The MBA Institute

Unbalanced Assignment Problem: Definition, Formulation, and Solution Methods

Table of Contents

Are you familiar with the assignment problem in Operations Research (OR)? This problem deals with assigning tasks to workers in a way that minimizes the total cost or time needed to complete the tasks. But what if the number of tasks and workers is not equal? In this case, we face the Unbalanced Assignment Problem (UAP). This blog will help you understand what the UAP is, how to formulate it, and how to solve it.

What is the Unbalanced Assignment Problem?

The Unbalanced Assignment Problem is an extension of the Assignment Problem in OR, where the number of tasks and workers is not equal. In the UAP, some tasks may remain unassigned, while some workers may not be assigned any task. The objective is still to minimize the total cost or time required to complete the assigned tasks, but the UAP has additional constraints that make it more complex than the traditional assignment problem.

Formulation of the Unbalanced Assignment Problem

To formulate the UAP, we start with a matrix that represents the cost or time required to assign each task to each worker. If the matrix is square, we can use the Hungarian algorithm to solve the problem. But when the matrix is not square, we need to add dummy tasks or workers to balance the matrix. These dummy tasks or workers have zero costs and are used to make the matrix square.

Once we have a square matrix, we can apply the Hungarian algorithm to find the optimal assignment. However, we need to be careful in interpreting the results, as the assignment may include dummy tasks or workers that are not actually assigned to anything.

Solutions for the Unbalanced Assignment Problem

Besides the Hungarian algorithm, there are other methods to solve the UAP, such as the transportation algorithm and the auction algorithm. The transportation algorithm is based on transforming the UAP into a transportation problem, which can be solved with the transportation simplex method. The auction algorithm is an iterative method that simulates a bidding process between the tasks and workers to find the optimal assignment.

In summary, the Unbalanced Assignment Problem is a variant of the traditional Assignment Problem in OR that deals with assigning tasks to workers when the number of tasks and workers is not equal. To solve the UAP, we need to balance the matrix by adding dummy tasks or workers and then apply algorithms such as the Hungarian algorithm, the transportation algorithm, or the auction algorithm. Understanding the UAP can help businesses and organizations optimize their resource allocation and improve their operational efficiency.

How useful was this post?

Click on a star to rate it!

Average rating 1.5 / 5. Vote count: 2

No votes so far! Be the first to rate this post.

We are sorry that this post was not useful for you! 😔

Let us improve this post!

Tell us how we can improve this post?

Operations Research

1 Operations Research-An Overview

  • History of O.R.
  • Approach, Techniques and Tools
  • Phases and Processes of O.R. Study
  • Typical Applications of O.R
  • Limitations of Operations Research
  • Models in Operations Research
  • O.R. in real world

2 Linear Programming: Formulation and Graphical Method

  • General formulation of Linear Programming Problem
  • Optimisation Models
  • Basics of Graphic Method
  • Important steps to draw graph
  • Multiple, Unbounded Solution and Infeasible Problems
  • Solving Linear Programming Graphically Using Computer
  • Application of Linear Programming in Business and Industry

3 Linear Programming-Simplex Method

  • Principle of Simplex Method
  • Computational aspect of Simplex Method
  • Simplex Method with several Decision Variables
  • Two Phase and M-method
  • Multiple Solution, Unbounded Solution and Infeasible Problem
  • Sensitivity Analysis
  • Dual Linear Programming Problem

4 Transportation Problem

  • Basic Feasible Solution of a Transportation Problem
  • Modified Distribution Method
  • Stepping Stone Method
  • Unbalanced Transportation Problem
  • Degenerate Transportation Problem
  • Transhipment Problem
  • Maximisation in a Transportation Problem

5 Assignment Problem

  • Solution of the Assignment Problem
  • Unbalanced Assignment Problem
  • Problem with some Infeasible Assignments
  • Maximisation in an Assignment Problem
  • Crew Assignment Problem

6 Application of Excel Solver to Solve LPP

  • Building Excel model for solving LP: An Illustrative Example

7 Goal Programming

  • Concepts of goal programming
  • Goal programming model formulation
  • Graphical method of goal programming
  • The simplex method of goal programming
  • Using Excel Solver to Solve Goal Programming Models
  • Application areas of goal programming

8 Integer Programming

  • Some Integer Programming Formulation Techniques
  • Binary Representation of General Integer Variables
  • Unimodularity
  • Cutting Plane Method
  • Branch and Bound Method
  • Solver Solution

9 Dynamic Programming

  • Dynamic Programming Methodology: An Example
  • Definitions and Notations
  • Dynamic Programming Applications

10 Non-Linear Programming

  • Solution of a Non-linear Programming Problem
  • Convex and Concave Functions
  • Kuhn-Tucker Conditions for Constrained Optimisation
  • Quadratic Programming
  • Separable Programming
  • NLP Models with Solver

11 Introduction to game theory and its Applications

  • Important terms in Game Theory
  • Saddle points
  • Mixed strategies: Games without saddle points
  • 2 x n games
  • Exploiting an opponent’s mistakes

12 Monte Carlo Simulation

  • Reasons for using simulation
  • Monte Carlo simulation
  • Limitations of simulation
  • Steps in the simulation process
  • Some practical applications of simulation
  • Two typical examples of hand-computed simulation
  • Computer simulation

13 Queueing Models

  • Characteristics of a queueing model
  • Notations and Symbols
  • Statistical methods in queueing
  • The M/M/I System
  • The M/M/C System
  • The M/Ek/I System
  • Decision problems in queueing
  

the assignment problem is said to be unbalanced if



> > Assignment Problem example (Using Hungarian method)
( ) )



4. Unbalanced Assignment Problem

\ IIIIIIIV
A9141915
B7172019
C9182118
D10121819
E10152116
   `I`  `II`  `III`  `IV`    
 `A` 
 `B` 
 `C` 
 `D` 
 `E` 
   
   `I`  `II`  `III`  `IV`  `J_5`    
 `A` 
 `B` 
 `C` 
 `D` 
 `E` 
   
   `I`  `II`  `III`  `IV`  `J_5`    
 `A`   `9=9-0`  `14=14-0`  `19=19-0`  `15=15-0`  `0=0-0`  Minimum element of `1^(st)` row
 `B`   `7=7-0`  `17=17-0`  `20=20-0`  `19=19-0`  `0=0-0`  Minimum element of `2^(nd)` row
 `C`   `9=9-0`  `18=18-0`  `21=21-0`  `18=18-0`  `0=0-0`  Minimum element of `3^(rd)` row
 `D`   `10=10-0`  `12=12-0`  `18=18-0`  `19=19-0`  `0=0-0`  Minimum element of `4^(th)` row
 `E`   `10=10-0`  `15=15-0`  `21=21-0`  `16=16-0`  `0=0-0`  Minimum element of `5^(th)` row
   
   `I`  `II`  `III`  `IV`  `J_5`    
 `A`   `2=9-7`  `2=14-12`  `1=19-18`  `0=15-15`  `0=0-0`
 `B`   `0=7-7`  `5=17-12`  `2=20-18`  `4=19-15`  `0=0-0`
 `C`   `2=9-7`  `6=18-12`  `3=21-18`  `3=18-15`  `0=0-0`
 `D`   `3=10-7`  `0=12-12`  `0=18-18`  `4=19-15`  `0=0-0`
 `E`   `3=10-7`  `3=15-12`  `3=21-18`  `1=16-15`  `0=0-0`
     Minimum element of `1^(st)` column  Minimum element of `2^(nd)` column  Minimum element of `3^(rd)` column  Minimum element of `4^(th)` column  Minimum element of `5^(th)` column
   `I`  `II`  `III`  `IV`  `J_5`    
 `A`   (4) Columnwise cell `(A,IV)` is assigned  Columnwise `(A,J_5)` crossed off because
(1) Rowwise cell `(C,J_5)` is assigned
 `B`   (2) Columnwise cell `(B,I)` is assigned  Columnwise `(B,J_5)` crossed off because
(1) Rowwise cell `(C,J_5)` is assigned
 `C`   (1) Rowwise cell `(C,J_5)` is assigned
so columnwise cell `(A,J_5)`,`(B,J_5)`,`(D,J_5)`,`(E,J_5)` crossed off.
 `D`   (3) Columnwise cell `(D,II)` is assigned
so rowwise cell `(D,III)` crossed off.
 Rowwise `(D,III)` crossed off because
(3) Columnwise cell `(D,II)` is assigned
 Columnwise `(D,J_5)` crossed off because
(1) Rowwise cell `(C,J_5)` is assigned
 `E`   Columnwise `(E,J_5)` crossed off because
(1) Rowwise cell `(C,J_5)` is assigned
   
   `I`  `II`  `III`  `IV`  `J_5`    
 `A` 
 `B` 
 `C`   (3) Mark(✓) row `C` since column `J_5` has an assignment in this row `C`.
 `D` 
 `E`   (1) Mark(✓) row `E` since it has no assignment
     (2) Mark(✓) column `J_5` since row `E` has 0 in this column
   `I`  `II`  `III`  `IV`  `J_5`    
 `A`   cell covered by a line  cell covered by a line  cell covered by a line  cell covered by a line  `1=0+1`
intersection cell of two lines
 `B`   cell covered by a line  cell covered by a line  cell covered by a line  cell covered by a line  `1=0+1`
intersection cell of two lines
 `C`   `1=2-1`
cell not covered by a line
 `5=6-1`
cell not covered by a line
 `2=3-1`
cell not covered by a line
 `2=3-1`
cell not covered by a line
 cell covered by a line
 `D`   cell covered by a line  cell covered by a line  cell covered by a line  cell covered by a line  `1=0+1`
intersection cell of two lines
 `E`   `2=3-1`
cell not covered by a line
 `2=3-1`
cell not covered by a line
 `2=3-1`
cell not covered by a line
 `0=1-1`
cell not covered by a line
 cell covered by a line
   
   `I`  `II`  `III`  `IV`  `J_5`    
 `A`   (1) Rowwise cell `(A,IV)` is assigned
so columnwise cell `(E,IV)` crossed off.
 `B`   (2) Rowwise cell `(B,I)` is assigned
 `C`   (3) Rowwise cell `(C,J_5)` is assigned
so columnwise cell `(E,J_5)` crossed off.
 `D`   (4) Columnwise cell `(D,II)` is assigned
so rowwise cell `(D,III)` crossed off.
 Rowwise `(D,III)` crossed off because
(4) Columnwise cell `(D,II)` is assigned
 `E`   Columnwise `(E,IV)` crossed off because
(1) Rowwise cell `(A,IV)` is assigned
 Columnwise `(E,J_5)` crossed off because
(3) Rowwise cell `(C,J_5)` is assigned
   
   `I`  `II`  `III`  `IV`  `J_5`    
 `A`   (4) Mark(✓) row `A` since column `IV` has an assignment in this row `A`.
 `B` 
 `C`   (5) Mark(✓) row `C` since column `J_5` has an assignment in this row `C`.
 `D` 
 `E`   (1) Mark(✓) row `E` since it has no assignment
     (2) Mark(✓) column `IV` since row `E` has 0 in this column  (3) Mark(✓) column `J_5` since row `E` has 0 in this column
   `I`  `II`  `III`  `IV`  `J_5`    
 `A`   `1=2-1`
cell not covered by a line
 `1=2-1`
cell not covered by a line
 `0=1-1`
cell not covered by a line
 cell covered by a line  cell covered by a line
 `B`   cell covered by a line  cell covered by a line  cell covered by a line  `5=4+1`
intersection cell of two lines
 `2=1+1`
intersection cell of two lines
 `C`   `0=1-1`
cell not covered by a line
 `4=5-1`
cell not covered by a line
 `1=2-1`
cell not covered by a line
 cell covered by a line  cell covered by a line
 `D`   cell covered by a line  cell covered by a line  cell covered by a line  `5=4+1`
intersection cell of two lines
 `2=1+1`
intersection cell of two lines
 `E`   `1=2-1`
cell not covered by a line
 `1=2-1`
cell not covered by a line
 `1=2-1`
cell not covered by a line
 cell covered by a line  cell covered by a line
   
   `I`  `II`  `III`  `IV`  `J_5`    
 `A`   (5) Columnwise cell `(A,III)` is assigned  Columnwise `(A,IV)` crossed off because
(3) Rowwise cell `(E,IV)` is assigned
 `B`   (1) Rowwise cell `(B,I)` is assigned
so columnwise cell `(C,I)` crossed off.
 `C`   Columnwise `(C,I)` crossed off because
(1) Rowwise cell `(B,I)` is assigned
 (2) Rowwise cell `(C,J_5)` is assigned
so columnwise cell `(E,J_5)` crossed off.
 `D`   (4) Columnwise cell `(D,II)` is assigned
so rowwise cell `(D,III)` crossed off.
 Rowwise `(D,III)` crossed off because
(4) Columnwise cell `(D,II)` is assigned
 `E`   (3) Rowwise cell `(E,IV)` is assigned
so columnwise cell `(A,IV)` crossed off.
 Columnwise `(E,J_5)` crossed off because
(2) Rowwise cell `(C,J_5)` is assigned
   
   `I`  `II`  `III`  `IV`  `J_5`    
 `A`   Original cost 9  Original cost 14  Original cost 19  Original cost 15  Original cost 0
 `B`   Original cost 7  Original cost 17  Original cost 20  Original cost 19  Original cost 0
 `C`   Original cost 9  Original cost 18  Original cost 21  Original cost 18  Original cost 0
 `D`   Original cost 10  Original cost 12  Original cost 18  Original cost 19  Original cost 0
 `E`   Original cost 10  Original cost 15  Original cost 21  Original cost 16  Original cost 0
   
WorkJobCost
`A``III`
`B``I`
`C``J_5`
`D``II`
`E``IV`
Total54

the assignment problem is said to be unbalanced if

the assignment problem is said to be unbalanced if

Unbalanced Assignment Problem

In the previous section, the number of persons and the number of jobs were assumed to be the same. In this section, we remove this assumption and consider a situation where the number of persons is not equal to the number of jobs . In all such cases, fictitious rows and/or columns are added in the matrix to make it a square matrix.

  • Maximization Problem
  • Multiple Optimal Solutions

Example: Unbalanced Assignment Problem

Job
Person 1 2 3 4
A 20 25 22 28
B 15 18 23 17
C 19 17 21 24

Since the number of persons is less than the number of jobs, we introduce a dummy person (D) with zero values. The revised assignment problem is given below:

Use Horizontal Scrollbar to View Full Table Calculation.

Job
Person 1 2 3 4
A 20 25 22 28
B 15 18 23 17
C 19 17 21 24
D (dummy) 0 0 0 0

Now use the Hungarian method to obtain the optimal solution yourself. Ans. = 20 + 17 + 17 + 0 = 54.

Share and Recommend

Operations Research Simplified Back Next

Goal programming Linear programming Simplex Method Transportation Problem

Quantitative Techniques: Theory and Problems by P. C. Tulsian, Vishal Pandey

Get full access to Quantitative Techniques: Theory and Problems and 60K+ other titles, with a free 10-day trial of O'Reilly.

There are also live events, courses curated by job role, and more.

UNBALANCED ASSIGNMENT PROBLEM

Unbalanced Assignment problem is an assignment problem where the number of facilities is not equal to the number of jobs. To make unbalanced assignment problem, a balanced one, a dummy facility(s) or a dummy job(s) (as the case may be) is introduced with zero cost or time.

Get Quantitative Techniques: Theory and Problems now with the O’Reilly learning platform.

O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.

Don’t leave empty-handed

Get Mark Richards’s Software Architecture Patterns ebook to better understand how to design components—and how they should interact.

It’s yours, free.

Cover of Software Architecture Patterns

Check it out now on O’Reilly

Dive in for free with a 10-day trial of the O’Reilly learning platform—then explore all the other resources our members count on to build skills and solve problems every day.

the assignment problem is said to be unbalanced if

Assignment Problem: Meaning, Methods and Variations | Operations Research

the assignment problem is said to be unbalanced if

After reading this article you will learn about:- 1. Meaning of Assignment Problem 2. Definition of Assignment Problem 3. Mathematical Formulation 4. Hungarian Method 5. Variations.

Meaning of Assignment Problem:

An assignment problem is a particular case of transportation problem where the objective is to assign a number of resources to an equal number of activities so as to minimise total cost or maximize total profit of allocation.

The problem of assignment arises because available resources such as men, machines etc. have varying degrees of efficiency for performing different activities, therefore, cost, profit or loss of performing the different activities is different.

Thus, the problem is “How should the assignments be made so as to optimize the given objective”. Some of the problem where the assignment technique may be useful are assignment of workers to machines, salesman to different sales areas.

Definition of Assignment Problem:

ADVERTISEMENTS:

Suppose there are n jobs to be performed and n persons are available for doing these jobs. Assume that each person can do each job at a term, though with varying degree of efficiency, let c ij be the cost if the i-th person is assigned to the j-th job. The problem is to find an assignment (which job should be assigned to which person one on-one basis) So that the total cost of performing all jobs is minimum, problem of this kind are known as assignment problem.

The assignment problem can be stated in the form of n x n cost matrix C real members as given in the following table:

the assignment problem is said to be unbalanced if

Solving the Unbalanced Assignment Problem: Simpler Is Better

Profile image of Francis Vasko

American Journal of Operations Research

Related Papers

Dr Avanish Kumar

the assignment problem is said to be unbalanced if

Bhausaheb G Kore

In this paper I have proposed a new approach to solve an unbalanced assignment problem (UBAP). This approach includes two parts. First is to obtain an initial basic feasible solution (IBFS) and second part is to test optimality of an IBFS. I have proposed two new methods Row Penalty Assignment Method (RPAM) and Column Penalty Assignment Method (CPAM) to obtain an IBFS of an UBAP. Also I have proposed a new method Non-basic Smallest Effectiveness Method (NBSEM) to test optimality of an IBFS. We can solve an assignment problem of maximization type using this new approach in opposite sense. By this new approach, we achieve the goal with less number of computations and steps. Further we illustrate the new approach by suitable examples. INTRODUCTION The assignment problem is a special case of the transportation problem where the resources are being allocated to the activities on a one-to-one basis. Thus, each resource (e.g. an employee, machine or time slot) is to be assigned uniquely to a particular activity (e.g. a task, site or event). In assignment problems, supply in each row represents the availability of a resource such as a man, machine, vehicle, product, salesman, etc. and demand in each column represents different activities to be performed such as jobs, routes, factories, areas, etc. for each of which only one man or vehicle or product or salesman respectively is required. Entries in the square being costs, times or distances. The assignment method is a special linear programming technique for solving problems like choosing the right man for the right job when more than one choice is possible and when each man can perform all of the jobs. The ultimate objective is to assign a number of tasks to an equal number of facilities at minimum cost (or maximum profit) or some other specific goal. Let there be 'm' resources and 'n' activities. Let c ij be the effectiveness (in terms of cost, profit, time, etc.) of assigning resource i to activity j (i = 1, 2, …., m; j = 1, 2,…., n). Let x ij = 0, if resource i is not assigned to activity j and x ij = 1, if resource i is assigned to activity j. Then the objective is to determine x ij 's that will optimize the total effectiveness (Z) satisfying all the resource constraints and activity constraints. 1. Mathematical Formulation Let number of rows = m and number of columns = n. If m = n then an AP is said to be BAP otherwise it is said to be UBAP. A) Case 1: If m < n then mathematically the UBAP can be stated as follows:

Malaya Journal of Matematik

DR ANJU KHANDELWAL

International Journal for Research in Applied Science & Engineering Technology (IJRASET)

IJRASET Publication

In this paper a new method is proposed for finding an optimal solution of a wide range of assignment problems, directly. A numerical illustration is established and the optimality of the result yielded by this method is also checked. The most attractive feature of this method is that it requires very simple arithmetical and logical calculations. The method is illustrated through an example.

Hussein Ali Hussein Al-Dallal Al-Saeedi

archana pandey

Assignment problems arise in different situation where we have to find an optimal way to assign n-objects to mother objects in an injective fashion. The assignment problems are a well studied topic in combinatorial optimization. These problems find numerous application in production planning, telecommunication VLSI design, economic etc. The assignment problems is a special case of Transportation problem. Depending on the objective we want to optimize, we obtain the typical assignment problems. Assignment problem is an important subject discussed in real physical world we endeavor in this paper to introduce a new approach to assignment problem namely, matrix ones assignment method or MOA-method for solving wide range of problem. An example using matrix ones assignment methods and the existing Hungarian method have been solved and compared it graphically. Also some of the variations and some special cases in assignment problem and its applications have been discussed in the paper.

Sultana Rafi

The assignment problem is a particular type of linear programming problem. In this paper, we analyzed the standard and existing proposed methods. After studying these methods, we proposed a new alternative method for solving the assignment problem. We examined the newly proposed method by a couple of numerical examples and compare this result with the standard method. The main characteristic of this newly proposed method is that it constructed a very easy logical and arithmetical algorithm. Here we point out some advantages and limitations of the new proposed method. Programming code for the newly proposed method has been added in this paper.

Ranjan Kumar Mondal

Thecloudcomputingpresentsatypeofassignmentsandsystemswhichoccupydistributedresources toexecutearoleinadistributedway.Cloudcomputingmakeuseoftheonlinesystemsonthewebto assisttheimplementationofcomplicatedassignments;thatneedhuge-scalecomputation.Itwassaid withtheintentionofinourlivingworld;wecanfinditchallengingtobalanceworkloadsofcloud computingamongassignments(jobsortasks)andsystems(machinesornodes),sothemajorityofthe timewehavetopromoteaconditiontounbalancedassignmentproblems(unequaltaskallocations). The present article submits a new technique to solve the unequal task allocation problems. The techniqueisofferedinanalgorithmicmodelandputintopracticeontheseveralgroupsofinputto investigatethepresentationandusefulnessoftheworks.Anevaluationispreparedwiththepresented approach.Itmakessurethattheproposedapproachprovidesabetteroutcomebycomparingwith someotherexistingalgorithms.

Industrial Engineering Journal

Shridhar Mhalsekar

Journal of Advances in Mathematics and Computer Science

Hudu Mohammed

Assignment problem is an important area in Operation Research and is also discussed in real physical world. In this paper an attempt has been made to solve the assignment problem using a new Method called the Penalty method. We discuss a numerical example by using the new Method and compare it with standard existing method which is the Hungarian method. We compare the optimal solution of the new Method and the Hungarian method. The new method is a simple procedure, easy to apply for solving assignment problem.

Loading Preview

Sorry, preview is currently unavailable. You can download the paper by clicking the button above.

RELATED PAPERS

Philippe Laborie

Michael Florian

Journal of Mathematics and Informatics

Sophia Porchelvi

IOP Publishing

Ajit Pal Singh

YMER Digital

Kalpana Dahiya

Mr Ebenezer Quayson

Transportation Research Part B: Methodological

Michael Patriksson

Applied Mathematical Sciences

Anwar N Jasim

Trisna Darmawansyah

IOSR Journals

Springer eBooks

Mourad Baiou

Oksana Pichugina

Discrete Applied Mathematics

Kurt Jörnsten

European Journal of Operational Research

American Scientific Research Journal for Engineering, Technology, and Sciences

humayra afroz

Nanda Piersma

RELATED TOPICS

  •   We're Hiring!
  •   Help Center
  • Find new research papers in:
  • Health Sciences
  • Earth Sciences
  • Cognitive Science
  • Mathematics
  • Computer Science
  • Academia ©2024

Nash Balanced Assignment Problem

  • Conference paper
  • First Online: 21 November 2022
  • Cite this conference paper

the assignment problem is said to be unbalanced if

  • Minh Hieu Nguyen 11 ,
  • Mourad Baiou 11 &
  • Viet Hung Nguyen 11  

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13526))

Included in the following conference series:

  • International Symposium on Combinatorial Optimization

385 Accesses

2 Citations

In this paper, we consider a variant of the classic Assignment Problem (AP), called the Balanced Assignment Problem (BAP) [ 2 ]. The BAP seeks to find an assignment solution which has the smallest value of max-min distance : the difference between the maximum assignment cost and the minimum one. However, by minimizing only the max-min distance, the total cost of the BAP solution is neglected and it may lead to an inefficient solution in terms of total cost. Hence, we propose a fair way based on Nash equilibrium [ 1 , 3 , 4 ] to inject the total cost into the objective function of the BAP for finding assignment solutions having a better trade-off between the two objectives: the first aims at minimizing the total cost and the second aims at minimizing the max-min distance. For this purpose, we introduce the concept of Nash Fairness (NF) solutions based on the definition of proportional-fair scheduling adapted in the context of the AP: a transfer of utilities between the total cost and the max-min distance is considered to be fair if the percentage increase in the total cost is smaller than the percentage decrease in the max-min distance and vice versa.

We first show the existence of a NF solution for the AP which is exactly the optimal solution minimizing the product of the total cost and the max-min distance. However, finding such a solution may be difficult as it requires to minimize a concave function. The main result of this paper is to show that finding all NF solutions can be done in polynomial time. For that, we propose a Newton-based iterative algorithm converging to NF solutions in polynomial time. It consists in optimizing a sequence of linear combinations of the two objective based on Weighted Sum Method [ 5 ]. Computational results on various instances of the AP are presented and commented.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save.

  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
  • Available as EPUB and PDF
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

The fair owa one-to-one assignment problem: np-hardness and polynomial time special cases.

the assignment problem is said to be unbalanced if

An Efficient Primal-Dual Algorithm for Fair Combinatorial Optimization Problems

the assignment problem is said to be unbalanced if

Restricted Max-Min Allocation: Integrality Gap and Approximation Algorithm

Bertsimas, D., Farias, V.F., Trichakis, N.: The price of fairness. Oper. Res. January–February 59 (1), 17–31 (2011)

MathSciNet   MATH   Google Scholar  

Martello, S., Pulleyblank, W.R., Toth, P., De Werra, D.: Balanced optimization problems. Oper. Res. Lett. 3 (5), 275–278 (1984)

Article   MathSciNet   MATH   Google Scholar  

Kelly, F.P., Maullo, A.K., Tan, D.K.H.: Rate control for communication networks: shadow prices, proportional fairness and stability. J. Oper. Res. Soc. 49 (3), 237–252 (1997). https://doi.org/10.1057/palgrave.jors.2600523

Article   Google Scholar  

Ogryczak, W., Luss, H., Pioro, M., Nace, D., Tomaszewski, A.: Fair optimization and networks: a survey. J. Appl. Math. 2014 , 1–26 (2014)

Marler, R.T., Arora, J.S.: The weighted sum method for multi-objective optimization: new insights. Struct. Multi. Optim. 41 (6), 853–862 (2010)

Heller, I., Tompkins, C.B.: An extension of a theorem of Dantzig’s. Ann. Math. Stud. (38), 247–254 (1956)

Google Scholar  

Kuhn, H.W.: The Hungarian method for assignment problem. Naval Res. Logist. Q. 2 (1–2), 83–97 (1955)

Martello, S.: Most and least uniform spanning trees. Discrete Appl. Math. 15 (2), 181–197 (1986)

Beasley, J.E.: Linear programming on Clay supercomputer. J. Oper. Res. Soc. 41 , 133–139 (1990)

Nguyen, M.H, Baiou, M., Nguyen, V.H., Vo, T.Q.T.: Nash fairness solutions for balanced TSP. In: International Network Optimization Conference (INOC2022) (2022)

Download references

Author information

Authors and affiliations.

INP Clermont Auvergne, Univ Clermont Auvergne, Mines Saint-Etienne, CNRS, UMR 6158 LIMOS, 1 Rue de la Chebarde, Aubiere Cedex, France

Minh Hieu Nguyen, Mourad Baiou & Viet Hung Nguyen

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to Viet Hung Nguyen .

Editor information

Editors and affiliations.

ESSEC Business School of Paris, Cergy Pontoise Cedex, France

Ivana Ljubić

IBM TJ Watson Research Center, Yorktown Heights, NY, USA

Francisco Barahona

Georgia Institute of Technology, Atlanta, GA, USA

Santanu S. Dey

Université Paris-Dauphine, Paris, France

A. Ridha Mahjoub

Proposition 1 . There may be more than one NF solution for the AP.

Let us illustrate this by an instance of the AP having the following cost matrix

By verifying all feasible assignment solutions in this instance, we obtain easily three assignment solutions \((1-1, 2-2, 3-3), (1-2, 2-3, 3-1)\) , \((1-3, 2-2, 3-1)\) and \((1-3, 2-1, 3-2)\) corresponding to 4 NF solutions (280, 36), (320, 32), (340, 30) and (364, 28). Note that \(i-j\) where \(1 \le i,j \le 3\) represents the assignment between worker i and job j in the solution of this instance.     \(\square \)

We recall below the proofs of some recent results that we have published in [ 10 ]. They are needed to prove the new results presented in this paper.

Theorem 2 [ 10 ] . \((P^{*},Q^{*}) = {{\,\mathrm{arg\,min}\,}}_{(P,Q) \in \mathcal {S}} PQ\) is a NF solution.

Obviously, there always exists a solution \((P^{*},Q^{*}) \in \mathcal {S}\) such that

Now \(\forall (P',Q') \in \mathcal {S}\) we have \(P'Q' \ge P^{*}Q^{*}\) . Then

The first inequality holds by the Cauchy-Schwarz inequality.

Hence, \((P^{*},Q^{*})\) is a NF solution.     \(\square \)

Theorem 3 [ 10 ] . \((P^{*},Q^{*}) \in \mathcal {S}\) is a NF solution if and only if \((P^{*},Q^{*})\) is an optimal solution of \(\mathcal {P(\alpha ^{*})}\) where \(\alpha ^{*} = \frac{Q^{*}}{P^{*}}\) .

Firstly, let \((P^{*},Q^{*})\) be a NF solution and \(\alpha ^{*} = \frac{Q^{*}}{P^{*}}\) . We will show that \((P^{*},Q^{*})\) is an optimal solution of \(\mathcal {P(\alpha ^{*})}\) .

Since \((P^{*},Q^{*})\) is a NF solution, we have

Since \(\alpha ^{*} = \frac{Q^{*}}{P^{*}}\) , we have \(\alpha ^{*}P^{*}+Q^{*} = 2Q^{*}\) .

Dividing two sides of ( 6 ) by \(P^{*} > 0\) we obtain

So we deduce from ( 7 )

Hence, \((P^{*},Q^{*})\) is an optimal solution of \(\mathcal {P}(\alpha ^{*})\) .

Now suppose \(\alpha ^{*} = \frac{Q^{*}}{P^{*}}\) and \((P^{*},Q^{*})\) is an optimal solution of \(\mathcal {P}(\alpha ^{*})\) , we show that \((P^{*},Q^{*})\) is a NF solution.

If \((P^{*},Q^{*})\) is not a NF solution, there exists a solution \((P',Q') \in \mathcal {S}\) such that

We have then

which contradicts the optimality of \((P^{*},Q^{*})\) .     \(\square \)

Lemma 3 [ 10 ] . Let \(\alpha , \alpha ' \in \mathbb {R}_+\) and \((P_{\alpha }, Q_{\alpha })\) , \((P_{\alpha '}, Q_{\alpha '})\) be the optimal solutions of \(\mathcal {P(\alpha )}\) and \(\mathcal {P(\alpha ')}\) respectively, if \(\alpha \le \alpha '\) then \(P_{\alpha } \ge P_{\alpha '}\) and \(Q_{\alpha } \le Q_{\alpha '}\) .

The optimality of \((P_{\alpha }, Q_{\alpha })\) and \((P_{\alpha '}, Q_{\alpha '})\) gives

By adding both sides of ( 8a ) and ( 8b ), we obtain \((\alpha - \alpha ') (P_{\alpha } - P_{\alpha '}) \le 0\) . Since \(\alpha \le \alpha '\) , it follows that \(P_{\alpha } \ge P_{\alpha '}\) .

On the other hand, inequality ( 8a ) implies \(Q_{\alpha '} - Q_{\alpha } \ge \alpha (P_{\alpha } - P_{\alpha '}) \ge 0\) that leads to \(Q_{\alpha } \le Q_{\alpha '}\) .     \(\square \)

Lemma 4 [ 10 ] . During the execution of Procedure Find ( \(\alpha _{0})\) in Algorithm 1 , \(\alpha _{i} \in [0,1], \, \forall i \ge 1\) . Moreover, if \(T_{0} \ge 0\) then the sequence \(\{\alpha _i\}\) is non-increasing and \(T_{i} \ge 0, \, \forall i \ge 0\) . Otherwise, if \(T_{0} \le 0\) then the sequence \(\{\alpha _i\}\) is non-decreasing and \(T_{i} \le 0, \, \forall i \ge 0\) .

Since \(P \ge Q \ge 0, \, \forall (P, Q) \in \mathcal {S}\) , it follows that \(\alpha _{i+1} = \frac{Q_i}{P_i} \in [0,1], \, \forall i \ge 0\) .

We first consider \(T_{0} \ge 0\) . We proof \(\alpha _i \ge \alpha _{i+1}, \, \forall i \ge 0\) by induction on i . For \(i = 0\) , we have \(T_{0} = \alpha _{0} P_{0} - Q_{0} = P_{0}(\alpha _{0}-\alpha _{1}) \ge 0\) , it follows that \(\alpha _{0} \ge \alpha _{1}\) . Suppose that our hypothesis is true until \(i = k \ge 0\) , we will prove that it is also true with \(i = k+1\) .

Indeed, we have

The inductive hypothesis gives \(\alpha _k \ge \alpha _{k+1}\) that implies \(P_{k+1} \ge P_k > 0\) and \(Q_{k} \ge Q_{k+1} \ge 0\) according to Lemma 3 . It leads to \(Q_{k}P_{k+1} - P_{k}Q_{k+1} \ge 0\) and then \(\alpha _{k+1} - \alpha _{k+2} \ge 0\) .

Hence, we have \(\alpha _{i} \ge \alpha _{i+1}, \, \forall i \ge 0\) .

Consequently, \(T_{i} = \alpha _{i}P_{i} - Q_{i} = P_{i}(\alpha _{i}-\alpha _{i+1}) \ge 0, \, \forall i \ge 0\) .

Similarly, if \(T_{0} \le 0\) we obtain that the sequence \(\{\alpha _i\}\) is non-decreasing and \(T_{i} \le 0, \, \forall i \ge 0\) . That concludes the proof.     \(\square \)

Lemma 5 [ 10 ] . From each \(\alpha _{0} \in [0,1]\) , Procedure Find \((\alpha _{0})\) converges to a coefficient \(\alpha _{k} \in \mathcal {C}_{0}\) satisfying \(\alpha _{k}\) is the unique element \(\in \mathcal {C}_{0}\) between \(\alpha _{0}\) and \(\alpha _{k}\) .

As a consequence of Lemma 4 , Procedure \(\textit{Find}(\alpha _{0})\) converges to a coefficient \(\alpha _{k} \in [0,1], \forall \alpha _{0} \in [0,1]\) .

By the stopping criteria of Procedure Find \((\alpha _{0})\) , when \(T_{k} = \alpha _{k} P_{k} - Q_{k} = 0\) we obtain \(\alpha _{k} \in C_{0}\) and \((P_{k},Q_{k})\) is a NF solution. (Theorem 3 )

If \(T_{0} = 0\) then obviously \(\alpha _{k} = \alpha _{0}\) . We consider \(T_{0} > 0\) and the sequence \(\{\alpha _i\}\) is now non-negative, non-increasing. We will show that \([\alpha _{k},\alpha _{0}] \cap \mathcal {C}_{0} = \alpha _{k}\) .

Suppose that we have \(\alpha \in (\alpha _{k},\alpha _{0}]\) and \(\alpha \in \mathcal {C}_{0}\) corresponding to a NF solution ( P ,  Q ). Then there exists \(1 \le i \le k\) such that \(\alpha \in (\alpha _{i}, \alpha _{i-1}]\) . Since \(\alpha \le \alpha _{i-1}\) , \(P \ge P_{i-1}\) and \(Q \le Q_{i-1}\) due to Lemma 3 . Thus, we get

By the definitions of \(\alpha \) and \(\alpha _{i}\) , inequality ( 9 ) is equivalent to \(\alpha \le \alpha _{i}\) which leads to a contradiction.

By repeating the same argument for \(T_{0} < 0\) , we also have a contradiction.     \(\square \)

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Cite this paper.

Nguyen, M.H., Baiou, M., Nguyen, V.H. (2022). Nash Balanced Assignment Problem. In: Ljubić, I., Barahona, F., Dey, S.S., Mahjoub, A.R. (eds) Combinatorial Optimization. ISCO 2022. Lecture Notes in Computer Science, vol 13526. Springer, Cham. https://doi.org/10.1007/978-3-031-18530-4_13

Download citation

DOI : https://doi.org/10.1007/978-3-031-18530-4_13

Published : 21 November 2022

Publisher Name : Springer, Cham

Print ISBN : 978-3-031-18529-8

Online ISBN : 978-3-031-18530-4

eBook Packages : Computer Science Computer Science (R0)

Share this paper

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

  • Publish with us

Policies and ethics

  • Find a journal
  • Track your research
  • DOI: 10.4236/AJOR.2016.64028
  • Corpus ID: 124980289

Solving the Unbalanced Assignment Problem: Simpler Is Better

  • Nathan K. Betts , Francis J. Vasko
  • Published 24 June 2016
  • Mathematics
  • American Journal of Operations Research

Tables from this paper

table 1

9 Citations

An amalgamated approach for solving unbalanced assignment problem, modified hungarian method for unbalanced assignment problem with multiple jobs, modified hungarian method for solving balanced fuzzy transportation problems.

  • Highly Influenced

Application of WinQSB for Assignment Models

A general statistical physics framework for assignment problems, where will the next emergency event occur predicting ambulance demand in emergency medical services using artificial intelligence, multi-sensor dynamic scheduling for defending uav swarms with fresnel zone under complex terrain., novel optimization method for unbalanced assignment problems with multiple jobs: the dhouib-matrix-ap2, graph based twin cost matrices for unbalanced assignment problem with improved ant colony algorithm, 6 references, a new approach of solving single objective unbalanced assignment problem.

  • Highly Influential

Operations research : applications and algorithms

The hungarian method for the assignment problem, introduction to operations research, a lexisearch approach to some combinatorial programming problems, related papers.

Showing 1 through 3 of 0 Related Papers

Tim Walz's military record: What to know about potential VP's National Guard service

the assignment problem is said to be unbalanced if

Democratic presidential candidate Kamala Harris selected Minnesota Governor Tim Walz as her running mate on Tuesday, choosing a progressive yet plain-spoken VP candidate from America’s heartland to help her win over rural, white voters.

“I’m pleased to share that I’ve made my decision: Minnesota Governor Tim Walz will join our campaign as my running mate,” Harris said via text to supporters. “Tim is a battle-tested leader who has an incredible track record of getting things done for Minnesota families. I know that he will bring that same principled leadership to our campaign, and to the office of the vice president.”

We look at Walz, a 60-year-old U.S. Army National Guard veteran, and his military career over the years.

More: Tim Walz is Kamala Harris' VP pick: Minnesota governor named running mate: Live updates

How long was Walz in the military?

Walz served in the military for 24 years, enlisting in the Nebraska National Guard at 17 in 1981 and then transferring to the Minnesota National Guard in 1996. He retired in 2005 to begin his successful run for the U.S. House, representing Minnesota as command sergeant major, among the highest ranks for enlisted soldiers. His battalion went on to deploy to Iraq shortly after Walz's retirement.

Walz specialized in heavy artillery and had proficiency ribbons in sharpshooting and hand grenades.

But during the 21 years that Walz spent working with large artillery pieces, he suffered hearing loss and tinnitus in both ears, Minnesota Public Radio reported. He was allowed to continue his service after undergoing surgery, which partially resolved his hearing loss.

Where did Walz serve, and what did he do in the National Guard?

During his service, Walz responded to natural disasters, including floods and tornadoes in Minnesota and Nebraska, and was deployed overseas for months at a time, according to MPR.

In 2003, he was sent to Italy, where he served with the European Security Force to support the war in Afghanistan. He was also stationed in Norway for joint training with other NATO militaries.

Walz told MPR that he reenlisted in the National Guard after the September 11 attacks but never saw active combat in his years in the military.

Stars and Stripes reported in 2020 that Walz credited his Army experience with helping him steer Minnesota through the COVID-19 pandemic as governor.

As governor of Minnesota, Walz is commander in chief of the 13,000-soldier Minnesota National Guard. “I’m certainly proud of my military service, but it’s one piece of me,” he told Minnesota Public Radio in 2018. “It doesn’t define me.”

Reuters and USA TODAY reporter Tom Vanden Brook contributed to this story.

The assignment problem is said to be unbalance if - Mathematics and Statistics

Advertisements.

The assignment problem is said to be unbalance if ______

Number of rows is greater than number of columns

Number of rows is lesser than number of columns

Number of rows is equal to number of columns

Both (a) and (b)

Solution Show Solution

Both (a) and (b) .

Video Tutorials VIEW ALL [1]

  • view Video Tutorials For All Subjects
  • Assignment Problem video tutorial 00:20:25

RELATED QUESTIONS

A job production unit has four jobs A, B, C, D which can be manufactured on each of the four machines P, Q, R and S. The processing cost of each job is given in the following table:

         Jobs

 

 

                          Machines

P

Q

R

S

                Processing Cost (Rs.)

 

A

31

25

33

29

B

25

24

23

21

C

19

21

23

24

D

38

36

34

40

 How should the jobs be assigned to the four machines so that the total processing cost is minimum?

Solve the following minimal assignment problem and hence find the minimum value : 

 
2 10 9 7
13 2 12 2
3 4 6 1
4 15 4 9

Suggest optimum solution to the following assignment. Problem, also find the total minimum service time.                                              Service Time ( in hrs.)

41 72 39 52
22 29 49 65
27 39 60 51
45 50 48 52

Solve the following minimal assignment problem : 

Machines A B C D E
M 27 18 20 21
M 31 24 21 12 17
M 20 17 20 16
M 21 28 20 16 27

A departmental head has three jobs and four subordinates. The subordinates differ in their capabilities and the jobs differ in their work contents. With the help of the performance matrix given below, find out which of the four subordinates should be assigned which jobs ?

Subordinates Jobs
I II III
A 7 3 5
B 2 7 4
C 6 5 3
D 3 4 7

A job production unit has four jobs A, B, C, D which can be manufactured on each of the four machines P, Q, R and S. The processing cost of each job for each machine is given in the following table:


A 31 25 33 29
B 25 24 23 21
C 19 21 23 24
D 38 36 34 40

Find the optimal assignment to minimize the total processing cost.

Five wagons are available at stations 1, 2, 3, 4, and 5. These are required at 5 stations I, II, III, IV, and V. The mileage between various stations are given in the table below. How should the wagons be transported so as to minimize the mileage covered?

 
10 5 9 18 11
13 9 6 12 14
3 2 4 4 5
18 9 12 17 15
11 6 14 19 10

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

30 37 40 28 40
40 24 27 21 36
40 32 33 30 35
25 38 40 36 36
29 62 41 34 39

Find the optimal assignment schedule.

Choose the correct alternative :

The assignment problem is said to be balanced if it is a ______.

In an assignment problem if number of rows is greater than number of columns then

Fill in the blank :

When an assignment problem has more than one solution, then it is _______ optimal solution.

An _______ is a special type of linear programming problem.

In an assignment problem, if number of column is greater than number of rows, then a dummy column is added.

State whether the following is True or False :

In assignment problem, each facility is capable of performing each task.

It is not necessary to express an assignment problem into n x n matrix.

Solve the following problem :

A plant manager has four subordinates, and four tasks to be performed. The subordinates differ in efficiency and the tasks differ in their intrinsic difficulty. This estimate of the time each man would take to perform each task is given in the effectiveness matrix below.

 
7 25 26 10
12 27 3 25
37 18 17 14
18 25 23 9

How should the tasks be allocated, one to a man, as to minimize the total man hours?

A dairy plant has five milk tankers, I, II, III, IV and V. These milk tankers are to be used on five delivery routes A, B, C, D and E. The distances (in kms) between the dairy plant and the delivery routes are given in the following distance matrix.

 
150 120 175 180 200
125 110 120 150 165
130 100 145 160 175
40 40 70 70 100
45 25 60 70 95

How should the milk tankers be assigned to the chilling center so as to minimize the distance travelled?

Choose the correct alternative:

The assignment problem is generally defined as a problem of ______

Choose the correct alternative: 

Assignment Problem is special case of ______

When an assignment problem has more than one solution, then it is ______

The assignment problem is said to be balanced if ______

If the given matrix is ______ matrix, the assignment problem is called balanced problem

In an assignment problem if number of rows is greater than number of columns, then dummy ______ is added

State whether the following statement is True or False:

The objective of an assignment problem is to assign number of jobs to equal number of persons at maximum cost

In assignment problem, if number of columns is greater than number of rows, then a dummy row is added

State whether the following statement is True or False: 

In assignment problem each worker or machine is assigned only one job

What is the Assignment problem?

What is the difference between Assignment Problem and Transportation Problem?

Three jobs A, B and C one to be assigned to three machines U, V and W. The processing cost for each job machine combination is shown in the matrix given below. Determine the allocation that minimizes the overall processing cost.

    Machine
    U V W
Jobs A 17 25 31
B 10 25 16
C 12 14 11

(cost is in ₹ per unit)

A computer centre has got three expert programmers. The centre needs three application programmes to be developed. The head of the computer centre, after studying carefully the programmes to be developed, estimates the computer time in minitues required by the experts to the application programme as follows.

  Programmers
    P Q R
Programmers 1 120 100 80
  2 80 90 110
  3 110 140 120

Assign the programmers to the programme in such a way that the total computer time is least.

A departmental head has four subordinates and four tasks to be performed. The subordinates differ in efficiency and the tasks differ in their intrinsic difficulty. His estimates of the time each man would take to perform each task is given below:

    Tasks
    1 2 3 4
Subordinates P 8 26 17 11
  Q 13 28 4 26
  R 38 19 18 15
  S 9 26 24 10

How should the tasks be allocated to subordinates so as to minimize the total manhours?

Number of basic allocation in any row or column in an assignment problem can be

The solution for an assignment problem is optimal if

In an assignment problem involving four workers and three jobs, total number of assignments possible are

A car hire company has one car at each of five depots a, b, c, d and e. A customer in each of the fine towers A, B, C, D and E requires a car. The distance (in miles) between the depots (origins) and the towers(destinations) where the customers are given in the following distance matrix.

  a b c d e
A 160 130 175 190 200
B 135 120 130 160 175
C 140 110 155 170 185
D 50 50 80 80 110
E 55 35 70 80 105

How should the cars be assigned to the customers so as to minimize the distance travelled?

A natural truck-rental service has a surplus of one truck in each of the cities 1, 2, 3, 4, 5 and 6 and a deficit of one truck in each of the cities 7, 8, 9, 10, 11 and 12. The distance(in kilometers) between the cities with a surplus and the cities with a deficit are displayed below:

    To
    7 8 9 10 11 12
From 1 31 62 29 42 15 41
2 12 19 39 55 71 40
3 17 29 50 41 22 22
4 35 40 38 42 27 33
5 19 30 29 16 20 33
6 72 30 30 50 41 20

How should the truck be dispersed so as to minimize the total distance travelled?

A dairy plant has five milk tankers, I, II, III, IV and V. Three milk tankers are to be used on five delivery routes A, B, C, D and E. The distances (in kms) between the dairy plant and the delivery routes are given in the following distance matrix.

 
150 120 175 180 200
125 110 120 150 165
130 100 145 160 170
40 40 70 70 100
45 25 60 70 95

A job production unit has four jobs P, Q, R, and S which can be manufactured on each of the four machines I, II, III, and IV. The processing cost of each job for each machine is given in the following table:


P 31 25 33 29
Q 25 24 23 21
R 19 21 23 24
S 38 36 34 40

A department store has four workers to pack goods. The times (in minutes) required for each worker to complete the packings per item sold is given below. How should the manager of the store assign the jobs to the workers, so as to minimize the total time of packing?

  Books Toys Crockery Cutlery
3 11 10 8
13 2 12 12
3 4 6 1
4 15 4 9

Five wagons are available at stations 1, 2, 3, 4 and 5. These are required at 5 stations I, II, III, IV and V. The mileage between various stations are given in the table below. How should the wagons be transported so as to minimize the mileage covered?

 
10 5 9 18 11
13 9 6 12 14
7 2 4 4 5
18 9 12 17 15
11 6 14 19 10

Download the Shaalaa app from the Google Play Store

  • Maharashtra Board Question Bank with Solutions (Official)
  • Balbharati Solutions (Maharashtra)
  • Samacheer Kalvi Solutions (Tamil Nadu)
  • NCERT Solutions
  • RD Sharma Solutions
  • RD Sharma Class 10 Solutions
  • RD Sharma Class 9 Solutions
  • Lakhmir Singh Solutions
  • TS Grewal Solutions
  • ICSE Class 10 Solutions
  • Selina ICSE Concise Solutions
  • Frank ICSE Solutions
  • ML Aggarwal Solutions
  • NCERT Solutions for Class 12 Maths
  • NCERT Solutions for Class 12 Physics
  • NCERT Solutions for Class 12 Chemistry
  • NCERT Solutions for Class 12 Biology
  • NCERT Solutions for Class 11 Maths
  • NCERT Solutions for Class 11 Physics
  • NCERT Solutions for Class 11 Chemistry
  • NCERT Solutions for Class 11 Biology
  • NCERT Solutions for Class 10 Maths
  • NCERT Solutions for Class 10 Science
  • NCERT Solutions for Class 9 Maths
  • NCERT Solutions for Class 9 Science
  • CBSE Study Material
  • Maharashtra State Board Study Material
  • Tamil Nadu State Board Study Material
  • CISCE ICSE / ISC Study Material
  • Mumbai University Engineering Study Material
  • CBSE Previous Year Question Paper With Solution for Class 12 Arts
  • CBSE Previous Year Question Paper With Solution for Class 12 Commerce
  • CBSE Previous Year Question Paper With Solution for Class 12 Science
  • CBSE Previous Year Question Paper With Solution for Class 10
  • Maharashtra State Board Previous Year Question Paper With Solution for Class 12 Arts
  • Maharashtra State Board Previous Year Question Paper With Solution for Class 12 Commerce
  • Maharashtra State Board Previous Year Question Paper With Solution for Class 12 Science
  • Maharashtra State Board Previous Year Question Paper With Solution for Class 10
  • CISCE ICSE / ISC Board Previous Year Question Paper With Solution for Class 12 Arts
  • CISCE ICSE / ISC Board Previous Year Question Paper With Solution for Class 12 Commerce
  • CISCE ICSE / ISC Board Previous Year Question Paper With Solution for Class 12 Science
  • CISCE ICSE / ISC Board Previous Year Question Paper With Solution for Class 10
  • Entrance Exams
  • Video Tutorials
  • Question Papers
  • Question Bank Solutions
  • Question Search (beta)
  • More Quick Links
  • Privacy Policy
  • Terms and Conditions
  • Shaalaa App
  • Ad-free Subscriptions

Select a course

  • Class 1 - 4
  • Class 5 - 8
  • Class 9 - 10
  • Class 11 - 12
  • Search by Text or Image
  • Textbook Solutions
  • Study Material
  • Remove All Ads
  • Change mode

Advertisement

Supported by

As Republicans Attack Harris on Immigration, Here’s What Her Record Shows

Republicans blame Vice President Kamala Harris for the surge of migrants into the United States over the past several years. But a review of her involvement shows a more nuanced record.

  • Share full article

Vice President Kamala Harris gestures while speaking in the foreground with mountains looming behind her.

By Zolan Kanno-Youngs and Jazmine Ulloa

Reporting from Washington

As they seek effective attack lines against Vice President Kamala Harris, Republicans are focusing on her role in the Biden administration’s border and immigration policies, seeking to blame her for the surge of migrants into the United States over the past several years.

A review of her involvement in the issue shows a more nuanced record.

President Biden did not assign her the job title of “border czar” or the responsibility of overseeing the enforcement policies at the U.S.-Mexico border, as the Trump campaign suggested on Tuesday in its first ad against her. But she did have a prominent role in trying to ensure that a record surge of global migration did not become worse.

After the number of migrants crossing the southern border hit record levels at times during the administration’s first three years, crossings have now dropped to their lowest levels since Mr. Biden and Ms. Harris took office.

Her early efforts at handling her role and the administration’s policies were widely panned, even by some Democrats, as clumsy and counterproductive, especially in displaying defensiveness over why she had not visited the border. Some of her allies felt she had been handed a no-win portfolio.

Early in the administration, Ms. Harris was given a role that came to be defined as a combination of chief fund-raiser and conduit between business leaders and the economies of Guatemala, Honduras and El Salvador. Her attempt to convince companies across the world to invest in Central America and create jobs for would-be migrants had some success, according to immigration experts and current and former government officials.

But those successes only underlined the scale of the gulf in economic opportunity between the United States and Central America, and how policies to narrow that gulf could take years or even generations to show results.

We are having trouble retrieving the article content.

Please enable JavaScript in your browser settings.

Thank you for your patience while we verify access. If you are in Reader mode please exit and  log into  your Times account, or  subscribe  for all of The Times.

Thank you for your patience while we verify access.

Already a subscriber?  Log in .

Want all of The Times?  Subscribe .

Doubtnut Promotions Sticky

  • Bihar Board
  • Online Class
  • Ask Doubt on Whatsapp
  • Search Doubtnut

The assignment problem is said to be balanced if…

no. of rows = no. of columns

no. of rows ≠ no. of columns

no. of rows < no. of columns

no. of rows > no. of columns

More from this Exercise

The correct Answer is: A

Step by step video, text & image solution for The assignment problem is said to be balanced if… by Maths experts to help you in doubts & scoring excellent marks in Class 12 exams.

Topper's Solved these Questions

QUESTION BANK 2021

PROBABILITY DISTRIBUTION

THREE DIMENSIONAL GEOMETRY

Similar Questions

If the given matrix is …… matrix, the assignment problem is called balanced problem.

An unbalanced assignment problems can be balanced by adding dummy rows or columns with …… cost.

Knowledge Check

The assignment problem is solved by ….

On sending the current in the bridge, the bridge is said to be balanced, if

The assignment problem is generally defined as a problem of …......

On sending the current in the Wheatstone's network, the network is said to be balanced, if

State True or False: To convert the assignment problem into maximization problem, the smallest element in the matrix is to deducted from all other elements.

State True or False: The objective of an assignment problem is to assign number of jobs to equal number of persons at maximum cost.

Assignment Problem is special case of ….

When an assignment problem has more than one solution, then it is…

NAVNEET PUBLICATION - MAHARASHTRA BOARD - QUESTION BANK 2021 - Part II ASSIGNMENT PROBLEMS AND SEQUENCING (I. Select and write the most appropriate answer from the given alternatives for each sub question.)

The cost matrix of an unbalanced assignment problem is not a …

The optimal sequence for above data is

In sequencing, an optimal path is one that minimizes ….......

If there are 3 machines A, B and C, conditions for reducing a 3machine...

The objective of sequencing problem is

If there are n jobs and m machines, then there will be ......….sequenc...

In solving 2 machine and n jobs sequencing problem, the following assu...

Watch CBS News

Tim Walz's military record under scrutiny as he joins Kamala Harris on Democratic ticket

By James LaPorta

Updated on: August 9, 2024 / 12:40 AM EDT / CBS News

Minnesota Gov. Tim Walz 's military record has come under renewed scrutiny following Vice President Kamala Harris' announcement of Walz as her running mate on the Democratic ticket. 

On Wednesday, former President Donald Trump's running mate, Sen. JD Vance of Ohio, who is an Iraq War veteran, seized the opportunity to target his opponent's military record, resurfacing claims about his deployments and his retirement from the guard.

Walz served honorably in both the Nebraska and Minnesota Army National Guards, earning medals and deploying in support of Operation Enduring Freedom. But his final days of service have been called into question, centering on his rank and if he retired to avoid a 2005 deployment to Iraq. 

A CBS News review of Walz's military record and statements from the Minnesota Army National Guard show Walz achieved the rank of command sergeant major but was reduced in rank to master sergeant after retirement since he had not completed coursework for the U.S. Army Sergeants Major Academy. 

On Iraq, records show Walz had retired before his battalion was mobilized and deployed to Iraq. A 2005 statement from his website indicates Walz was initially prepared to deploy to Iraq amid his bid for Congress. CBS News has asked Walz for comment on when he decided to retire. 

A snapshot of Walz in the military

Walz retired from the Minnesota Army National Guard's 1st Battalion, 125th Field Artillery in 2005 after more than 24 years in service, the Minnesota Army National Guard told CBS News. 

Walz first enlisted in the Nebraska Army National Guard in April 1981, serving as an infantry senior sergeant and administrative specialist. In 1996, Walz transferred to the Minnesota Army National Guard, where he first worked as a cannon crewmember and field artillery senior sergeant. 

An undated photo of Tim Walz in uniform

Minnesota National Guard spokesperson Lt. Col. Kristen Augé told CBS News that Walz "held multiple positions within field artillery such as firing battery chief, operations sergeant, first sergeant, and culminated his career serving as the command sergeant major for the battalion." 

Walz earned several Army commendation and achievement medals during his more than 24 years of service. 

Walz deployed in August 2003 in support of Operation Enduring Freedom. The Minnesota National Guard told CBS News the battalion supported security missions at various locations in Europe and Turkey. Walz was stationed at Vicenza, Italy, at the time and returned to Minnesota in April 2004. 

Controversy over a 2005 Iraq deployment

On Wednesday, Vance resurfaced claims that Walz retired from the National Guard to avoid deploying to Iraq. 

"When the United States Marine Corps, when the United States of America, asked me to go to Iraq to serve my country I did it. I did what they asked me to do, and I did it honorably and I'm very proud of that service," said Vance. 

He added: "When Tim Walz was asked by his country to go to Iraq, you know what he did? He dropped out of the Army and allowed his unit to go without him — a fact that he's been criticized for aggressively by a lot of the people he served with." 

The Harris-Walz campaign responded with a statement saying: "After 24 years of military service, Governor Walz retired in 2005 and ran for Congress, where he [served as the ranking member] of Veterans Affairs and was a tireless advocate for our men and women in uniform — and as Vice President of the United States he will continue to be a relentless champion for our veterans and military families." The statement incorrectly stated Walz chaired the Veterans Affairs committee. 

The campaign also said, "In his 24 years of service, the Governor carried, fired and trained others to use weapons of war innumerable times. Governor Walz would never insult or undermine any American's service to this country -- in fact, he thanks Senator Vance for putting his life on the line for our country. It's the American way."  

The claims raised by Vance first gained prominence when Walz ran for governor of Minnesota in 2018. At the time, retired Army veterans Thomas Behrends and Paul Herr, who both served as command sergeant majors, posted on Facebook a lengthy letter accusing Walz of "embellishing" his military career and abandoning his Army National Guard battalion ahead of a 2005 deployment to Iraq.

In the letter, Behrends and Herr write that in early 2005, Walz's unit — 1st Battalion, 125th Field Artillery — was slated to deploy to Iraq. At the time, Walz was serving as the unit's command sergeant major. 

Behrends and Herr claimed that from the time the unit was told to prepare for an Iraq deployment and when Walz retired, he told other Army leaders he would be going to Iraq but later resigned his position before the deployment to avoid going to a combat zone. 

Walz has said he left the guard to run for Congress, according to the Star Tribune . In 2006, Walz won his election to Congress against a six-term Republican incumbent. 

Records show Walz officially filed paperwork with the Federal Election Commission on Feb. 10, 2005. 

In March 2005, the National Guard announced a possible partial mobilization of roughly 2,000 troops from the Minnesota National Guard, according to an archived press release from Tim Walz for U.S. Congress.  

"I do not yet know if my artillery unit will be part of this mobilization and I am unable to comment further on the specifics of the deployment," said Walz in the March 2005 statement . 

The statement continued: "As Command Sergeant Major I have a responsibility not only to ready my battalion for Iraq, but also to serve if called on. I am dedicated to serving my country to the best of my ability, whether that is in Washington DC or Iraq," said Walz, who indicated at the time he had no plans to drop out of the race. "I am fortunate to have a strong group of enthusiastic support and a very dedicated and intelligent wife. Both will be a major part of my campaign, whether I am in Minnesota or Iraq." 

The Minnesota Army National Guard told CBS News that Walz retired on May 16, 2005. CBS News has asked Walz to clarify when he submitted his retirement papers. 

The Minnesota National Guard told CBS News that Walz's unit — 1st Battalion, 125th Field Artillery — received an alert order for mobilization to Iraq on July 14, 2005 – two months after Walz retired, according to Lt. Col. Ryan Rossman, who serves as the Minnesota National Guard's director of operations. The official mobilization order was received on August 14 of the same year, and the unit mobilized in October. 

CBS News reviewed the deployment history for the Minnesota Army National Guard which shows that in the fall of 2005, 1st Battalion, 125th Field Artillery was mobilized in preparation for a deployment in support of Operation Iraqi Freedom. The battalion trained at Camp Shelby in Mississippi and deployed to Iraq as a motorized security task force. 

In 2018, Tom Hagen, a military reservist who served in Iraq, wrote a letter to The Winona Daily News claiming Walz was not being candid about his service record and wanted people to know that the future Minnesota governor did not serve in Iraq or Afghanistan. 

Walz responded in the same newspaper and criticized Hagan as dishonoring a fellow veteran, according to MPR News. Walz wrote: "There's a code of honor among those who've served, and normally this type of partisan political attack only comes from one who's never worn a uniform."

Joseph Eustice, a 32-year veteran of the guard who also led Walz's battalion, told CBS Minnesota that while he doesn't agree with Walz's politics, he does believe Walz's record in the military is sound.

"Tim Walz as a soldier, he was a good soldier. I don't think anyone can honestly say that he wasn't," Eustice said. "...He was a good leader in those 24 years that he served."

Walz's rank as a command sergeant major

Official biographies on the Minnesota government website and Vice President Kamala Harris' website  have described Walz as a "retired Command Sergeant Major." However, documents reviewed by CBS News show this is not accurate; while Walz served at one point as a command sergeant major, he retired at a lower rank. 

Army veteran Anthony Anderson, who routinely obtains military records from the Defense Department using the Freedom of Information Act and has worked with CBS News on similar stories, provided Walz's records for review. CBS News has also requested the documents from the National Guard. 

One of the documents shows Walz reverted back to master sergeant from command sergeant major when he retired from the Minnesota National Guard in May 2005. 

Army soldiers promoted to the rank of sergeant major or command sergeant major are required to attend the Sergeants Major Course, or what was formerly known as the U.S. Army Sergeants Major Academy.  

Lt. Col. Augé, the Minnesota National Guard spokesperson, told CBS News that Walz retired as a master sergeant in 2005 for "benefit purposes" because he did not complete additional coursework at the U.S. Army Sergeants Major Academy.

While Walz can say he served as a command sergeant major in the Minnesota Army National Guard, his official biographies are incorrect in referring to him as a "retired Command Sergeant Major."

On Aug. 8, the campaign website updated its description of his service. It omits his rank upon retirement and now reads, "The son of an Army veteran who served as a command sergeant major, Walz was the ranking member on the House Veterans Affairs Committee, where he passed legislation to help stem veterans' suicides."

Editor's Note: This story has been updated to address an error in the statement from the Harris-Walz campaign.

Caroline Cummings contributed to this report.

  • Minnesota National Guard

erv4p7nad-u06r378pasz-8ba9ab77e677-512.png

James LaPorta is a verification producer with CBS News Confirmed. He is a former U.S. Marine infantryman and veteran of the Afghanistan war.

More from CBS News

Trump falsely claims Harris campaign used AI to fake crowd in Detroit

Vance says "Trump is right" that VPs rarely matter on election outcomes

Transcript: Sen. JD Vance on "Face the Nation with Margaret Brennan," Aug. 11, 2024

Highlights from Biden's "CBS Sunday Morning" interview

  • Election 2024
  • Entertainment
  • Newsletters
  • Photography
  • AP Buyline Personal Finance
  • AP Buyline Shopping
  • Press Releases
  • Israel-Hamas War
  • Russia-Ukraine War
  • Global elections
  • Asia Pacific
  • Latin America
  • Middle East
  • Delegate Tracker
  • AP & Elections
  • 2024 Paris Olympic Games
  • Auto Racing
  • Movie reviews
  • Book reviews
  • Financial Markets
  • Business Highlights
  • Financial wellness
  • Artificial Intelligence
  • Social Media

Five things to know about Tim Walz

On Tuesday, Vice President Kamala Harris decided on Minnesota Gov. Tim Walz as her running mate in her bid for the White House.

Image

Minnesota voters gathered outside Governor Tim Walz’s residence react as Walz was announced as the running mate of Kamala Harris in the U.S. presidential election. (AP Video by Mark Vancleave)

Image

Vice President Kamala Harris has picked Minnesota Gov. Tim Walz to be her running mate, turning to a Midwestern governor, military veteran and union supporter who helped enact an ambitious Democratic agenda for his state.

Image

FILE - Minnesota Gov. Tim Walz, right, laughs as he stands with Fridley, Minn., Mayor Scott Lund during a visit to the Cummins Power Generation Facility in Fridley, Minn., Monday, April 3, 2023. (AP Photo/Carolyn Kaster, File)

  • Copy Link copied

FILE - Minnesota Gov. Tim Walz applauds as President Joe Biden speaks at Dutch Creek Farms in Northfield, Minn., Nov. 1, 2023. (AP Photo/Andrew Harnik, File)

FILE - Minnesota Gov. Tim Walz listens after meeting with President Joe Biden, July 3, 2024, at the White House in Washington. (AP Photo/Jacquelyn Martin, File)

Minnesota Gov. Tim Walz speaks during a news conference for the Biden-Harris campaign discussing the Project 2025 plan during the third day of the 2024 Republican National Convention near the Fiserv Forum, Wednesday, July 17, 2024, in Milwaukee. (AP Photo/Joe Lamberti)

FILE - Minnesota Governor Tim Walz greets reporters before Vice President Kamala Harris speaks at Planned Parenthood, March 14, 2024, in St. Paul, Minn. (AP Photo/Adam Bettcher, File)

FILE - Rep. Betty McCullum, D-Minn., left, and Minnesota Governor Tim Walz, listen as Vice President Kamala Harris speaks at Planned Parenthood, March 14, 2024, in St. Paul, Minn. (AP Photo/Adam Bettcher, File)

▶ Follow AP’s live coverage of the 2024 election

MINNEAPOLIS (AP) — Vice President Kamala Harris has decided on Minnesota Gov. Tim Walz as her running mate in her bid for the White House. The 60-year-old Democrat and military veteran rose to the forefront with a series of plain-spoken television appearances in the days after President Joe Biden decided not to seek a second term. He has made his state a bastion of liberal policy and, this year, one of the few states to protect fans buying tickets online for Taylor Swift concerts and other live events.

Some things to know about Walz:

Walz comes from rural America

It would be hard to find a more vivid representative of the American heartland than Walz. Born in West Point, Nebraska, a community of about 3,500 people northwest of Omaha, Walz joined the Army National Guard and became a teacher in Nebraska.

He and his wife moved to Mankato in southern Minnesota in the 1990s. That’s where he taught social studies and coached football at Mankato West High School, including for the 1999 team that won the first of the school’s four state championships. He still points to his union membership there.

Walz served 24 years in the Army National Guard, rising to command sergeant major, one of the highest enlisted ranks in the military, although he didn’t complete all the training before he retired so his rank for benefits purposes was set at master sergeant.

Image

He has a proven ability to connect with conservative voters

In his first race for Congress, Walz upset a Republican incumbent. That was in 2006, when he won in a largely rural, southern Minnesota congressional district against six-term Rep. Gil Gutknecht. Walz capitalized on voter anger with then-President George W. Bush and the Iraq war.

During six terms in the U.S. House, Walz championed veterans’ issues.

He’s also shown a down-to-earth side, partly through social media video posts with his daughter, Hope. One last fall showed them trying a Minnesota State Fair ride, “The Slingshot,” after they bantered about fair food and her being a vegetarian.

Image

He could help the ticket in key Midwestern states

While Walz isn’t from one of the crucial “blue wall” states of Wisconsin, Michigan and Pennsylvania, where both sides believe they need to win, he’s right next door. He also could ensure that Minnesota stays in the hands of Democrats.

That’s important because former President Donald Trump has portrayed Minnesota as being in play this year, even though the state hasn’t elected a Republican to statewide office since 2006. A GOP presidential candidate hasn’t carried the state since President Richard Nixon’s landslide in 1972, but Trump has already campaigned there .

When Democratic Gov. Mark Dayton decided not to seek a third term in 2018, Walz campaigned and won the office on a “One Minnesota” theme.

Walz also speaks comfortably about issues that matter to voters in the Rust Belt. He’s been a champion of Democratic causes, including union organizing, workers’ rights and a $15-an-hour minimum wage.

He has experience with divided government

In his first term as governor, Walz faced a Legislature split between a Democratic-led House and a Republican-controlled Senate that resisted his proposals to use higher taxes to boost money for schools, health care and roads. But he and lawmakers brokered compromises that made the state’s divided government still seem productive.

Bipartisan cooperation became tougher during his second year as he used the governor’s emergency power during the COVID-19 pandemic to shutter businesses and close schools. Republicans pushed back and forced out some agency heads. Republicans also remain critical of Walz over what they see as his slow response to sometimes violent unrest that followed the murder of George Floyd by a Minneapolis police officer in 2020.

What to know about the 2024 Election

  • Today’s news: Follow live updates from the campaign trail from the AP.
  • Ground Game: Sign up for AP’s weekly politics newsletter to get it in your inbox every Monday.
  • AP’s Role: The Associated Press is the most trusted source of information on election night, with a history of accuracy dating to 1848. Learn more.

Things got easier for Walz in his second term, after he defeated Republican Scott Jensen , a physician known nationally as a vaccine skeptic. Democrats gained control of both legislative chambers, clearing the way for a more liberal course in state government, aided by a huge budget surplus.

Walz and lawmakers eliminated nearly all of the state abortion restrictions enacted in the past by Republicans, protected gender-affirming care for transgender youth and legalized the recreational use of marijuana.

Rejecting Republican pleas that the state budget surplus be used to cut taxes, Democrats funded free school meals for children, free tuition at public colleges for students in families earning under $80,000 a year, a paid family and medical leave program and health insurance coverage regardless of a person’s immigration status.

Image

He has an ear for sound-bite politics

Walz called Republican nominee Donald Trump and running mate JD Vance “just weird” in an MSNBC interview last month and the Democratic Governors Association — which Walz chairs — amplified the point in a post on X . Walz later reiterated the characterization on CNN, citing Trump’s repeated mentions of the fictional serial killer Hannibal Lecter from the film “Silence of the Lambs” in stump speeches.

The word quickly morphed into a theme for Harris and other Democrats and has a chance to be a watchword of the undoubtedly weird 2024 election.

Hanna reported from Topeka, Kansas.

Image

IMAGES

  1. UNBALANCED ASSIGNMENT PROBLEM EXAMPLE NO. 1 BY DR KUNAL KHATRI #STATISTICS4ALL #ASSIGNMENT #EDU

    the assignment problem is said to be unbalanced if

  2. HOW TO SOLVE UNBALANCED ASSIGNMENT PROBLEM

    the assignment problem is said to be unbalanced if

  3. Lecture 19 Assignment problem : Unbalanced and maximal Assignment Problems

    the assignment problem is said to be unbalanced if

  4. Unbalanced Assignment Problem

    the assignment problem is said to be unbalanced if

  5. Assignment Problem example 3 (unbalanced problem)

    the assignment problem is said to be unbalanced if

  6. MEANING OF UNBALANCED ASSIGNMENT PROBLEM WITH EXAMPLE BY DR KUNAL

    the assignment problem is said to be unbalanced if

COMMENTS

  1. Unbalanced Assignment Problem: Definition, Formulation, and Solution

    The Unbalanced Assignment Problem is an extension of the Assignment Problem in OR, where the number of tasks and workers is not equal. In the UAP, some tasks may remain unassigned, while some workers may not be assigned any task. The objective is still to minimize the total cost or time required to complete the assigned tasks, but the UAP has ...

  2. Unbalanced Assignment Problems

    10 Feb 2019. Whenever the cost matrix of an assignment problem is not a square matrix, that is, whenever the number of sources is not equal to the number of destinations, the assignment problem is called an unbalanced assignment problem. In such problems, dummy rows (or columns) are added in the matrix so as to complete it to form a square matrix.

  3. Assignment problem

    The assignment problem consists of finding, in a weighted bipartite graph, a matching of a given size, in which the sum of weights of the edges is minimum. If the numbers of agents and tasks are equal, then the problem is called balanced assignment. Otherwise, it is called unbalanced assignment. [1] If the total cost of the assignment for all ...

  4. Solved 1. The assignment problem is said to be unbalanced if

    Transcribed image text: 1. The assignment problem is said to be unbalanced if a. Number of rows is greater than number of columns b. Number of rows is less than number of columns c. Number of rows is equal to number of columns d. None of these Ans: 2. For finding Initial basic solution to transportation problem Method is Used a. Simplex method b.

  5. 4. Unbalanced Assignment Problem

    Step-4: Number of assignments = 4, number of rows = 5. Which is not equal, so solution is not optimal. Step-5: Draw a set of horizontal and vertical lines to cover all the 0. Step-5: Cover the 0 with minimum number of lines. (1) Mark ( ) row E since it has no assignment.

  6. Unbalanced Assignment Problem

    Example: Unbalanced Assignment Problem. Solution. Since the number of persons is less than the number of jobs, we introduce a dummy person (D) with zero values. The revised assignment problem is given below: Table. Now use the Hungarian method to obtain the optimal solution yourself. Ans. = 20 + 17 + 17 + 0 = 54.

  7. linear programming

    How can I balance the following assignment problem (where machines are to be assigned the jobs in optimal way such that the profit is maximized). Cost matrix is given in the problem. First step is to convert it into minimization problem by subtracting all the entries in the matrix from maximum value in the matrix.

  8. Solving the Unbalanced Assignment Problem: Simpler Is Better

    The current Hungarian approach to solving unbalanced assignment issues is based on the notion that some tasks should be delegated to fictitious or covert components, and those studies should be ...

  9. Unbalanced Assignment Problem

    Unbalanced Assignment problem is an assignment problem where the number of facilities is not equal to the number of jobs. To make unbalanced assignment problem, a balanced one, a dummy facility (s) or a dummy job (s) (as the case may be) is introduced with zero cost or time. Get Quantitative Techniques: Theory and Problems now with the O ...

  10. PDF Solving the Unbalanced Assignment Problem: Simpler Is Better

    The typical textbook solution to the balanced assignment problem is then found using Kuhn's [3] Hungarian method. Problems in which there are more jobs than machines and more than one job can be ...

  11. Assignment Problem: Meaning, Methods and Variations

    Variations of the Assignment Problems: Unbalanced Assignment Problem: Any assignment problem is said to be unbalanced if the cost matrix is not a square matrix, i.e. the no of rows and the no of columns are not equal. To make it balanced we add a dummy row or dummy column with all the entries is zero. Example 3:

  12. Solving the Unbalanced Assignment Problem: Simpler Is Better

    The assignment problems are a well studied topic in combinatorial optimization. These problems find numerous application in production planning, telecommunication VLSI design, economic etc. The assignment problems is a special case of Transportation problem. Depending on the objective we want to optimize, we obtain the typical assignment problems.

  13. A Comparative Analysis of Assignment Problem

    unbalanced assignment problems is based on the assumption that some jobs should be assigned to pseudo or dummy machines, but these jobs are left unexecuted by the dummy machines in the Hungarian method. However, it is sometimes impractical in real-world situations. Moreover, Lampang, Boonjing, and Chanvarasuth introduced a new space- ...

  14. The assignment problem revisited

    The Hungarian and the FlowAssign algorithms are designed to directly solve the assignment problem on unbalanced graphs, while the auction algorithm is not. ... Given \(\epsilon >0\), a pseudoflow f is said to be \(\epsilon \)-optimal, with respect to the price function p, if every arc of \(E_f\) satisfies the following:

  15. Nash Balanced Assignment Problem

    The Assignment Problem (AP) is a fundamental combinatorial optimization problem. It can be formally defined as follows. Given a set n workers, a set of n jobs and a \(n \times n\) cost matrix whose elements are positive representing the assignment of any worker to any job, the AP aims at finding an one-to-one worker-job assignment (i.e., a bipartite perfect matching) that minimizes certain ...

  16. Solving the Unbalanced Assignment Problem: Simpler Is Better

    1997. 7. PDF. Recently, Yadaiah and Haragopal published in the American Journal of Operations Research a new approach to solving the unbalanced assignment problem. They also provide a numerical example which they solve with their approach and get a cost of 1550 which they claim is optimum. This approach might be of interest; however, their ...

  17. An Alternative Approach for Solving Unbalanced Assignment Problems

    nt is added to any row or column in the assignmen. cost matrix [ cij ], then the optimal solution remains th. ow the proposed algorithm consists of the following steps:Step 1:Balance the given assignment problem if either (number of row(s) number of column(s)) or (number of row(s) number of colu.

  18. The assignment problem is said to be balanced if ______.

    The assignment problem is said to be unbalance if _____ Choose the correct alternative : The assignment problem is said to be balanced if it is a _____. The objective of an assignment problem is to assign _____. Fill in the blank : When an assignment problem has more than one solution, then it is _____ optimal solution.

  19. Assignment problems

    Unit 8: Assignment Problem - Unbalanced. When an assignment problem has more than one solution, then it is Notes (a) Multiple Optimal solution (b) The problem is unbalanced (c) Maximization problem (d) Balanced problem. 8 Unbalanced Assignment Problem. If the given matrix is not a square matrix, the assignment problem is called an unbalanced ...

  20. Fill in the blank : An assignment problem is said to be unbalanced when

    An unbalanced assignment problems can be balanced by adding dummy rows or columns with _____ cost. A _____ assignment problem does not allow some worker(s) to be assign to some job(s) State whether the following statement is True or False: To convert the assignment problem into maximization problem, the smallest element in the matrix is to ...

  21. An assignment problem is said to be unbalanced when

    An assignment problem is said to be unbalanced when ..... More from this Exercise. 9 videos. Text Solution. Verified by Experts. The correct Answer is: Number of rows is not equal to the number of columns. | Share Save. Updated on: 21/07/2023. Class 12 MATHS ASSIGNMENT PROBLEM AND SEQUENCING.

  22. Tim Walz's military career: What to know about potential VP's service

    Democratic vp pick Tim Walz served for decades in the Army National Guard, serving in the U.S. and overseas.

  23. The assignment problem is said to be unbalance if

    41. 34. 39. Find the optimal assignment schedule. Choose the correct alternative : The assignment problem is said to be balanced if it is a ______. The objective of an assignment problem is to assign ______. Fill in the blank : When an assignment problem has more than one solution, then it is _______ optimal solution.

  24. As Republicans Attack Harris on Immigration, Here's What Her Record

    Representative Henry Cuellar, Democrat of Texas, who worked with Mr. Biden when he had the assignment as vice president, said her task was inherently connected to the record numbers of crossings ...

  25. The assignment problem is said to be balanced if…

    Step by step video, text & image solution for The assignment problem is said to be balanced if… by Maths experts to help you in doubts & scoring excellent marks in Class 12 exams. Updated on: 21/07/2023

  26. Tim Walz's military record under scrutiny as he joins Kamala Harris on

    Walz has said he left the guard to run for Congress, according to the Star Tribune. In 2006, Walz won his election to Congress against a six-term Republican incumbent.

  27. What to know about Harris' VP pick Tim Walz

    He has an ear for sound-bite politics. Walz called Republican nominee Donald Trump and running mate JD Vance "just weird" in an MSNBC interview last month and the Democratic Governors Association — which Walz chairs — amplified the point in a post on X.Walz later reiterated the characterization on CNN, citing Trump's repeated mentions of the fictional serial killer Hannibal Lecter ...