The topic of assignment is a critical problem in mathematics and is further explored in the real
physical world. We try to implement a replacement method during this paper to solve assignment problems with
algorithm and solution steps. By using new method and computing by existing two methods, we analyse a
numerical example, also we compare the optimal solutions between this new method and two current methods. A
standardized technique, simple to use to solve assignment problems, may be the proposed method
The document contains sample questions from previous years' business statistics exams. It includes two questions:
1) A question from 2006 that involves calculating the mean, standard deviation, and coefficient of variation for age data grouped into classes with frequency counts.
2) A question from 2007 that involves calculating the mean and median income from frequency data grouped into classes. The document shows the work and calculations to arrive at the answers for both questions.
The least cost method is used to obtain an initial feasible solution for the transportation problem. It works by allocating units to the cell with the lowest cost first without exceeding supply or demand, then crosses out the exhausted row or column. This process repeats until all units are allocated. The method provides an accurate solution while considering transportation costs, but it does not guarantee finding the true optimal solution and may not be systematic in cases of tied costs.
1) The document discusses the Hungarian method for solving assignment problems by finding the optimal assignment of jobs to machines that minimizes costs.
2) It provides examples of using the Hungarian method to solve assignment problems by finding minimum costs in the cost matrix and obtaining a feasible assignment with zero costs.
3) The optimal solution is determined by selecting the assignments indicated by the cells with zero costs in the final cost matrix after applying the Hungarian method steps.
Role of small bussiness in indian economy.ppt 2007 sandhyaPrachi Bajaj
The document discusses definitions of small business across different countries and criteria used to define them such as total capital investment, assets, employment levels, and sales turnover. It notes size does not always reflect an enterprise's true nature and other characteristics like ownership, management, technology, and geographical operations also differentiate small and large businesses. The role of small businesses in India's economy is described including importance in employment, capital optimization, regional development, and industrial production.
This document provides an overview of Oriflame, a direct selling cosmetics company. It includes sections on Oriflame's operations, SWOT analysis, PESTEL analysis, client groups and empathy map, value proposition, mission/vision/values, and SMART strategic goals. Key details are that Oriflame has 3 million sales consultants operating in over 60 countries, with production facilities in several countries and approximately 7,000 employees.
This document discusses an introduction to linear programming and formulating a minimization problem. It presents a case study where the objective is to minimize the daily inspection cost of quality control inspectors at a company. There are constraints on the minimum number of pieces to be inspected and limits on the number of each type of inspector. The document formulates the linear programming model to minimize the objective function of total cost, subject to the constraints. It provides the objective function, constraints, and overall linear programming model to solve the optimization problem.
Mathematical formulation of lpp- properties and exampleSundar B N
The document discusses the mathematical formulation of linear programming problems (LPP). It begins by explaining how an LPP is translated into mathematical equations with decision variables. An example problem is given involving maximizing profit with constraints on machine hours and labor hours.
The objective function for the example problem is defined to maximize total profit (Z) which is expressed as a linear function of the decision variables x and y, which represent units of products A and B. The constraints define the limited available machine hours and labor hours in terms of inequalities involving x and y. Non-negativity restrictions are also included to ensure x and y are greater than or equal to 0.
The document outlines the presentation topic of Modified Distribution Method (MODI Method) for solving transportation problems. It first discusses the prerequisite methods of Least Cost Method, Vogel's Approximation Method and North-West Corner Method. It then explains the steps of MODI Method which involves setting up cost matrices for unallocated cells and introducing dual variables to find the implicit cost and evaluate unoccupied cells to determine if the initial solution can be improved. The document provides an example problem and solution to demonstrate the application of MODI Method.
The North-West Corner Rule is a method for solving transportation problems that involves identifying the cell in the north-west corner of the transportation matrix, allocating units to that cell up to the supply or demand limit, crossing out the exhausted row or column, reducing the corresponding supply or demand, and repeating with the new north-west cell until all requirements are satisfied.
This document presents a linear programming problem involving assigning quality inspectors to minimize total inspection costs. There are two types of inspectors (Grade I and Grade II) with different inspection rates and accuracy. The objective is to minimize total costs based on wages, inspection pieces, and error costs with constraints on minimum inspection pieces and available inspectors.
Asian Paints Ltd is India's largest and Asia's third largest paint company with operations spanning 26 countries. It produces decorative paints, industrial coatings, and chemicals. The company has 10 manufacturing plants across India and focuses on quality control through techniques like prevention, inspection, correction and improvement. Asian Paints aims to be among the top five global decorative coatings companies and ensure environmental sustainability at its plants. It has an effective supply chain network with raw material suppliers, processing centers, distribution centers and depots integrated across the country.
Section 13.6 solving quadratic equations using the zero-factor propertyGlenSchlee
This document discusses solving quadratic equations using the zero-factor property. It begins by defining quadratic equations and the zero-factor property. It then presents the steps to solve quadratic equations by factoring: 1) write the equation in standard form, 2) factor completely, 3) set each factor equal to 0 using the zero-factor property, 4) solve the resulting equations, and 5) check the solutions. Several examples are worked through demonstrating this process. It notes that not all quadratic equations can be solved by factoring and more general methods will be discussed later. It concludes by solving another equation using the zero-product property.
This document discusses transportation problems and three methods to solve them: the North West Corner Method, Least Cost Method, and Vogel Approximation Method. The objective of transportation problems is to minimize the cost of distributing products from sources to destinations while satisfying supply and demand constraints. The document provides examples to illustrate how each method works step-by-step to arrive at a basic feasible solution.
Melvin T Mathew presents on linear programming problems. A linear programming problem involves determining the optimal allocation of limited resources to meet objectives. It includes a set of simultaneous linear equations or inequalities that represent resource restrictions and a linear objective function expressing total profit or cost. Linear programming is defined as a method of determining an optimal program of interdependent activities given available resources, with the objective of maximizing profit or minimizing cost subject to constraints. The solution shows the optimal amounts to produce, sell, or purchase to satisfy objectives and constraints. Linear programming is a powerful technique that can be used to solve production scheduling, manufacturing, and marketing problems.
This document discusses adding and subtracting polynomials. It explains that to add polynomials, terms with the same variables and exponents are combined. To subtract polynomials, the opposite of the second polynomial is taken and then the polynomials are added like normal. Examples are provided of rearranging terms in decreasing exponential order, stacking like terms, and combining them to solve polynomial addition and subtraction problems.
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This is an introduction to Linear Programming and a few real world applications are included.
This document discusses social entrepreneurship in the Indian context. It defines social entrepreneurship as creating social change and social capital through a venture that improves productivity and team building. Social entrepreneurship can positively impact economic development policies and outcomes. Key characteristics of social entrepreneurship include having an exclusively social mission, autonomy, innovation, sustainability, and equal opportunities. Applications in industry include employment development, innovating new goods/services, building social capital, and promoting equity. Examples highlighted are microfinance initiatives and policies promoting women's participation. The conclusion states that social enterprises foster equitable and sustainable development through ethical profit-making and should be more organized to build stronger corporate citizenship in India.
The document discusses brand awareness and preferences towards shampoo products in rural areas of Erode City, India. It presents a study conducted by J. Boopathi to fulfill the requirements for an MBA degree from Anna University. The study examines brand awareness, preferences, and factors influencing shampoo purchases among 300 respondents in Sivagiri, Erode through questionnaires and statistical analysis tools like percentage analysis, chi-square, ANOVA, ranking, and factor analysis. The objectives were to understand brand awareness levels and preferences toward shampoo brands in the target rural region.
This document discusses linear programming and its application to marketing. It covers topics like the requirements, methods, advantages/disadvantages of linear programming. It also provides steps to formulate a linear programming problem, including understanding the problem, identifying the objective and constraints, defining decision variables, and writing the mathematical model. Finally, it formulates an example problem to maximize advertisement reach within a budget, finds the optimal solution is 175 radio ads and 10 TV ads reaching 595,000 people.
Solving ONE’S interval linear assignment problemIJERA Editor
This document presents a new method called the Matrix Ones Interval Linear Assignment Method (MOILA) for solving assignment problems with interval costs. It begins with definitions of assignment problems and interval analysis concepts. Then it describes the existing Hungarian method and provides an example solved using both Hungarian and MOILA. MOILA involves creating ones in the assignment matrix and making assignments based on the ones. The document outlines algorithms for MOILA as well as extensions to unbalanced and interval assignment problems. It provides an example of applying MOILA to solve a balanced interval assignment problem and compares the solutions to Hungarian. The document introduces MOILA as a systematic alternative to Hungarian for solving a variety of assignment problem types.
This document discusses and compares different methods for solving assignment problems. It begins with an abstract that defines assignment problems as optimally assigning n objects to m other objects in an injective (one-to-one) fashion. It then provides an introduction to the Hungarian method and a new proposed Matrix Ones Assignment (MOA) method. The body of the document provides details on modeling assignment problems with cost matrices, formulations as linear programs, and step-by-step explanations of the Hungarian and MOA methods. It includes an example solved using the Hungarian method.
A Comparative Analysis Of Assignment ProblemJim Webb
This document provides a comparative analysis of different methods for solving assignment problems, including the Hungarian method and a new proposed Matrix Ones Assignment (MOA) method. It first introduces assignment problems and describes their applications. It then explains the Hungarian method in detail through examples. Finally, it outlines the steps of the new MOA method, which aims to create ones in the assignment matrix to find optimal assignments. The document compares the two approaches and provides an example solved using the MOA method.
The document discusses the assignment problem, which involves assigning people, jobs, machines, etc. to minimize costs or maximize profits. It provides an example of assigning 4 men to 4 jobs to minimize total cost, walking through the Hungarian method steps. It also discusses how to handle imbalance by adding dummy rows or columns, and how to convert a maximization problem to minimization.
The document provides information on operations research and the assignment problem. It discusses the steps to solve an assignment problem, which include: (1) writing the problem in a matrix form, (2) obtaining a reduced cost matrix through row and column operations, and (3) making assignments on a one-to-one basis by considering zeros in rows and columns. It also addresses issues like unbalanced matrices, maximization problems, and infeasible assignments.
The document discusses assignment problems and provides examples to illustrate how to solve them. Assignment problems involve allocating jobs to people or machines in a way that minimizes costs or maximizes profits. The key steps to solve assignment problems are: (1) construct a cost matrix, (2) perform row and column reductions to obtain zeros, (3) draw lines to cover zeros and determine optimal assignments. Traveling salesman problems, which involve finding the lowest cost route to visit all cities once, can also be formulated as assignment problems.
This is one of the topic covered here to give a flavour of the Operations Research(OR) topics covered in the CD ROM.This ebook will be available by the end of September 2014 on snapdeal website.The OR topics covered are simplified through a number of solved illustrations and will be useful to BMS,MMS.MBA and CA students.
This document discusses assignment problems and the Hungarian method for solving them. Assignment problems involve assigning n jobs to n workers or machines in a way that minimizes costs or maximizes effectiveness. The Hungarian method is an algorithm that can be used to find the optimal assignment. It involves row and column reductions on the cost or effectiveness matrix, followed by finding a complete assignment with zeros or modifying the matrix to create more zeros until a complete assignment is possible. Examples demonstrate applying the Hungarian method to solve different assignment problems step-by-step.
Ashish garg research paper 660_CamReadyAshish Garg
This document presents a hybrid sorting technique called CutShort that aims to optimize the runtime of sorting algorithms. It works by first dividing the input array into subarrays based on the number of bits needed to represent each element. The elements are then repositioned within the input array according to their subarray. Each subarray is then sorted independently using an optimal sorting algorithm like insertion sort. Experimental results on random, worst-case, and favorable data show that combining CutShort with quicksort, mergesort, or insertion sort reduces sorting time significantly compared to using the base algorithms alone. The technique is most effective when the input can be divided into many subarrays of more equal sizes.
The document discusses the Hungarian method for solving assignment problems. It begins by defining an assignment problem as minimizing the cost of completing jobs by assigning workers to tasks, where each job is assigned to exactly one worker. It then outlines the steps of the Hungarian method, which involves constructing a cost matrix, subtracting rows and columns to find zeros, and using the zeros to determine the optimal assignment. Finally, it provides an example and lists some applications of the Hungarian method like assigning machines, salespeople, contracts, teachers, and accountants.
Assignment Chapter - Q & A Compilation by Niraj ThapaCA Niraj Thapa
My name is Niraj Thapa. I have compiled Assignment Chapter including SM, PM & Exam Questions of AMA.
You feedback on this will be valuable inputs for me to proceed further.
This document presents a method for solving the traveling salesman problem (TSP) using an assignment problem formulation. It begins by mathematically formulating the TSP as an assignment problem. It then describes the revised ones assignment method (ROA) to solve assignment problems by creating ones in the assignment matrix. The ROA method is applied to an example of finding the optimal route for the Ashtavinayaka Yatra pilgrimage in India involving 9 cities. The ROA method finds the shortest route in 3 cycles totaling 675 km, and identifies a second shortest route of 987 km by considering additional minimum values. The paper concludes the ROA method can be used to both minimize and maximize assignment problem objectives and to
MATLAB is an interactive development environment and programming language used by engineers and scientists for technical computing, data analysis, and algorithm development. It allows users to access data from files, web services, applications, hardware, and databases, and perform data analysis and visualization. MATLAB can be used for applications in areas like control systems, signal processing, communications, and more.
This document discusses assignment problems and how to solve them using the Hungarian method. Assignment problems involve efficiently allocating people to tasks when each person has varying abilities. The Hungarian method is an algorithm that can find the optimal solution to an assignment problem in polynomial time. It involves constructing a cost matrix and then subtracting elements in rows and columns to create zeros, which indicate assignments. The method is iterated until all tasks are assigned with the minimum total cost. While typically used for minimization, the method can also solve maximization problems by converting the cost matrix.
This document discusses assignment problems and how to solve them using the Hungarian method. Assignment problems involve efficiently allocating people or resources to tasks when only one task can be assigned to each person. The Hungarian method is an algorithm that can find the optimal solution to an assignment problem in polynomial time. It involves constructing a cost matrix and then subtracting elements in rows and columns to create zeros, which indicate assignments. The method is iterated until all tasks are assigned with the minimum total cost. The document provides an example using this method to assign 5 workers to 5 jobs with the goal of minimizing total work hours.
Operations research : Assignment problem (One's method) presentationPankaj Kumar
The document describes the process of assigning jobs to machines to maximize total return or minimize total cost. It involves creating an assignment matrix with the return/cost of assigning each job to each machine. The matrix is transformed through operations like finding minimum/maximum elements in rows and columns to create a feasible assignment with all ones. If this is not possible after the transformations, additional steps like drawing lines through ones are taken to find the optimal assignment. An example optimal assignment that yields a total return of 50 is provided.
This document provides an overview of brute force and divide-and-conquer algorithms. It discusses various brute force algorithms like computing an, string matching, closest pair problem, convex hull problems, and exhaustive search algorithms like the traveling salesman problem and knapsack problem. It also analyzes the time efficiency of these brute force algorithms. The document then discusses the divide-and-conquer approach and provides examples like merge sort, quicksort, and matrix multiplication. It provides pseudocode and analysis for mergesort. In summary, the document covers brute force and divide-and-conquer techniques for solving algorithmic problems.
- The document discusses matrices, including definitions, operations, and examples of matrix addition, subtraction, transposition, and multiplication. It also covers linear programming, defining it as a method to optimize a mathematical model to achieve the best outcome.
- Key concepts covered include the definitions of a matrix and its elements, how to perform basic operations like addition and subtraction on matrices, and how matrices are multiplied using the dot product of rows and columns. Linear programming is introduced as a method using linear relationships to find the maximum or minimum value of an objective function.
This document provides information about the Introduction to Finite Elements course taught by Professor Suvranu De. It includes contact information for the course instructor, practicum instructor, and teaching assistant. It outlines the course texts, grades which are based on homework, practicum exercises, a course project, and quizzes. It describes collaboration policies and provides details on homework, practicum exercises, the course project, course content, and a linear algebra recap.
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Talk covering Guardrails , Jailbreak, What is an alignment problem? RLHF, EU AI Act, Machine & Graph unlearning, Bias, Inconsistency, Probing, Interpretability, Bias
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Profiling of Cafe Business in Talavera, Nueva Ecija: A Basis for Development ...IJAEMSJORNAL
This study aimed to profile the coffee shops in Talavera, Nueva Ecija, to develop a standardized checklist for aspiring entrepreneurs. The researchers surveyed 10 coffee shop owners in the municipality of Talavera. Through surveys, the researchers delved into the Owner's Demographic, Business details, Financial Requirements, and other requirements needed to consider starting up a coffee shop. Furthermore, through accurate analysis, the data obtained from the coffee shop owners are arranged to derive key insights. By analyzing this data, the study identifies best practices associated with start-up coffee shops’ profitability in Talavera. These findings were translated into a standardized checklist outlining essential procedures including the lists of equipment needed, financial requirements, and the Traditional and Social Media Marketing techniques. This standardized checklist served as a valuable tool for aspiring and existing coffee shop owners in Talavera, streamlining operations, ensuring consistency, and contributing to business success.
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modeling principles. In the age of digital communication, social media platforms
have become indispensable for connecting people, sharing content, and fostering
online communities. However, their complex nature requires meticulous planning
and organization.This project addresses the challenge of creating a feature-rich and
user-friendly social media platform by applying key object-oriented modeling
concepts. It entails the identification and definition of essential objects such as
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& Engineering for Offshore Drilling Rigs, to deliver
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teaches the inspection & maintenance procedures
required to ensure equipment integrity. Candidates
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1. VIVA-Tech International Journal for Research and Innovation
ISSN(Online): 2581-7280
Volume 1, Issue 4 (2021)
VIVA Institute of Technology
9th
National Conference on Role of Engineers in Nation Building – 2021 (NCRENB-2021)
E-21
A study on solving Assignment Problem
Prof. Ramashankar Prajapati, Dr. Ajazul Haque,
Dr. Jayesh Jain, Prof. Shiksha Singh
(Humanities & Applied Sciences, Viva Institute of Technology, India)
Abstract: The topic of assignment is a critical problem in mathematics and is further explored in the real
physical world. We try to implement a replacement method during this paper to solve assignment problems with
algorithm and solution steps. By using new method and computing by existing two methods, we analyse a
numerical example, also we compare the optimal solutions between this new method and two current methods. A
standardized technique, simple to use to solve assignment problems, may be the proposed method.
Keywords: Assignment issue, HA-method, assignment method of Matrix one, Proposed method, Optimization.
I. Introduction
We often encounter situations during which we have we’ve got to assign n jobs to n workers. All n workers are
capable of doing all jobs, but with a varying cost. Hence our task is to search out the simplest possible assignment
that offers maximum efficiency and minimum cost. Example, assigning activities to students, subjects to teachers,
different routes of pizza delivery boys, salesmen to different regions, jobs to machines, products to factories,
research problems to groups, vehicles and drivers to different routes etc. An issue of this nature is named an
assignment problem.
II. Definition
Assignment problem may be a special kind of problem which deals with allocation of assorted resources to varied
activities on one to 1 basis. It’s tired such some way that the whole cost or time involved within the process is
minimum or the whole profit is maximum.
III. Conditions
i) Number of jobs is capable number of machines or workers.
ii) Each worker or machine is assigned to just one job.
iii) Each worker or machine is independently capable of handling any job.
iv) Objective of the assignment is clearly specified (minimizing cost or maximizing profit)
3.1 Assignment Model:
Given n workers and n jobs with the price of each worker for each job, the matter is to assign each worker to at
least one and only 1 job so on to optimize the full cost.
2. VIVA-Tech International Journal for Research and Innovation
ISSN(Online): 2581-7280
Volume 1, Issue 4 (2021)
VIVA Institute of Technology
9th
National Conference on Role of Engineers in Nation Building – 2021 (NCRENB-2021)
E-22
𝑖=1
𝑖𝑗
𝑖𝑗
Let 𝐶𝑖𝑗 be the cost of assigning 𝑖𝑡ℎ to 𝑗𝑡ℎ job, 𝑥𝑖𝑗 be the assignment of 𝑖𝑡ℎ worker to 𝑗𝑡ℎ job and 𝑥𝑖𝑗 = 1, if 𝑖𝑡ℎ
worker is assigned to 𝑗𝑡ℎ job = 0, otherwise
Following table represents the value of assigning n workers to n jobs.
Worker Jobs
1 2 3 … … n
1 𝐶11 𝐶12 𝐶13 𝐶1𝑛
2 𝐶21 𝐶22 𝐶23 𝐶2𝑛
. . . . . . .
. . . . . . .
. . . . . . .
N 𝐶𝑛1 𝐶𝑛2 𝐶𝑛3 … … 𝐶𝑛𝑛
The objective is to form assignments that minimize the entire cost.
Thus, an assignment problem will be represented by n x n matrix which covers all the n! possible ways of
constructing assignments.
Assignment Problem may be a special case of Applied Math Problem.
Assignment problem will be expressed symbolically as follows:
Minimize Z = ∑𝑛 𝑛
𝑖=1 𝐶𝑖𝑗 𝑥𝑖𝑗
Subject to constraints
𝑛
∑ 𝑥 = 1; 𝑖 = 1, 2, 3, …𝑛
𝑗=1
(exactly one job is assigned to 𝑖𝑡ℎ worker)
𝑛
∑ 𝑥 = 1; 𝑖 = 1, 2, 3, … 𝑛
𝑖=1
(exactly one worker is assigned to 𝑗𝑡ℎ job where 𝑥𝑖𝑗 takes a worth 0 or 1.
3.2 Hungarian method is predicated on the subsequent properties:
1) If a relentless (positive or negative) is added to each element of any row or column within the given cost matrix,
an assignment that minimizes the overall cost within the original matrix also minimizes the overall cost within the
revised matrix.
2) In an assignment problem, an answer having zero total cost of assignment is an optimal solution.
The Hungarian algorithm is explained with the assistance of the subsequent example.
Consider an example where 4 jobs have to be performed by 4 workers, one job per worker. The matrix below
shows the value of assigning a specific worker to a particular job. The target is to attenuate the whole cost of
assignment.
Workers Jobs
𝐽1 𝐽2 𝐽3 𝐽4
𝑊
1
62 63 50 72
𝑊
2
57 35 49 60
𝑊
3
21 49 15 56
𝑊
4
18 19 78 23
3.2 Let us solve this problem by Hungarian method.
Step 1: Subtract the littlest element of every row from every element of that row.
∑
3. VIVA-Tech International Journal for Research and Innovation
ISSN(Online): 2581-7280
Volume 1, Issue 4 (2021)
VIVA Institute of Technology
9th
National Conference on Role of Engineers in Nation Building – 2021 (NCRENB-2021)
E-23
Workers Jobs
𝐽1 𝐽2 𝐽3 𝐽4
𝑊
1
12 13 0 22
𝑊
2
22 0 14 25
𝑊
3
6 34 0 41
𝑊
4
0 1 60 5
Step 2: Subtract the littlest element of every column from every element of that column.
Workers Jobs
𝐽1 𝐽2 𝐽3 𝐽4
𝑊
1
12 13 0 17
𝑊
2
22 0 14 20
𝑊
3
6 34 0 36
𝑊
4
0 1 60 0
Step 3: Assign through zeros.
Workers Jobs
√
√
√
𝑊1 12 13 ⓪ 17
𝑊2 22 ⓪ 14 20
𝑊3 6 34 0 36
𝑊4 ⓪ 1 60 0
Observe that third row doesn’t contain an assignment.
Step 4: 1. Mark (√) the row (𝑅3).
2. Mark (√) the columns (𝐶3) having zeros within the marked rows.
3. Mark (√) the row (𝑅3) which contains assignment in marked column.
4. Draw lines through the marked columns and unmarked rows.
Workers Jobs
√
𝑊1 12 13 ⓪ 17
√
√
𝑊2 22 ⓪ 14 20
𝑊3 6 34 0 36
𝑊4 ⓪ 1 60 0
All zeros will be covered using 3 lines
So, number of lines = 3 and order of matrix = 4
Hence, the quantity of lines required ≠ order of matrix.
Therefore, we continue with the subsequent step to form additional zeros.
Step 4: (i) Find the littlest uncovered element (6)
(ii) Subtract this number
3.3 Steps of the Hungarian Method:
Following steps describe the Hungarian Method.
Step 1. Subtract the minimum cost in each row of the price matrix from all the weather within the respective row.
4. VIVA-Tech International Journal for Research and Innovation
ISSN(Online): 2581-7280
Volume 1, Issue 4 (2021)
VIVA Institute of Technology
9th
National Conference on Role of Engineers in Nation Building – 2021 (NCRENB-2021)
E-24
Step 2. Subtract the minimum cost in each column of the value matrix from all the weather in the respective
column
Step 3. Starting with the primary row, check the rows step by step until a row containing exactly single zero is
found. Make an assignment by marking () that zero. Then cross (×) all other zeros within the column within
which the assignment was made. This eliminates the livelihood of constructing further assignments in this column.
Step 4. After examining all the rows, repeat the same procedure for columns. i.e. examine the columns one by one
until a column containing exactly one zero is found. Make an assignment by marking () that zero. Then cross
(×) all other zeros within the row within which the assignment was made.
Step 5. Continue these successive operations on rows and columns until all the zeros are either assigned or crossed
out and there’s exactly one assignment for each row and each column. In such case optimal solution is obtained.
Step 6. There could be some rows (or columns) without assignments i.e. the entire number of marked zeros is a
smaller amount than the order of the price matrix. In such case, proceed to step 7.
Step 7. Draw the smallest amount possible number of horizontal and vertical lines to hide all zeros.
This can be done as follows:
i) Mark ( ) the rows within which no assignment has been made.
ii) Mark ( ) the column having zeros within the marked rows.
iii) Mark ( ) rows which contain assignments in marked columns.
iv) Repeat 2 and three until the chain of marking is completed.
v) Draw straight lines through marked columns.
vi) Draw straight lines through unmarked rows.
By this fashion we draw the minimum number of horizontal and vertical lines required to cover all zeros. If the
amount of lines is less than the order of matrix, then there’s no solution. And if the minimum number of lines is
adequate to the order of matrix, then there is an answer and it’s optimal.
Step 8. If minimum number of lines < order of matrix, then
a) Select the littlest element not covered by any of the lines of the table.
3.4 Solve the following assignment using Hungarian Assignment Method:
Operator Machine
I II III IV V
1 18 24 19 20 23
2 19 21 20 18 22
3 22 23 20 21 23
4 20 18 21 19 19
5 18 22 23 22 21
Step 1: Subtract the smallest element of each row from each element of that row.
I II III IV V
1 0 6 1 2 4
2 1 3 2 0 3
3 2 3 0 1 3
4 2 0 3 1 1
5 0 4 5 4 3
5. VIVA-Tech International Journal for Research and Innovation
ISSN(Online): 2581-7280
Volume 1, Issue 4 (2021)
VIVA Institute of Technology
9th
National Conference on Role of Engineers in Nation Building – 2021 (NCRENB-2021)
E-25
Step 2: Subtract the smallest element of column from each element of that column.
I II III IV V
1 0 6 1 2 4
2 1 3 2 0 3
3 2 3 0 1 2
4 2 0 3 1 0
5 0 4 5 4 2
Step 3: Draw minimum number of lines (horizontal and vertical) that are required to cover all zeros in the matrix.
⓪
Here, minimum number of lines (4) < order of matrix (5). Therefore, we continue with the next step to create
additional zeros.
Step 4: (i) Find the smallest uncovered element (1)
(ii) Subtract this number from all uncovered elements and add it to all elements which lie at the intersection of
two lines.
I II III IV V
1 0 5 0 1 3 √
√
√
2 2 3 2 ⓪ 3
3 3 2 ⓪ 1 2
4 3 ⓪ 3 1 0
5 ⓪ 3 4 3 1
Here, minimum number of lines (4) < order of matrix (5). Therefore, we continue with the next step to create
additional zeros.
Step 5: (i) Find the smallest uncovered element (1)
(ii) Subtract this number from all uncovered elements and add it to all elements which lie at the intersection of
two lines.
(iii) Then assign through zeros.
I II III IV V
1 ⓪ 4 0 0 2
2 4 3 3 ⓪ 3
3 3 1 ⓪ 0 1
4 4 ⓪ 4 0 0
5 0 2 4 2 ⓪
Optimal Solution: 1→I, 2→IV, 3→III, 4→II, 5→V
Minimum Value = 18 + 18 + 20 +18 + 21 = 95
IV. Conclusion
I II III IV V
√
√
1 ⓪ 6 1 2 4
2 1 3 2 ⓪ 3
3 2 3 1 2
4 2 ⓪ 3 1 0
5 0 4 5 4 2
6. VIVA-Tech International Journal for Research and Innovation
ISSN(Online): 2581-7280
Volume 1, Issue 4 (2021)
VIVA Institute of Technology
9th
National Conference on Role of Engineers in Nation Building – 2021 (NCRENB-2021)
E-26
In this paper, we explained the proposed algorithm and, by numerical illustration, demonstrated its effectiveness.
And we get the optimal solution, which is the same as the HA-method and MOA-method optimal solutions. This
paper therefore presents a new approach that is easy to address the issue of assignment.
V. References
[1]. Operation Research – An Introduction by H A Taha
[2]. Hamdy A. Tsaha, 2007, Operations Research, an introduction, 8th
Ed..
[3]. Operation Research by Gupta Prem Kumar and Hira D S
[4]. Operation Research by Panneerselvam and R