while solving an assignment problem an activity is assigned to a resource

While solving an assignment problem an activity is assigned to a...

While solving an assignment problem, an activity is assigned to a resource through a square with zero opportunity cost because the objective is to?

A. Minimize total cost of assignment

B. Reduce the cost of assignment to zero

C. Reduce the cost of that particular assignment to zero

D. All of the above

Answer: Option A

Solution(By Examveda Team)

This Question Belongs to Management >> Operations Research

Join The Discussion

Related Questions on Operations Research

The use of decision models.

A. Is possible when the variables value is known

B. Reduces the scope of judgement & intuition known with certainty in decision-making

C. Require the use of computer software

D. None of the above

Every mathematical model.

A. Must be deterministic

B. Requires computer aid for its solution

C. Represents data in numerical form

A physical model is example of.

A. An iconic model

B. An analogue model

C. A verbal model

D. A mathematical model

The qualitative approach to decision analysis relies on.

A. Experience

B. Judgement

C. Intuition

More Related Questions on Operations Research

Read More: MCQ Type Questions and Answers

•   Arithmetic Ability
•   Competitive Reasoning
•   Competitive English
•   Data Interpretation
•   General Knowledge
•   State GK
•   History
•   Geography
•   Current Affairs
•   Banking Awareness
•   Computer Fundamentals
•   Networking
•   C Program
•   Java Program
•   Database
•   HTML
•   Javascript
•   Computer Science
•   Electronics and Communications Engineering
•   Electrical Engineering
•   Mechanical Engineering
•   Civil Engineering
•   Chemical Engineering
•   Automobile Engineering
•   Biotechnology Engineering
•   Mining Engineering
•   Commerce
•   Management
•   Philosophy
•   Agriculture
•   Sociology
•   Political Science
•   Pharmacy

Assignment Problem: Meaning, Methods and Variations | Operations Research

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:

Mathematical Formulation of the Assignment Problem:

• Google OR-Tools
• Español – América Latina
• Português – Brasil
• Tiếng Việt

One of the most well-known combinatorial optimization problems is the assignment problem . Here's an example: suppose a group of workers needs to perform a set of tasks, and for each worker and task, there is a cost for assigning the worker to the task. The problem is to assign each worker to at most one task, with no two workers performing the same task, while minimizing the total cost.

You can visualize this problem by the graph below, in which there are four workers and four tasks. The edges represent all possible ways to assign workers to tasks. The labels on the edges are the costs of assigning workers to tasks.

An assignment corresponds to a subset of the edges, in which each worker has at most one edge leading out, and no two workers have edges leading to the same task. One possible assignment is shown below.

The total cost of the assignment is 70 + 55 + 95 + 45 = 265 .

The next section shows how solve an assignment problem, using both the MIP solver and the CP-SAT solver.

Other tools for solving assignment problems

OR-Tools also provides a couple of other tools for solving assignment problems, which can be faster than the MIP or CP solvers:

• Linear sum assignment solver
• Minimum cost flow solver

However, these tools can only solve simple types of assignment problems. So for general solvers that can handle a wide variety of problems (and are fast enough for most applications), we recommend the MIP and CP-SAT solvers.

Except as otherwise noted, the content of this page is licensed under the Creative Commons Attribution 4.0 License , and code samples are licensed under the Apache 2.0 License . For details, see the Google Developers Site Policies . Java is a registered trademark of Oracle and/or its affiliates.

Last updated 2023-01-02 UTC.

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