Question

Give an example of how you might apply the transportation model or assignment model concepts- either at work, school, an organization you are familiar with, or in your personal life.

Answer 1

An assignment problem can be seen as a special type of transportation problem in which the main objective is to find out the optimum assignment of different activities to the different resources so that the total cost of allocation can be minimized.

For example, the university has to assign the guest lecturer to the different classes. The cost of each guest lecturer and the class are shown below=

	L1	L2	L3	L4
C1	8	10	17	9
C2	3	8	5	6
C3	10	12	11	9
C4	6	13	9	7

In order to find out the right allocation of lecturers to the different classes, first of all, we will find the row minimum and subtract it with the rest row values

So the above table will be as below-

	L1	L2	L3	L4
C1	0	2	9	1
C2	0	5	2	3
C3	1	3	2	0
C4	0	7	3	1

Similarly, we will do for the columns

	L1	L2	L3	L4
C1	0	0	7	1
C2	0	3	0	3
C3	1	1	0	0
C4	0	5	1	1

Now we will assign zero to the different lecturers

In above picture, RED cells are unallocated zero while Green cells are the allocated Zeros.

So Green cells are representing the allocated classes to the corresponding lecturers.

So the final assignment will be

Lecturer 1= Class 4

Lecturer 2= Class 1

Lecturer 3= Class 2

Lecturer 4= Class 3

So the above assignment indicates how the university can minimize the cost of assigning the different classes to the different guest lecturers.