# Difference Between Assignment and Transportation Model

## Difference Between Assignment and Transportation Model

### Comparison Between Assignment and Transportation Model With Tabular Form

The Major Difference Between Assignment and Transportation model is that Assignment model may be regarded as a special case of the transportation model. However, the Transportation algorithm is not very useful to solve this model because of degeneracy. ### Comparison Chart

Transportation Model Assignment Model
The problem may have a rectangular matrix or a square matrix. The assignment algorithm can not be used to solve the transportation model.
The rows and columns may have any number of allocations depending on the rim conditions. The rows and columns must have one-to-one allocation. Because of this property, the matrix must be a square matrix.
The basic feasible solution is obtained by the northwest corner method or LCM method or VAM The basic feasible solution is obtained by the Hungarian method or Flood’s technique or by Assignment algorithm.
The optimality test is given by the stepping stone method or by the MODI method. The optimality test is given by drawing a minimum number of horizontal and vertical lines to cover all the zeros in the matrix.
The rim requirement may have any positive numbers. The optimality test is given by drawing a minimum number of horizontal and vertical lines to cover all the zeros in the matrix.
The transportation algorithm can be used to solve the assignment model. The assignment algorithm can not be used to solve the transportation model.

### Similarities

• Both are special types of linear programming problems.
• Both have an objective function, structural constraints, and non-negativity constraints. And the relationship between variables and constraints is linear.
• The coefficients of variables in the solution will be either 1 or zero in both cases.
• Both are basically minimization problems. For converting them into maximization problems same procedure is used.