Question 16.SP.1: The assignment method. The following table contains informat...

In order for us to be able to use the assignment method, the numbers of jobs and machines must be equal. To remedy this situation, add a dummy job with costs of 0, and then solve as usual.

a. Subtract the smallest number from each row. The results are

b. Subtract the smallest number in each column. (Because of the dummy zeros in each column, the resulting table will be unchanged.)

c. Determine the minimum number of lines needed to cross out the zeros. One possible way is as follows:

d. Because the number of lines is less than the number of rows, modify the numbers.

(1) Subtract the smallest uncovered number (1) from each uncovered number.

(2) Add the smallest uncovered number to numbers at line intersections. The result is:

e. Test for optimality:

Because the minimum number of lines equals the number of rows, an optimum assignment can be made.

f. Assign jobs to machines. Start with rows 1 and 3, since they each have one zero, and columns A and C, also with one zero each. After each assignment, cross out all the numbers in that row and column. The result is:

Notice that there is only one assignment in each row, and only one assignment in each column.

g. Compute total costs, referring to the original table.

h. The implication of assignment 4-A is that machine A will not be assigned a job. It may remain idle or be used for another job.