Because one of the indices is negative, the current solution is not optimal. Now it is necessary to trace only the one closed path, for Fort Lauderdale–Albuquerque, in order to proceed with the solu- tion procedures. The steps we follow to develop an improved solution after the improvement indices have been computed are outlined briefly:
1. Beginning at the square with the best improvement index (Fort Lauderdale–Albuquerque), trace a closed path back to the original square via squares that are currently being used. 2. Beginning with a plus (+) sign at the unused square, place alternate minus () signs and plus signs on each corner square of the closed path just traced. 3. Select the smallest quantity found in those squares containing minus signs. Add that num- ber to all squares on the closed path with plus signs; subtract the number from all squares assigned minus signs. 4. Compute new improvement indices for this new solution using the MODI method.