Assignment Problem

Abu Bashar

It involves assignment of people to projects jobs to machines workers to jobs and teachers to classes etc while minimizing the total assignment costs

One of the important characteristics of assignment problem is that only one job (or worker) is assigned to one machine (or project)

An assignment problem is a special type of linear programming problem where the objective is to minimize the cost or time of completing a number of jobs by a number of persons

Introduction

This method was developed by D Konig a Hungarian mathematician and is therefore known as the Hungarian method of assignment problem

In order to use this method one needs to know only the cost of making all the possible assignments

Each assignment problem has a matrix (table) associated with it Normally the objects (or people) one wishes to assign are expressed in rows whereas the columns represent the tasks (or things) assigned to them

The number in the table would then be the costs associated with each particular assignment

Though assignment problem finds applicability in various diverse business situations we discuss some of its main application areas

In assigning machines to factory orders In assigning salesmarketing people to sales

territories In assigning contracts to bidders by

systematic bid-evaluation In assigning teachers to classes In assigning accountants to accounts of the

clients

Application Areas of Assignment Problem

Cost Matrix in Assignment Problem

Mathematically the assignment problem can be expressed as

The objective function is Minimize C11X11 + C12X12 + ------- + CnnXnn

Step 1 Determine the cost table from the given problem

(i) If the no of sources is equal to no of destinations go to step 3

(ii) If the no of sources is not equal to the no of destination go to step2

Step 2 Add a dummy source or dummy destination so that the cost table becomes a square matrix The cost entries of the dummy sourcedestinations are always zero

Step 3 Locate the smallest element in each row of the given cost matrix and then subtract the same from each element of the row

Method for Solving Assignment Prob

Step 4 In the reduced matrix obtained in the step 3 locate the smallest element of each column and then subtract the same from each element of that column Each column and row now have at least one zero

Step 5 In the modified matrix obtained in the step 4 search for the optimal assignment as follows

(a) Examine the rows successively until a row with a single zero is found Enrectangle this row ( )and cross off (X) all other zeros in its column Continue in this manner until all the rows have been taken care of

(b) Repeat the procedure for each column of the reduced matrix

(c) If a row andor column has two or more zeros and one cannot be chosen by inspection then assign arbitrary any one of these zeros and cross off all other zeros of that row column

(d) Repeat (a) through (c) above successively until the chain of assigning ( ) or cross (X) ends

Step 6 If the number of assignment (1048576) is equal to n (the order of the cost matrix) an optimum solution is reached

If the number of assignment is less than n(the order of the matrix) go to the next step

Step7 Draw the minimum number of horizontal andor vertical lines to cover all the zeros of the reduced matrix

Step 8 Develop the new revised cost matrix as follows

(a)Find the smallest element of the reduced matrix not covered by any of the lines

(b)Subtract this element from all uncovered elements and add the same to all the elements laying at the intersection of any two lines

Step 9 Go to step 6 and repeat the procedure until an optimum solution is attained

A job has four men available for work on four separate jobs Only one man can work on any one job The cost of assigning each man to each job is given in the following table The objective is to assign men to jobs such that the total cost of assignment is minimum

Examples

Step 1 Identify the minimum element in each row

and subtract it from every element of that row

Step 2 Identify the minimum element in each

column and subtract it from every element of that column

Make the assignment for the reduced matrix obtain from steps 1 and 2 in the following way

Draw the minimum number of vertical and horizontal lines necessary to cover all the zeros in the reduced matrix obtained from last step

Select the smallest element from all the uncovered elements Subtract this smallest element from all the uncovered elements and add it to the elements which lie at the intersection of two lines Thus we obtain another reduced matrix for fresh assignment

Since the number of assignments is equal to the number of rows (amp columns) this is the optimal solution The total cost of assignment = A1 + B4 + C2 + D3 Substitute the values from original table 20 + 17 + 24 + 17 = 78

Some assignment problems entail maximizing the profit effectiveness or layoff of an assignment of persons to tasks or of jobs to machines

The conversion is accomplished by subtracting all the elements of the given effectiveness matrix from the highest element

It turns out that minimizing opportunity loss produces the same assignment solution as the original maximization problem

Five different machines can do any of the five required jobs with different profits resulting from each assignment as given below

Find out the maximum profit possible through optimum assignment

Here the highest element is 62 So we subtract each value from 62

The maximum profit through this assignment is 214

It is an assignment problem where the number of persons is not equal to the number of jobs

If the number of persons is less than the number of jobs then we introduce one or more dummy persons (rows) with zero values to make the assignment problem balanced

Likewise if the number of jobs is less than the number of persons then we introduce one or more dummy jobs (columns) with zero values to make the assignment problem balanced

Unbalanced Assignment Problem

THANK YOU VERY MUCH

• Assignment Problem
• Introduction
• Slide 3
• Application Areas of Assignment Problem
• Cost Matrix in Assignment Problem
• Slide 6
• Method for Solving Assignment Prob
• Slide 8
• Slide 9
• Examples
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Find out the maximum profit possible through optimum assignment
• Slide 21
• Slide 22
• Unbalanced Assignment Problem
• Slide 24
• Slide 25
• THANK YOU VERY MUCH

It involves assignment of people to projects jobs to machines workers to jobs and teachers to classes etc while minimizing the total assignment costs

One of the important characteristics of assignment problem is that only one job (or worker) is assigned to one machine (or project)

An assignment problem is a special type of linear programming problem where the objective is to minimize the cost or time of completing a number of jobs by a number of persons

Introduction

This method was developed by D Konig a Hungarian mathematician and is therefore known as the Hungarian method of assignment problem

In order to use this method one needs to know only the cost of making all the possible assignments

Each assignment problem has a matrix (table) associated with it Normally the objects (or people) one wishes to assign are expressed in rows whereas the columns represent the tasks (or things) assigned to them

The number in the table would then be the costs associated with each particular assignment

Though assignment problem finds applicability in various diverse business situations we discuss some of its main application areas

In assigning machines to factory orders In assigning salesmarketing people to sales

territories In assigning contracts to bidders by

systematic bid-evaluation In assigning teachers to classes In assigning accountants to accounts of the

clients

Application Areas of Assignment Problem

Cost Matrix in Assignment Problem

Mathematically the assignment problem can be expressed as

The objective function is Minimize C11X11 + C12X12 + ------- + CnnXnn

Step 1 Determine the cost table from the given problem

(i) If the no of sources is equal to no of destinations go to step 3

(ii) If the no of sources is not equal to the no of destination go to step2

Step 2 Add a dummy source or dummy destination so that the cost table becomes a square matrix The cost entries of the dummy sourcedestinations are always zero

Step 3 Locate the smallest element in each row of the given cost matrix and then subtract the same from each element of the row

Method for Solving Assignment Prob

Step 4 In the reduced matrix obtained in the step 3 locate the smallest element of each column and then subtract the same from each element of that column Each column and row now have at least one zero

Step 5 In the modified matrix obtained in the step 4 search for the optimal assignment as follows

(a) Examine the rows successively until a row with a single zero is found Enrectangle this row ( )and cross off (X) all other zeros in its column Continue in this manner until all the rows have been taken care of

(b) Repeat the procedure for each column of the reduced matrix

(c) If a row andor column has two or more zeros and one cannot be chosen by inspection then assign arbitrary any one of these zeros and cross off all other zeros of that row column

(d) Repeat (a) through (c) above successively until the chain of assigning ( ) or cross (X) ends

Step 6 If the number of assignment (1048576) is equal to n (the order of the cost matrix) an optimum solution is reached

If the number of assignment is less than n(the order of the matrix) go to the next step

Step7 Draw the minimum number of horizontal andor vertical lines to cover all the zeros of the reduced matrix

Step 8 Develop the new revised cost matrix as follows

(a)Find the smallest element of the reduced matrix not covered by any of the lines

(b)Subtract this element from all uncovered elements and add the same to all the elements laying at the intersection of any two lines

Step 9 Go to step 6 and repeat the procedure until an optimum solution is attained

A job has four men available for work on four separate jobs Only one man can work on any one job The cost of assigning each man to each job is given in the following table The objective is to assign men to jobs such that the total cost of assignment is minimum

Examples

Step 1 Identify the minimum element in each row

and subtract it from every element of that row

Step 2 Identify the minimum element in each

column and subtract it from every element of that column

Make the assignment for the reduced matrix obtain from steps 1 and 2 in the following way

Draw the minimum number of vertical and horizontal lines necessary to cover all the zeros in the reduced matrix obtained from last step

Select the smallest element from all the uncovered elements Subtract this smallest element from all the uncovered elements and add it to the elements which lie at the intersection of two lines Thus we obtain another reduced matrix for fresh assignment

Since the number of assignments is equal to the number of rows (amp columns) this is the optimal solution The total cost of assignment = A1 + B4 + C2 + D3 Substitute the values from original table 20 + 17 + 24 + 17 = 78

Some assignment problems entail maximizing the profit effectiveness or layoff of an assignment of persons to tasks or of jobs to machines

The conversion is accomplished by subtracting all the elements of the given effectiveness matrix from the highest element

It turns out that minimizing opportunity loss produces the same assignment solution as the original maximization problem

Five different machines can do any of the five required jobs with different profits resulting from each assignment as given below

Find out the maximum profit possible through optimum assignment

Here the highest element is 62 So we subtract each value from 62

The maximum profit through this assignment is 214

It is an assignment problem where the number of persons is not equal to the number of jobs

If the number of persons is less than the number of jobs then we introduce one or more dummy persons (rows) with zero values to make the assignment problem balanced

Likewise if the number of jobs is less than the number of persons then we introduce one or more dummy jobs (columns) with zero values to make the assignment problem balanced

Unbalanced Assignment Problem

THANK YOU VERY MUCH

• Assignment Problem
• Introduction
• Slide 3
• Application Areas of Assignment Problem
• Cost Matrix in Assignment Problem
• Slide 6
• Method for Solving Assignment Prob
• Slide 8
• Slide 9
• Examples
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Find out the maximum profit possible through optimum assignment
• Slide 21
• Slide 22
• Unbalanced Assignment Problem
• Slide 24
• Slide 25
• THANK YOU VERY MUCH

This method was developed by D Konig a Hungarian mathematician and is therefore known as the Hungarian method of assignment problem

In order to use this method one needs to know only the cost of making all the possible assignments

Each assignment problem has a matrix (table) associated with it Normally the objects (or people) one wishes to assign are expressed in rows whereas the columns represent the tasks (or things) assigned to them

The number in the table would then be the costs associated with each particular assignment

Though assignment problem finds applicability in various diverse business situations we discuss some of its main application areas

In assigning machines to factory orders In assigning salesmarketing people to sales

territories In assigning contracts to bidders by

systematic bid-evaluation In assigning teachers to classes In assigning accountants to accounts of the

clients

Application Areas of Assignment Problem

Cost Matrix in Assignment Problem

Mathematically the assignment problem can be expressed as

The objective function is Minimize C11X11 + C12X12 + ------- + CnnXnn

Step 1 Determine the cost table from the given problem

(i) If the no of sources is equal to no of destinations go to step 3

(ii) If the no of sources is not equal to the no of destination go to step2

Step 2 Add a dummy source or dummy destination so that the cost table becomes a square matrix The cost entries of the dummy sourcedestinations are always zero

Step 3 Locate the smallest element in each row of the given cost matrix and then subtract the same from each element of the row

Method for Solving Assignment Prob

Step 4 In the reduced matrix obtained in the step 3 locate the smallest element of each column and then subtract the same from each element of that column Each column and row now have at least one zero

Step 5 In the modified matrix obtained in the step 4 search for the optimal assignment as follows

(a) Examine the rows successively until a row with a single zero is found Enrectangle this row ( )and cross off (X) all other zeros in its column Continue in this manner until all the rows have been taken care of

(b) Repeat the procedure for each column of the reduced matrix

(c) If a row andor column has two or more zeros and one cannot be chosen by inspection then assign arbitrary any one of these zeros and cross off all other zeros of that row column

(d) Repeat (a) through (c) above successively until the chain of assigning ( ) or cross (X) ends

Step 6 If the number of assignment (1048576) is equal to n (the order of the cost matrix) an optimum solution is reached

If the number of assignment is less than n(the order of the matrix) go to the next step

Step7 Draw the minimum number of horizontal andor vertical lines to cover all the zeros of the reduced matrix

Step 8 Develop the new revised cost matrix as follows

(a)Find the smallest element of the reduced matrix not covered by any of the lines

(b)Subtract this element from all uncovered elements and add the same to all the elements laying at the intersection of any two lines

Step 9 Go to step 6 and repeat the procedure until an optimum solution is attained

A job has four men available for work on four separate jobs Only one man can work on any one job The cost of assigning each man to each job is given in the following table The objective is to assign men to jobs such that the total cost of assignment is minimum

Examples

Step 1 Identify the minimum element in each row

and subtract it from every element of that row

Step 2 Identify the minimum element in each

column and subtract it from every element of that column

Make the assignment for the reduced matrix obtain from steps 1 and 2 in the following way

Draw the minimum number of vertical and horizontal lines necessary to cover all the zeros in the reduced matrix obtained from last step

Select the smallest element from all the uncovered elements Subtract this smallest element from all the uncovered elements and add it to the elements which lie at the intersection of two lines Thus we obtain another reduced matrix for fresh assignment

Since the number of assignments is equal to the number of rows (amp columns) this is the optimal solution The total cost of assignment = A1 + B4 + C2 + D3 Substitute the values from original table 20 + 17 + 24 + 17 = 78

Some assignment problems entail maximizing the profit effectiveness or layoff of an assignment of persons to tasks or of jobs to machines

The conversion is accomplished by subtracting all the elements of the given effectiveness matrix from the highest element

It turns out that minimizing opportunity loss produces the same assignment solution as the original maximization problem

Five different machines can do any of the five required jobs with different profits resulting from each assignment as given below

Find out the maximum profit possible through optimum assignment

Here the highest element is 62 So we subtract each value from 62

The maximum profit through this assignment is 214

It is an assignment problem where the number of persons is not equal to the number of jobs

If the number of persons is less than the number of jobs then we introduce one or more dummy persons (rows) with zero values to make the assignment problem balanced

Likewise if the number of jobs is less than the number of persons then we introduce one or more dummy jobs (columns) with zero values to make the assignment problem balanced

Unbalanced Assignment Problem

THANK YOU VERY MUCH

• Assignment Problem
• Introduction
• Slide 3
• Application Areas of Assignment Problem
• Cost Matrix in Assignment Problem
• Slide 6
• Method for Solving Assignment Prob
• Slide 8
• Slide 9
• Examples
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Find out the maximum profit possible through optimum assignment
• Slide 21
• Slide 22
• Unbalanced Assignment Problem
• Slide 24
• Slide 25
• THANK YOU VERY MUCH

Though assignment problem finds applicability in various diverse business situations we discuss some of its main application areas

In assigning machines to factory orders In assigning salesmarketing people to sales

territories In assigning contracts to bidders by

systematic bid-evaluation In assigning teachers to classes In assigning accountants to accounts of the

clients

Application Areas of Assignment Problem

Cost Matrix in Assignment Problem

Mathematically the assignment problem can be expressed as

The objective function is Minimize C11X11 + C12X12 + ------- + CnnXnn

Step 1 Determine the cost table from the given problem

(i) If the no of sources is equal to no of destinations go to step 3

(ii) If the no of sources is not equal to the no of destination go to step2

Step 2 Add a dummy source or dummy destination so that the cost table becomes a square matrix The cost entries of the dummy sourcedestinations are always zero

Step 3 Locate the smallest element in each row of the given cost matrix and then subtract the same from each element of the row

Method for Solving Assignment Prob

Step 4 In the reduced matrix obtained in the step 3 locate the smallest element of each column and then subtract the same from each element of that column Each column and row now have at least one zero

Step 5 In the modified matrix obtained in the step 4 search for the optimal assignment as follows

(a) Examine the rows successively until a row with a single zero is found Enrectangle this row ( )and cross off (X) all other zeros in its column Continue in this manner until all the rows have been taken care of

(b) Repeat the procedure for each column of the reduced matrix

(c) If a row andor column has two or more zeros and one cannot be chosen by inspection then assign arbitrary any one of these zeros and cross off all other zeros of that row column

(d) Repeat (a) through (c) above successively until the chain of assigning ( ) or cross (X) ends

Step 6 If the number of assignment (1048576) is equal to n (the order of the cost matrix) an optimum solution is reached

If the number of assignment is less than n(the order of the matrix) go to the next step

Step7 Draw the minimum number of horizontal andor vertical lines to cover all the zeros of the reduced matrix

Step 8 Develop the new revised cost matrix as follows

(a)Find the smallest element of the reduced matrix not covered by any of the lines

(b)Subtract this element from all uncovered elements and add the same to all the elements laying at the intersection of any two lines

Step 9 Go to step 6 and repeat the procedure until an optimum solution is attained

A job has four men available for work on four separate jobs Only one man can work on any one job The cost of assigning each man to each job is given in the following table The objective is to assign men to jobs such that the total cost of assignment is minimum

Examples

Step 1 Identify the minimum element in each row

and subtract it from every element of that row

Step 2 Identify the minimum element in each

column and subtract it from every element of that column

Make the assignment for the reduced matrix obtain from steps 1 and 2 in the following way

Draw the minimum number of vertical and horizontal lines necessary to cover all the zeros in the reduced matrix obtained from last step

Select the smallest element from all the uncovered elements Subtract this smallest element from all the uncovered elements and add it to the elements which lie at the intersection of two lines Thus we obtain another reduced matrix for fresh assignment

Since the number of assignments is equal to the number of rows (amp columns) this is the optimal solution The total cost of assignment = A1 + B4 + C2 + D3 Substitute the values from original table 20 + 17 + 24 + 17 = 78

Some assignment problems entail maximizing the profit effectiveness or layoff of an assignment of persons to tasks or of jobs to machines

The conversion is accomplished by subtracting all the elements of the given effectiveness matrix from the highest element

It turns out that minimizing opportunity loss produces the same assignment solution as the original maximization problem

Five different machines can do any of the five required jobs with different profits resulting from each assignment as given below

Find out the maximum profit possible through optimum assignment

Here the highest element is 62 So we subtract each value from 62

The maximum profit through this assignment is 214

It is an assignment problem where the number of persons is not equal to the number of jobs

If the number of persons is less than the number of jobs then we introduce one or more dummy persons (rows) with zero values to make the assignment problem balanced

Likewise if the number of jobs is less than the number of persons then we introduce one or more dummy jobs (columns) with zero values to make the assignment problem balanced

Unbalanced Assignment Problem

THANK YOU VERY MUCH

• Assignment Problem
• Introduction
• Slide 3
• Application Areas of Assignment Problem
• Cost Matrix in Assignment Problem
• Slide 6
• Method for Solving Assignment Prob
• Slide 8
• Slide 9
• Examples
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Find out the maximum profit possible through optimum assignment
• Slide 21
• Slide 22
• Unbalanced Assignment Problem
• Slide 24
• Slide 25
• THANK YOU VERY MUCH

Cost Matrix in Assignment Problem

Mathematically the assignment problem can be expressed as

The objective function is Minimize C11X11 + C12X12 + ------- + CnnXnn

Step 1 Determine the cost table from the given problem

(i) If the no of sources is equal to no of destinations go to step 3

(ii) If the no of sources is not equal to the no of destination go to step2

Step 2 Add a dummy source or dummy destination so that the cost table becomes a square matrix The cost entries of the dummy sourcedestinations are always zero

Step 3 Locate the smallest element in each row of the given cost matrix and then subtract the same from each element of the row

Method for Solving Assignment Prob

Step 4 In the reduced matrix obtained in the step 3 locate the smallest element of each column and then subtract the same from each element of that column Each column and row now have at least one zero

Step 5 In the modified matrix obtained in the step 4 search for the optimal assignment as follows

(a) Examine the rows successively until a row with a single zero is found Enrectangle this row ( )and cross off (X) all other zeros in its column Continue in this manner until all the rows have been taken care of

(b) Repeat the procedure for each column of the reduced matrix

(c) If a row andor column has two or more zeros and one cannot be chosen by inspection then assign arbitrary any one of these zeros and cross off all other zeros of that row column

(d) Repeat (a) through (c) above successively until the chain of assigning ( ) or cross (X) ends

Step 6 If the number of assignment (1048576) is equal to n (the order of the cost matrix) an optimum solution is reached

If the number of assignment is less than n(the order of the matrix) go to the next step

Step7 Draw the minimum number of horizontal andor vertical lines to cover all the zeros of the reduced matrix

Step 8 Develop the new revised cost matrix as follows

(a)Find the smallest element of the reduced matrix not covered by any of the lines

(b)Subtract this element from all uncovered elements and add the same to all the elements laying at the intersection of any two lines

Step 9 Go to step 6 and repeat the procedure until an optimum solution is attained

A job has four men available for work on four separate jobs Only one man can work on any one job The cost of assigning each man to each job is given in the following table The objective is to assign men to jobs such that the total cost of assignment is minimum

Examples

Step 1 Identify the minimum element in each row

and subtract it from every element of that row

Step 2 Identify the minimum element in each

column and subtract it from every element of that column

Make the assignment for the reduced matrix obtain from steps 1 and 2 in the following way

Draw the minimum number of vertical and horizontal lines necessary to cover all the zeros in the reduced matrix obtained from last step

Select the smallest element from all the uncovered elements Subtract this smallest element from all the uncovered elements and add it to the elements which lie at the intersection of two lines Thus we obtain another reduced matrix for fresh assignment

Since the number of assignments is equal to the number of rows (amp columns) this is the optimal solution The total cost of assignment = A1 + B4 + C2 + D3 Substitute the values from original table 20 + 17 + 24 + 17 = 78

Some assignment problems entail maximizing the profit effectiveness or layoff of an assignment of persons to tasks or of jobs to machines

The conversion is accomplished by subtracting all the elements of the given effectiveness matrix from the highest element

It turns out that minimizing opportunity loss produces the same assignment solution as the original maximization problem

Five different machines can do any of the five required jobs with different profits resulting from each assignment as given below

Find out the maximum profit possible through optimum assignment

Here the highest element is 62 So we subtract each value from 62

The maximum profit through this assignment is 214

It is an assignment problem where the number of persons is not equal to the number of jobs

If the number of persons is less than the number of jobs then we introduce one or more dummy persons (rows) with zero values to make the assignment problem balanced

Likewise if the number of jobs is less than the number of persons then we introduce one or more dummy jobs (columns) with zero values to make the assignment problem balanced

Unbalanced Assignment Problem

THANK YOU VERY MUCH

• Assignment Problem
• Introduction
• Slide 3
• Application Areas of Assignment Problem
• Cost Matrix in Assignment Problem
• Slide 6
• Method for Solving Assignment Prob
• Slide 8
• Slide 9
• Examples
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Find out the maximum profit possible through optimum assignment
• Slide 21
• Slide 22
• Unbalanced Assignment Problem
• Slide 24
• Slide 25
• THANK YOU VERY MUCH

Mathematically the assignment problem can be expressed as

The objective function is Minimize C11X11 + C12X12 + ------- + CnnXnn

Step 1 Determine the cost table from the given problem

(i) If the no of sources is equal to no of destinations go to step 3

(ii) If the no of sources is not equal to the no of destination go to step2

Step 2 Add a dummy source or dummy destination so that the cost table becomes a square matrix The cost entries of the dummy sourcedestinations are always zero

Step 3 Locate the smallest element in each row of the given cost matrix and then subtract the same from each element of the row

Method for Solving Assignment Prob

Step 4 In the reduced matrix obtained in the step 3 locate the smallest element of each column and then subtract the same from each element of that column Each column and row now have at least one zero

Step 5 In the modified matrix obtained in the step 4 search for the optimal assignment as follows

(a) Examine the rows successively until a row with a single zero is found Enrectangle this row ( )and cross off (X) all other zeros in its column Continue in this manner until all the rows have been taken care of

(b) Repeat the procedure for each column of the reduced matrix

(c) If a row andor column has two or more zeros and one cannot be chosen by inspection then assign arbitrary any one of these zeros and cross off all other zeros of that row column

(d) Repeat (a) through (c) above successively until the chain of assigning ( ) or cross (X) ends

Step 6 If the number of assignment (1048576) is equal to n (the order of the cost matrix) an optimum solution is reached

If the number of assignment is less than n(the order of the matrix) go to the next step

Step7 Draw the minimum number of horizontal andor vertical lines to cover all the zeros of the reduced matrix

Step 8 Develop the new revised cost matrix as follows

(a)Find the smallest element of the reduced matrix not covered by any of the lines

(b)Subtract this element from all uncovered elements and add the same to all the elements laying at the intersection of any two lines

Step 9 Go to step 6 and repeat the procedure until an optimum solution is attained

A job has four men available for work on four separate jobs Only one man can work on any one job The cost of assigning each man to each job is given in the following table The objective is to assign men to jobs such that the total cost of assignment is minimum

Examples

Step 1 Identify the minimum element in each row

and subtract it from every element of that row

Step 2 Identify the minimum element in each

column and subtract it from every element of that column

Make the assignment for the reduced matrix obtain from steps 1 and 2 in the following way

Draw the minimum number of vertical and horizontal lines necessary to cover all the zeros in the reduced matrix obtained from last step

Select the smallest element from all the uncovered elements Subtract this smallest element from all the uncovered elements and add it to the elements which lie at the intersection of two lines Thus we obtain another reduced matrix for fresh assignment

Since the number of assignments is equal to the number of rows (amp columns) this is the optimal solution The total cost of assignment = A1 + B4 + C2 + D3 Substitute the values from original table 20 + 17 + 24 + 17 = 78

Some assignment problems entail maximizing the profit effectiveness or layoff of an assignment of persons to tasks or of jobs to machines

The conversion is accomplished by subtracting all the elements of the given effectiveness matrix from the highest element

It turns out that minimizing opportunity loss produces the same assignment solution as the original maximization problem

Five different machines can do any of the five required jobs with different profits resulting from each assignment as given below

Find out the maximum profit possible through optimum assignment

Here the highest element is 62 So we subtract each value from 62

The maximum profit through this assignment is 214

It is an assignment problem where the number of persons is not equal to the number of jobs

If the number of persons is less than the number of jobs then we introduce one or more dummy persons (rows) with zero values to make the assignment problem balanced

Likewise if the number of jobs is less than the number of persons then we introduce one or more dummy jobs (columns) with zero values to make the assignment problem balanced

Unbalanced Assignment Problem

THANK YOU VERY MUCH

• Assignment Problem
• Introduction
• Slide 3
• Application Areas of Assignment Problem
• Cost Matrix in Assignment Problem
• Slide 6
• Method for Solving Assignment Prob
• Slide 8
• Slide 9
• Examples
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Find out the maximum profit possible through optimum assignment
• Slide 21
• Slide 22
• Unbalanced Assignment Problem
• Slide 24
• Slide 25
• THANK YOU VERY MUCH

Step 1 Determine the cost table from the given problem

(i) If the no of sources is equal to no of destinations go to step 3

(ii) If the no of sources is not equal to the no of destination go to step2

Step 2 Add a dummy source or dummy destination so that the cost table becomes a square matrix The cost entries of the dummy sourcedestinations are always zero

Step 3 Locate the smallest element in each row of the given cost matrix and then subtract the same from each element of the row

Method for Solving Assignment Prob

Step 4 In the reduced matrix obtained in the step 3 locate the smallest element of each column and then subtract the same from each element of that column Each column and row now have at least one zero

Step 5 In the modified matrix obtained in the step 4 search for the optimal assignment as follows

(a) Examine the rows successively until a row with a single zero is found Enrectangle this row ( )and cross off (X) all other zeros in its column Continue in this manner until all the rows have been taken care of

(b) Repeat the procedure for each column of the reduced matrix

(c) If a row andor column has two or more zeros and one cannot be chosen by inspection then assign arbitrary any one of these zeros and cross off all other zeros of that row column

(d) Repeat (a) through (c) above successively until the chain of assigning ( ) or cross (X) ends

Step 6 If the number of assignment (1048576) is equal to n (the order of the cost matrix) an optimum solution is reached

If the number of assignment is less than n(the order of the matrix) go to the next step

Step7 Draw the minimum number of horizontal andor vertical lines to cover all the zeros of the reduced matrix

Step 8 Develop the new revised cost matrix as follows

(a)Find the smallest element of the reduced matrix not covered by any of the lines

(b)Subtract this element from all uncovered elements and add the same to all the elements laying at the intersection of any two lines

Step 9 Go to step 6 and repeat the procedure until an optimum solution is attained

A job has four men available for work on four separate jobs Only one man can work on any one job The cost of assigning each man to each job is given in the following table The objective is to assign men to jobs such that the total cost of assignment is minimum

Examples

Step 1 Identify the minimum element in each row

and subtract it from every element of that row

Step 2 Identify the minimum element in each

column and subtract it from every element of that column

Make the assignment for the reduced matrix obtain from steps 1 and 2 in the following way

Draw the minimum number of vertical and horizontal lines necessary to cover all the zeros in the reduced matrix obtained from last step

Select the smallest element from all the uncovered elements Subtract this smallest element from all the uncovered elements and add it to the elements which lie at the intersection of two lines Thus we obtain another reduced matrix for fresh assignment

Since the number of assignments is equal to the number of rows (amp columns) this is the optimal solution The total cost of assignment = A1 + B4 + C2 + D3 Substitute the values from original table 20 + 17 + 24 + 17 = 78

Some assignment problems entail maximizing the profit effectiveness or layoff of an assignment of persons to tasks or of jobs to machines

The conversion is accomplished by subtracting all the elements of the given effectiveness matrix from the highest element

It turns out that minimizing opportunity loss produces the same assignment solution as the original maximization problem

Five different machines can do any of the five required jobs with different profits resulting from each assignment as given below

Find out the maximum profit possible through optimum assignment

Here the highest element is 62 So we subtract each value from 62

The maximum profit through this assignment is 214

It is an assignment problem where the number of persons is not equal to the number of jobs

If the number of persons is less than the number of jobs then we introduce one or more dummy persons (rows) with zero values to make the assignment problem balanced

Likewise if the number of jobs is less than the number of persons then we introduce one or more dummy jobs (columns) with zero values to make the assignment problem balanced

Unbalanced Assignment Problem

THANK YOU VERY MUCH

• Assignment Problem
• Introduction
• Slide 3
• Application Areas of Assignment Problem
• Cost Matrix in Assignment Problem
• Slide 6
• Method for Solving Assignment Prob
• Slide 8
• Slide 9
• Examples
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Find out the maximum profit possible through optimum assignment
• Slide 21
• Slide 22
• Unbalanced Assignment Problem
• Slide 24
• Slide 25
• THANK YOU VERY MUCH

Step 4 In the reduced matrix obtained in the step 3 locate the smallest element of each column and then subtract the same from each element of that column Each column and row now have at least one zero

Step 5 In the modified matrix obtained in the step 4 search for the optimal assignment as follows

(a) Examine the rows successively until a row with a single zero is found Enrectangle this row ( )and cross off (X) all other zeros in its column Continue in this manner until all the rows have been taken care of

(b) Repeat the procedure for each column of the reduced matrix

(c) If a row andor column has two or more zeros and one cannot be chosen by inspection then assign arbitrary any one of these zeros and cross off all other zeros of that row column

(d) Repeat (a) through (c) above successively until the chain of assigning ( ) or cross (X) ends

Step 6 If the number of assignment (1048576) is equal to n (the order of the cost matrix) an optimum solution is reached

If the number of assignment is less than n(the order of the matrix) go to the next step

Step7 Draw the minimum number of horizontal andor vertical lines to cover all the zeros of the reduced matrix

Step 8 Develop the new revised cost matrix as follows

(a)Find the smallest element of the reduced matrix not covered by any of the lines

(b)Subtract this element from all uncovered elements and add the same to all the elements laying at the intersection of any two lines

Step 9 Go to step 6 and repeat the procedure until an optimum solution is attained

A job has four men available for work on four separate jobs Only one man can work on any one job The cost of assigning each man to each job is given in the following table The objective is to assign men to jobs such that the total cost of assignment is minimum

Examples

Step 1 Identify the minimum element in each row

and subtract it from every element of that row

Step 2 Identify the minimum element in each

column and subtract it from every element of that column

Make the assignment for the reduced matrix obtain from steps 1 and 2 in the following way

Draw the minimum number of vertical and horizontal lines necessary to cover all the zeros in the reduced matrix obtained from last step

Select the smallest element from all the uncovered elements Subtract this smallest element from all the uncovered elements and add it to the elements which lie at the intersection of two lines Thus we obtain another reduced matrix for fresh assignment

Since the number of assignments is equal to the number of rows (amp columns) this is the optimal solution The total cost of assignment = A1 + B4 + C2 + D3 Substitute the values from original table 20 + 17 + 24 + 17 = 78

Some assignment problems entail maximizing the profit effectiveness or layoff of an assignment of persons to tasks or of jobs to machines

The conversion is accomplished by subtracting all the elements of the given effectiveness matrix from the highest element

It turns out that minimizing opportunity loss produces the same assignment solution as the original maximization problem

Five different machines can do any of the five required jobs with different profits resulting from each assignment as given below

Find out the maximum profit possible through optimum assignment

Here the highest element is 62 So we subtract each value from 62

The maximum profit through this assignment is 214

It is an assignment problem where the number of persons is not equal to the number of jobs

If the number of persons is less than the number of jobs then we introduce one or more dummy persons (rows) with zero values to make the assignment problem balanced

Likewise if the number of jobs is less than the number of persons then we introduce one or more dummy jobs (columns) with zero values to make the assignment problem balanced

Unbalanced Assignment Problem

THANK YOU VERY MUCH

• Assignment Problem
• Introduction
• Slide 3
• Application Areas of Assignment Problem
• Cost Matrix in Assignment Problem
• Slide 6
• Method for Solving Assignment Prob
• Slide 8
• Slide 9
• Examples
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Find out the maximum profit possible through optimum assignment
• Slide 21
• Slide 22
• Unbalanced Assignment Problem
• Slide 24
• Slide 25
• THANK YOU VERY MUCH

Step 6 If the number of assignment (1048576) is equal to n (the order of the cost matrix) an optimum solution is reached

If the number of assignment is less than n(the order of the matrix) go to the next step

Step7 Draw the minimum number of horizontal andor vertical lines to cover all the zeros of the reduced matrix

Step 8 Develop the new revised cost matrix as follows

(a)Find the smallest element of the reduced matrix not covered by any of the lines

(b)Subtract this element from all uncovered elements and add the same to all the elements laying at the intersection of any two lines

Step 9 Go to step 6 and repeat the procedure until an optimum solution is attained

A job has four men available for work on four separate jobs Only one man can work on any one job The cost of assigning each man to each job is given in the following table The objective is to assign men to jobs such that the total cost of assignment is minimum

Examples

Step 1 Identify the minimum element in each row

and subtract it from every element of that row

Step 2 Identify the minimum element in each

column and subtract it from every element of that column

Make the assignment for the reduced matrix obtain from steps 1 and 2 in the following way

Draw the minimum number of vertical and horizontal lines necessary to cover all the zeros in the reduced matrix obtained from last step

Select the smallest element from all the uncovered elements Subtract this smallest element from all the uncovered elements and add it to the elements which lie at the intersection of two lines Thus we obtain another reduced matrix for fresh assignment

Since the number of assignments is equal to the number of rows (amp columns) this is the optimal solution The total cost of assignment = A1 + B4 + C2 + D3 Substitute the values from original table 20 + 17 + 24 + 17 = 78

Some assignment problems entail maximizing the profit effectiveness or layoff of an assignment of persons to tasks or of jobs to machines

The conversion is accomplished by subtracting all the elements of the given effectiveness matrix from the highest element

It turns out that minimizing opportunity loss produces the same assignment solution as the original maximization problem

Five different machines can do any of the five required jobs with different profits resulting from each assignment as given below

Find out the maximum profit possible through optimum assignment

Here the highest element is 62 So we subtract each value from 62

The maximum profit through this assignment is 214

It is an assignment problem where the number of persons is not equal to the number of jobs

If the number of persons is less than the number of jobs then we introduce one or more dummy persons (rows) with zero values to make the assignment problem balanced

Likewise if the number of jobs is less than the number of persons then we introduce one or more dummy jobs (columns) with zero values to make the assignment problem balanced

Unbalanced Assignment Problem

THANK YOU VERY MUCH

• Assignment Problem
• Introduction
• Slide 3
• Application Areas of Assignment Problem
• Cost Matrix in Assignment Problem
• Slide 6
• Method for Solving Assignment Prob
• Slide 8
• Slide 9
• Examples
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Find out the maximum profit possible through optimum assignment
• Slide 21
• Slide 22
• Unbalanced Assignment Problem
• Slide 24
• Slide 25
• THANK YOU VERY MUCH

A job has four men available for work on four separate jobs Only one man can work on any one job The cost of assigning each man to each job is given in the following table The objective is to assign men to jobs such that the total cost of assignment is minimum

Examples

Step 1 Identify the minimum element in each row

and subtract it from every element of that row

Step 2 Identify the minimum element in each

column and subtract it from every element of that column

Make the assignment for the reduced matrix obtain from steps 1 and 2 in the following way

Draw the minimum number of vertical and horizontal lines necessary to cover all the zeros in the reduced matrix obtained from last step

Select the smallest element from all the uncovered elements Subtract this smallest element from all the uncovered elements and add it to the elements which lie at the intersection of two lines Thus we obtain another reduced matrix for fresh assignment

Since the number of assignments is equal to the number of rows (amp columns) this is the optimal solution The total cost of assignment = A1 + B4 + C2 + D3 Substitute the values from original table 20 + 17 + 24 + 17 = 78

Some assignment problems entail maximizing the profit effectiveness or layoff of an assignment of persons to tasks or of jobs to machines

The conversion is accomplished by subtracting all the elements of the given effectiveness matrix from the highest element

It turns out that minimizing opportunity loss produces the same assignment solution as the original maximization problem

Five different machines can do any of the five required jobs with different profits resulting from each assignment as given below

Find out the maximum profit possible through optimum assignment

Here the highest element is 62 So we subtract each value from 62

The maximum profit through this assignment is 214

It is an assignment problem where the number of persons is not equal to the number of jobs

If the number of persons is less than the number of jobs then we introduce one or more dummy persons (rows) with zero values to make the assignment problem balanced

Likewise if the number of jobs is less than the number of persons then we introduce one or more dummy jobs (columns) with zero values to make the assignment problem balanced

Unbalanced Assignment Problem

THANK YOU VERY MUCH

• Assignment Problem
• Introduction
• Slide 3
• Application Areas of Assignment Problem
• Cost Matrix in Assignment Problem
• Slide 6
• Method for Solving Assignment Prob
• Slide 8
• Slide 9
• Examples
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Find out the maximum profit possible through optimum assignment
• Slide 21
• Slide 22
• Unbalanced Assignment Problem
• Slide 24
• Slide 25
• THANK YOU VERY MUCH

Step 1 Identify the minimum element in each row

and subtract it from every element of that row

Step 2 Identify the minimum element in each

column and subtract it from every element of that column

Make the assignment for the reduced matrix obtain from steps 1 and 2 in the following way

Draw the minimum number of vertical and horizontal lines necessary to cover all the zeros in the reduced matrix obtained from last step

Select the smallest element from all the uncovered elements Subtract this smallest element from all the uncovered elements and add it to the elements which lie at the intersection of two lines Thus we obtain another reduced matrix for fresh assignment

Since the number of assignments is equal to the number of rows (amp columns) this is the optimal solution The total cost of assignment = A1 + B4 + C2 + D3 Substitute the values from original table 20 + 17 + 24 + 17 = 78

Some assignment problems entail maximizing the profit effectiveness or layoff of an assignment of persons to tasks or of jobs to machines

The conversion is accomplished by subtracting all the elements of the given effectiveness matrix from the highest element

It turns out that minimizing opportunity loss produces the same assignment solution as the original maximization problem

Five different machines can do any of the five required jobs with different profits resulting from each assignment as given below

Find out the maximum profit possible through optimum assignment

Here the highest element is 62 So we subtract each value from 62

The maximum profit through this assignment is 214

It is an assignment problem where the number of persons is not equal to the number of jobs

If the number of persons is less than the number of jobs then we introduce one or more dummy persons (rows) with zero values to make the assignment problem balanced

Likewise if the number of jobs is less than the number of persons then we introduce one or more dummy jobs (columns) with zero values to make the assignment problem balanced

Unbalanced Assignment Problem

THANK YOU VERY MUCH

• Assignment Problem
• Introduction
• Slide 3
• Application Areas of Assignment Problem
• Cost Matrix in Assignment Problem
• Slide 6
• Method for Solving Assignment Prob
• Slide 8
• Slide 9
• Examples
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Find out the maximum profit possible through optimum assignment
• Slide 21
• Slide 22
• Unbalanced Assignment Problem
• Slide 24
• Slide 25
• THANK YOU VERY MUCH

Step 2 Identify the minimum element in each

column and subtract it from every element of that column

Make the assignment for the reduced matrix obtain from steps 1 and 2 in the following way

Draw the minimum number of vertical and horizontal lines necessary to cover all the zeros in the reduced matrix obtained from last step

Select the smallest element from all the uncovered elements Subtract this smallest element from all the uncovered elements and add it to the elements which lie at the intersection of two lines Thus we obtain another reduced matrix for fresh assignment

Since the number of assignments is equal to the number of rows (amp columns) this is the optimal solution The total cost of assignment = A1 + B4 + C2 + D3 Substitute the values from original table 20 + 17 + 24 + 17 = 78

Some assignment problems entail maximizing the profit effectiveness or layoff of an assignment of persons to tasks or of jobs to machines

The conversion is accomplished by subtracting all the elements of the given effectiveness matrix from the highest element

It turns out that minimizing opportunity loss produces the same assignment solution as the original maximization problem

Five different machines can do any of the five required jobs with different profits resulting from each assignment as given below

Find out the maximum profit possible through optimum assignment

Here the highest element is 62 So we subtract each value from 62

The maximum profit through this assignment is 214

It is an assignment problem where the number of persons is not equal to the number of jobs

If the number of persons is less than the number of jobs then we introduce one or more dummy persons (rows) with zero values to make the assignment problem balanced

Likewise if the number of jobs is less than the number of persons then we introduce one or more dummy jobs (columns) with zero values to make the assignment problem balanced

Unbalanced Assignment Problem

THANK YOU VERY MUCH

• Assignment Problem
• Introduction
• Slide 3
• Application Areas of Assignment Problem
• Cost Matrix in Assignment Problem
• Slide 6
• Method for Solving Assignment Prob
• Slide 8
• Slide 9
• Examples
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Find out the maximum profit possible through optimum assignment
• Slide 21
• Slide 22
• Unbalanced Assignment Problem
• Slide 24
• Slide 25
• THANK YOU VERY MUCH

Make the assignment for the reduced matrix obtain from steps 1 and 2 in the following way

Draw the minimum number of vertical and horizontal lines necessary to cover all the zeros in the reduced matrix obtained from last step

Select the smallest element from all the uncovered elements Subtract this smallest element from all the uncovered elements and add it to the elements which lie at the intersection of two lines Thus we obtain another reduced matrix for fresh assignment

Since the number of assignments is equal to the number of rows (amp columns) this is the optimal solution The total cost of assignment = A1 + B4 + C2 + D3 Substitute the values from original table 20 + 17 + 24 + 17 = 78

Some assignment problems entail maximizing the profit effectiveness or layoff of an assignment of persons to tasks or of jobs to machines

The conversion is accomplished by subtracting all the elements of the given effectiveness matrix from the highest element

It turns out that minimizing opportunity loss produces the same assignment solution as the original maximization problem

Five different machines can do any of the five required jobs with different profits resulting from each assignment as given below

Find out the maximum profit possible through optimum assignment

Here the highest element is 62 So we subtract each value from 62

The maximum profit through this assignment is 214

It is an assignment problem where the number of persons is not equal to the number of jobs

If the number of persons is less than the number of jobs then we introduce one or more dummy persons (rows) with zero values to make the assignment problem balanced

Likewise if the number of jobs is less than the number of persons then we introduce one or more dummy jobs (columns) with zero values to make the assignment problem balanced

Unbalanced Assignment Problem

THANK YOU VERY MUCH

• Assignment Problem
• Introduction
• Slide 3
• Application Areas of Assignment Problem
• Cost Matrix in Assignment Problem
• Slide 6
• Method for Solving Assignment Prob
• Slide 8
• Slide 9
• Examples
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Find out the maximum profit possible through optimum assignment
• Slide 21
• Slide 22
• Unbalanced Assignment Problem
• Slide 24
• Slide 25
• THANK YOU VERY MUCH

Draw the minimum number of vertical and horizontal lines necessary to cover all the zeros in the reduced matrix obtained from last step

Select the smallest element from all the uncovered elements Subtract this smallest element from all the uncovered elements and add it to the elements which lie at the intersection of two lines Thus we obtain another reduced matrix for fresh assignment

Since the number of assignments is equal to the number of rows (amp columns) this is the optimal solution The total cost of assignment = A1 + B4 + C2 + D3 Substitute the values from original table 20 + 17 + 24 + 17 = 78

Some assignment problems entail maximizing the profit effectiveness or layoff of an assignment of persons to tasks or of jobs to machines

The conversion is accomplished by subtracting all the elements of the given effectiveness matrix from the highest element

It turns out that minimizing opportunity loss produces the same assignment solution as the original maximization problem

Five different machines can do any of the five required jobs with different profits resulting from each assignment as given below

Find out the maximum profit possible through optimum assignment

Here the highest element is 62 So we subtract each value from 62

The maximum profit through this assignment is 214

It is an assignment problem where the number of persons is not equal to the number of jobs

If the number of persons is less than the number of jobs then we introduce one or more dummy persons (rows) with zero values to make the assignment problem balanced

Likewise if the number of jobs is less than the number of persons then we introduce one or more dummy jobs (columns) with zero values to make the assignment problem balanced

Unbalanced Assignment Problem

THANK YOU VERY MUCH

• Assignment Problem
• Introduction
• Slide 3
• Application Areas of Assignment Problem
• Cost Matrix in Assignment Problem
• Slide 6
• Method for Solving Assignment Prob
• Slide 8
• Slide 9
• Examples
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Find out the maximum profit possible through optimum assignment
• Slide 21
• Slide 22
• Unbalanced Assignment Problem
• Slide 24
• Slide 25
• THANK YOU VERY MUCH

Select the smallest element from all the uncovered elements Subtract this smallest element from all the uncovered elements and add it to the elements which lie at the intersection of two lines Thus we obtain another reduced matrix for fresh assignment

Since the number of assignments is equal to the number of rows (amp columns) this is the optimal solution The total cost of assignment = A1 + B4 + C2 + D3 Substitute the values from original table 20 + 17 + 24 + 17 = 78

Some assignment problems entail maximizing the profit effectiveness or layoff of an assignment of persons to tasks or of jobs to machines

The conversion is accomplished by subtracting all the elements of the given effectiveness matrix from the highest element

It turns out that minimizing opportunity loss produces the same assignment solution as the original maximization problem

Five different machines can do any of the five required jobs with different profits resulting from each assignment as given below

Find out the maximum profit possible through optimum assignment

Here the highest element is 62 So we subtract each value from 62

The maximum profit through this assignment is 214

It is an assignment problem where the number of persons is not equal to the number of jobs

If the number of persons is less than the number of jobs then we introduce one or more dummy persons (rows) with zero values to make the assignment problem balanced

Likewise if the number of jobs is less than the number of persons then we introduce one or more dummy jobs (columns) with zero values to make the assignment problem balanced

Unbalanced Assignment Problem

THANK YOU VERY MUCH

• Assignment Problem
• Introduction
• Slide 3
• Application Areas of Assignment Problem
• Cost Matrix in Assignment Problem
• Slide 6
• Method for Solving Assignment Prob
• Slide 8
• Slide 9
• Examples
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Find out the maximum profit possible through optimum assignment
• Slide 21
• Slide 22
• Unbalanced Assignment Problem
• Slide 24
• Slide 25
• THANK YOU VERY MUCH

Since the number of assignments is equal to the number of rows (amp columns) this is the optimal solution The total cost of assignment = A1 + B4 + C2 + D3 Substitute the values from original table 20 + 17 + 24 + 17 = 78

Some assignment problems entail maximizing the profit effectiveness or layoff of an assignment of persons to tasks or of jobs to machines

The conversion is accomplished by subtracting all the elements of the given effectiveness matrix from the highest element

It turns out that minimizing opportunity loss produces the same assignment solution as the original maximization problem

Five different machines can do any of the five required jobs with different profits resulting from each assignment as given below

Find out the maximum profit possible through optimum assignment

Here the highest element is 62 So we subtract each value from 62

The maximum profit through this assignment is 214

It is an assignment problem where the number of persons is not equal to the number of jobs

If the number of persons is less than the number of jobs then we introduce one or more dummy persons (rows) with zero values to make the assignment problem balanced

Likewise if the number of jobs is less than the number of persons then we introduce one or more dummy jobs (columns) with zero values to make the assignment problem balanced

Unbalanced Assignment Problem

THANK YOU VERY MUCH

• Assignment Problem
• Introduction
• Slide 3
• Application Areas of Assignment Problem
• Cost Matrix in Assignment Problem
• Slide 6
• Method for Solving Assignment Prob
• Slide 8
• Slide 9
• Examples
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Find out the maximum profit possible through optimum assignment
• Slide 21
• Slide 22
• Unbalanced Assignment Problem
• Slide 24
• Slide 25
• THANK YOU VERY MUCH

Some assignment problems entail maximizing the profit effectiveness or layoff of an assignment of persons to tasks or of jobs to machines

The conversion is accomplished by subtracting all the elements of the given effectiveness matrix from the highest element

It turns out that minimizing opportunity loss produces the same assignment solution as the original maximization problem

Five different machines can do any of the five required jobs with different profits resulting from each assignment as given below

Find out the maximum profit possible through optimum assignment

Here the highest element is 62 So we subtract each value from 62

The maximum profit through this assignment is 214

It is an assignment problem where the number of persons is not equal to the number of jobs

If the number of persons is less than the number of jobs then we introduce one or more dummy persons (rows) with zero values to make the assignment problem balanced

Likewise if the number of jobs is less than the number of persons then we introduce one or more dummy jobs (columns) with zero values to make the assignment problem balanced

Unbalanced Assignment Problem

THANK YOU VERY MUCH

• Assignment Problem
• Introduction
• Slide 3
• Application Areas of Assignment Problem
• Cost Matrix in Assignment Problem
• Slide 6
• Method for Solving Assignment Prob
• Slide 8
• Slide 9
• Examples
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Find out the maximum profit possible through optimum assignment
• Slide 21
• Slide 22
• Unbalanced Assignment Problem
• Slide 24
• Slide 25
• THANK YOU VERY MUCH

Five different machines can do any of the five required jobs with different profits resulting from each assignment as given below

Find out the maximum profit possible through optimum assignment

Here the highest element is 62 So we subtract each value from 62

The maximum profit through this assignment is 214

It is an assignment problem where the number of persons is not equal to the number of jobs

If the number of persons is less than the number of jobs then we introduce one or more dummy persons (rows) with zero values to make the assignment problem balanced

Likewise if the number of jobs is less than the number of persons then we introduce one or more dummy jobs (columns) with zero values to make the assignment problem balanced

Unbalanced Assignment Problem

THANK YOU VERY MUCH

• Assignment Problem
• Introduction
• Slide 3
• Application Areas of Assignment Problem
• Cost Matrix in Assignment Problem
• Slide 6
• Method for Solving Assignment Prob
• Slide 8
• Slide 9
• Examples
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Find out the maximum profit possible through optimum assignment
• Slide 21
• Slide 22
• Unbalanced Assignment Problem
• Slide 24
• Slide 25
• THANK YOU VERY MUCH

Here the highest element is 62 So we subtract each value from 62

The maximum profit through this assignment is 214

It is an assignment problem where the number of persons is not equal to the number of jobs

If the number of persons is less than the number of jobs then we introduce one or more dummy persons (rows) with zero values to make the assignment problem balanced

Likewise if the number of jobs is less than the number of persons then we introduce one or more dummy jobs (columns) with zero values to make the assignment problem balanced

Unbalanced Assignment Problem

THANK YOU VERY MUCH

• Assignment Problem
• Introduction
• Slide 3
• Application Areas of Assignment Problem
• Cost Matrix in Assignment Problem
• Slide 6
• Method for Solving Assignment Prob
• Slide 8
• Slide 9
• Examples
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Find out the maximum profit possible through optimum assignment
• Slide 21
• Slide 22
• Unbalanced Assignment Problem
• Slide 24
• Slide 25
• THANK YOU VERY MUCH

It is an assignment problem where the number of persons is not equal to the number of jobs

If the number of persons is less than the number of jobs then we introduce one or more dummy persons (rows) with zero values to make the assignment problem balanced

Likewise if the number of jobs is less than the number of persons then we introduce one or more dummy jobs (columns) with zero values to make the assignment problem balanced

Unbalanced Assignment Problem

THANK YOU VERY MUCH

• Assignment Problem
• Introduction
• Slide 3
• Application Areas of Assignment Problem
• Cost Matrix in Assignment Problem
• Slide 6
• Method for Solving Assignment Prob
• Slide 8
• Slide 9
• Examples
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Find out the maximum profit possible through optimum assignment
• Slide 21
• Slide 22
• Unbalanced Assignment Problem
• Slide 24
• Slide 25
• THANK YOU VERY MUCH

THANK YOU VERY MUCH

• Assignment Problem
• Introduction
• Slide 3
• Application Areas of Assignment Problem
• Cost Matrix in Assignment Problem
• Slide 6
• Method for Solving Assignment Prob
• Slide 8
• Slide 9
• Examples
• Slide 11
• Slide 12
• Slide 13
• Slide 14
• Slide 15
• Slide 16
• Slide 17
• Slide 18
• Slide 19
• Find out the maximum profit possible through optimum assignment
• Slide 21
• Slide 22
• Unbalanced Assignment Problem
• Slide 24
• Slide 25
• THANK YOU VERY MUCH