**Assignment Method**

### Concept

Organizational resources are allocated using the assignment method. This involves assigning tasks and jobs to resources. People can be assigned to projects, machines to jobs, and salespeople to territories. It is most often aimed at minimizing total costs or the time required to complete the task. Assigning jobs or workers to machines (or projects) is an important characteristic of assignment problems.

**Characteristics of Assignment Method**

The characteristics of the Assignment Method are:

- Each project or machine is assigned one job or work. Production allocation is based on it.
- Known as the Hungarian method, it solves the assignment problem in polynomial time and anticipated the primal-dual method later on.

Tables are used in each assignment problem. Each row will indicate the cost or time associated with a particular assignment. Using the assignment method, the lowest opportunity costs for each assignment are calculated by adding and subtracting appropriate numbers. **Steps to follow are as follows:**

1) Take each row’s smallest number and subtract it from every row’s smallest number, and then take each column’s smallest number and subtract it from every column’s smallest number. This step has the effect of reducing the numbers in the table until a series of zeros, meaning zero opportunity costs, appear. In spite of the changes in numbers, this reduced problem will have the same optimal solution as the original.

2) Cover all zeros in the table by drawing as many straight lines as possible vertically and horizontally. We can make an optimal assignment (see step 4) if the number of lines equals one of the table’s rows or columns. We proceed to step 3 if the number of lines is less than the number of rows or columns.

3) Divide every uncovered number by the smallest number not covered by a line. If two lines intersect, add the same number to either number. If only one line covers a number, do not change its value. If an optimal assignment cannot be made, return to step 2 and continue until one can be made.

4) It is always optimal to assign values to zero locations in the table. Choosing a row or column with only one zero square is one systematic way of making a valid assignment. It is possible to assign a row and column to that square and then draw lines through them. Our next step is to choose another row or column with only one zero square among the uncovered rows and columns. Each person or machine is assigned to one task and the process is repeated until all tasks have been assigned.