown in Step 5 on page 401 with Table 10.5 and Table 10.6. Helpful hints:
-----o Start in a blank cell with a "+" and work counter-clockwise.
-----o You can only turn corners at cells that have units in them. The only indices are those in the corners--where you change directions.
-----o If all indices are greater than or equal to zero, an optimal solution has been reached.
-----o The largest negative improvement index ("-6" rather than "-1") for an unused cell indicates the cell that can be improved upon
• (see #3a above) Follow the steps for "Obtaining an Improved Solution" on pages 402-403.
-----o For the corners of the closed-loop (dashed boxes shown in text), find the cell with the smallest number. Note: View the "-" separately from the number. That is, if you have a 200 in a cell with a "-" and a 100 in a cell with a "-", 100 is the smallest number. You subtract this from the number in the cells with "-" and add it to the cell(s) with "+".
-----o Then calculate improvement indices again.