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.
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.
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.
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 defines and provides a method for solving assignment problems. An assignment problem involves determining the most efficient assignment of people to projects to minimize costs or time. The Hungarian method is described as a way to solve assignment problems through a 7 step process that transforms the cost matrix to reveal the optimal assignment with minimum lines and intersections.
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 balanced and unbalanced assignment problems and the Hungarian method for solving them. It provides the following key points:
- Assignment problems involve assigning jobs to workers or machines to minimize costs or maximize output. The Hungarian method is commonly used to solve them.
- Balanced problems have an equal number of jobs and workers, while unbalanced problems have different numbers.
- The Hungarian method uses a matrix and steps of row/column reduction, finding minimum uncovered values, and covering zeros with lines to find an optimal assignment.
- An example shows applying the method to assign four jobs to four machines and minimizing costs in the assignment matrix.
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.
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.
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.
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 defines and provides a method for solving assignment problems. An assignment problem involves determining the most efficient assignment of people to projects to minimize costs or time. The Hungarian method is described as a way to solve assignment problems through a 7 step process that transforms the cost matrix to reveal the optimal assignment with minimum lines and intersections.
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 balanced and unbalanced assignment problems and the Hungarian method for solving them. It provides the following key points:
- Assignment problems involve assigning jobs to workers or machines to minimize costs or maximize output. The Hungarian method is commonly used to solve them.
- Balanced problems have an equal number of jobs and workers, while unbalanced problems have different numbers.
- The Hungarian method uses a matrix and steps of row/column reduction, finding minimum uncovered values, and covering zeros with lines to find an optimal assignment.
- An example shows applying the method to assign four jobs to four machines and minimizing costs in the assignment matrix.
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.
This document discusses different methods for solving assignment problems. It begins by defining an assignment problem as determining an optimal way to assign jobs to workers or machines. It then describes the Hungarian method, traveling salesman problem, and simplex method for solving assignment problems. The Hungarian method involves row and column reductions to identify a minimum cost assignment. The traveling salesman problem aims to find the shortest route between multiple cities. The simplex method formulates assignment problems as integer programs that can be solved using simplex algorithms.
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.
The document discusses solving assignment problems using different methods like visual method, enumeration method, transportation method, and the Hungarian method. It provides an example problem of assigning four subassemblies to four contractors to minimize total cost. The Hungarian method is used to solve this example problem, resulting in a minimum total cost of 4,900 birr by assigning: subassembly 1 to contractor 2, subassembly 2 to contractor 1, subassembly 3 to contractor 4, and subassembly 4 to contractor 3.
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.
The document discusses three methods for allocating goods in transportation problems: the North-West Corner method, Least-Cost method, and Vogel's Approximation Method. It also discusses the Assignment Method for solving assignment problems. The North-West Corner method allocates goods starting from the upper-left corner based on row and column totals. The Least-Cost method allocates goods to the lowest cost cell without exceeding supply/demand. Vogel's Approximation Method considers cost differences and allocates to the highest difference cell. The Assignment Method solves assignment problems by subtracting costs and covering entries to find the optimal assignment.
1) The document discusses the Hungarian method for solving assignment problems. It involves minimizing the total cost or maximizing the total profit of assigning resources like employees or machines to activities like jobs.
2) The method includes steps like developing a cost matrix, finding the opportunity cost table, making assignments to zeros in the table, and revising the table until an optimal solution is reached.
3) There are examples showing the application of these steps to problems with unique and multiple optimal solutions, as well as an unbalanced problem with more resources than activities.
Algorithm for Hungarian Method of AssignmentRaja Adapa
The Hungarian assignment algorithm is used to solve assignment problems to maximize total profit or minimize total cost. It involves 9 steps: 1) add dummy rows or columns if needed, 2) subtract smallest row elements from each row, 3) subtract smallest column elements from each column, 4) examine rows/columns for single zeros and cross out other zeros, 5) check if number of assigned cells equals rows/columns, 6) draw lines through zeros, 7) check if minimum lines equals rows/columns, 8) revise matrix by subtracting smallest covered element and adding to line intersections, 9) repeat steps 4-8 until optimum solution is found.
The document discusses the assignment problem, which aims to assign jobs to persons so that time, cost, or profit is optimized. It describes the model of an assignment problem using a 3x3 matrix. It outlines the steps to solve an assignment problem, including checking if it is balanced, subtracting row/column minimums, and using the Hungarian method if the initial assignment is not complete. The Hungarian method involves tick marks and strikethroughs to identify the minimum cost assignment. Finally, it notes there can be maximization problems, unbalanced matrices, alternative solutions, and restricted assignments.
The document discusses the assignment problem and the Hungarian method for solving it. It provides definitions for key terms like balanced vs unbalanced assignment problems and dummy jobs/persons. It also outlines the mathematical formulation of assignment problems and lists some common application areas. The summary describes the Hungarian method as follows:
1) It is used to solve assignment problems by finding the minimum cost matching between people/objects and tasks.
2) The method works on a cost matrix representing all possible assignments.
3) It uses the principle that the optimal solution does not change if a constant is subtracted from rows/columns with a total cost of zero.
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.
The document defines linear programming and its key components. It explains that linear programming is a mathematical optimization technique used to allocate limited resources to achieve the best outcome, such as maximizing profit or minimizing costs. The document outlines the basic steps of the simplex method for solving linear programming problems and provides an example to illustrate determining the maximum value of a linear function given a set of constraints. It also discusses other applications of linear programming in fields like engineering, manufacturing, energy, and transportation for optimization.
The document discusses the stable marriage problem and its solution using the Gale-Shapley algorithm. The stable marriage problem aims to match pairs of men and women for marriage such that there are no two people who would both rather be matched with each other over their assigned partners. The Gale-Shapley algorithm solves this problem by having the men and women iteratively propose to their preferred partners until all pairs are in stable marriages. An example with 5 men and 5 women ranked by their preferences is provided to illustrate the algorithm's steps.
Undecidable Problems and Approximation AlgorithmsMuthu Vinayagam
The document discusses algorithm limitations and approximation algorithms. It begins by explaining that some problems have no algorithms or cannot be solved in polynomial time. It then discusses different algorithm bounds and how to derive lower bounds through techniques like decision trees. The document also covers NP-complete problems, approximation algorithms for problems like traveling salesman, and techniques like branch and bound. It provides examples of approximation algorithms that provide near-optimal solutions when an optimal solution is impossible or inefficient to find.
This document discusses the Hungarian method for solving assignment problems. It begins by explaining the assignment problem and providing an example with 2 machines and 2 operators. It then describes the Hungarian method, which finds the optimal assignment in polynomial time. The method is explained through a 4x4 example, with the key steps being: 1) row and column reductions, 2) finding a complete assignment or using adjustments to enable it. The document also notes the method works for balanced or minimization problems, and how maximization problems can be converted. It concludes by providing a professor-subject example and walking through applying the Hungarian method to find the optimal assignment.
Divide and conquer is an algorithm design paradigm where a problem is broken into smaller subproblems, those subproblems are solved independently, and then their results are combined to solve the original problem. Some examples of algorithms that use this approach are merge sort, quicksort, and matrix multiplication algorithms like Strassen's algorithm. The greedy method works in stages, making locally optimal choices at each step in the hope of finding a global optimum. It is used for problems like job sequencing with deadlines and the knapsack problem. Minimum cost spanning trees find subgraphs of connected graphs that include all vertices using a minimum number of edges.
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 discusses different methods for minimizing Boolean functions, including algebraic manipulation, tabular methods, and Karnaugh maps. The tabular method involves grouping minterms based on their binary representations and combining terms that differ by one bit. Karnaugh maps provide a visual way to group adjacent minterms and identify prime implicants to find a minimized expression. Both methods aim to cover all minterms with the fewest prime implicants.
A brief study on linear programming solving methodsMayurjyotiNeog
This document summarizes linear programming and two methods for solving linear programming problems: the graphical method and the simplex method. It outlines the key components of linear programming problems including decision variables, objective functions, and constraints. It then describes the steps of the graphical method and simplex method in solving linear programming problems. The graphical method involves plotting the feasible region and objective function on a graph to find the optimal point. The simplex method uses an algebraic table approach to iteratively find the optimal solution.
End-to-end pipeline agility - Berlin Buzzwords 2024Lars Albertsson
We describe how we achieve high change agility in data engineering by eliminating the fear of breaking downstream data pipelines through end-to-end pipeline testing, and by using schema metaprogramming to safely eliminate boilerplate involved in changes that affect whole pipelines.
A quick poll on agility in changing pipelines from end to end indicated a huge span in capabilities. For the question "How long time does it take for all downstream pipelines to be adapted to an upstream change," the median response was 6 months, but some respondents could do it in less than a day. When quantitative data engineering differences between the best and worst are measured, the span is often 100x-1000x, sometimes even more.
A long time ago, we suffered at Spotify from fear of changing pipelines due to not knowing what the impact might be downstream. We made plans for a technical solution to test pipelines end-to-end to mitigate that fear, but the effort failed for cultural reasons. We eventually solved this challenge, but in a different context. In this presentation we will describe how we test full pipelines effectively by manipulating workflow orchestration, which enables us to make changes in pipelines without fear of breaking downstream.
Making schema changes that affect many jobs also involves a lot of toil and boilerplate. Using schema-on-read mitigates some of it, but has drawbacks since it makes it more difficult to detect errors early. We will describe how we have rejected this tradeoff by applying schema metaprogramming, eliminating boilerplate but keeping the protection of static typing, thereby further improving agility to quickly modify data pipelines without fear.
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.
This document discusses different methods for solving assignment problems. It begins by defining an assignment problem as determining an optimal way to assign jobs to workers or machines. It then describes the Hungarian method, traveling salesman problem, and simplex method for solving assignment problems. The Hungarian method involves row and column reductions to identify a minimum cost assignment. The traveling salesman problem aims to find the shortest route between multiple cities. The simplex method formulates assignment problems as integer programs that can be solved using simplex algorithms.
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.
The document discusses solving assignment problems using different methods like visual method, enumeration method, transportation method, and the Hungarian method. It provides an example problem of assigning four subassemblies to four contractors to minimize total cost. The Hungarian method is used to solve this example problem, resulting in a minimum total cost of 4,900 birr by assigning: subassembly 1 to contractor 2, subassembly 2 to contractor 1, subassembly 3 to contractor 4, and subassembly 4 to contractor 3.
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.
The document discusses three methods for allocating goods in transportation problems: the North-West Corner method, Least-Cost method, and Vogel's Approximation Method. It also discusses the Assignment Method for solving assignment problems. The North-West Corner method allocates goods starting from the upper-left corner based on row and column totals. The Least-Cost method allocates goods to the lowest cost cell without exceeding supply/demand. Vogel's Approximation Method considers cost differences and allocates to the highest difference cell. The Assignment Method solves assignment problems by subtracting costs and covering entries to find the optimal assignment.
1) The document discusses the Hungarian method for solving assignment problems. It involves minimizing the total cost or maximizing the total profit of assigning resources like employees or machines to activities like jobs.
2) The method includes steps like developing a cost matrix, finding the opportunity cost table, making assignments to zeros in the table, and revising the table until an optimal solution is reached.
3) There are examples showing the application of these steps to problems with unique and multiple optimal solutions, as well as an unbalanced problem with more resources than activities.
Algorithm for Hungarian Method of AssignmentRaja Adapa
The Hungarian assignment algorithm is used to solve assignment problems to maximize total profit or minimize total cost. It involves 9 steps: 1) add dummy rows or columns if needed, 2) subtract smallest row elements from each row, 3) subtract smallest column elements from each column, 4) examine rows/columns for single zeros and cross out other zeros, 5) check if number of assigned cells equals rows/columns, 6) draw lines through zeros, 7) check if minimum lines equals rows/columns, 8) revise matrix by subtracting smallest covered element and adding to line intersections, 9) repeat steps 4-8 until optimum solution is found.
The document discusses the assignment problem, which aims to assign jobs to persons so that time, cost, or profit is optimized. It describes the model of an assignment problem using a 3x3 matrix. It outlines the steps to solve an assignment problem, including checking if it is balanced, subtracting row/column minimums, and using the Hungarian method if the initial assignment is not complete. The Hungarian method involves tick marks and strikethroughs to identify the minimum cost assignment. Finally, it notes there can be maximization problems, unbalanced matrices, alternative solutions, and restricted assignments.
The document discusses the assignment problem and the Hungarian method for solving it. It provides definitions for key terms like balanced vs unbalanced assignment problems and dummy jobs/persons. It also outlines the mathematical formulation of assignment problems and lists some common application areas. The summary describes the Hungarian method as follows:
1) It is used to solve assignment problems by finding the minimum cost matching between people/objects and tasks.
2) The method works on a cost matrix representing all possible assignments.
3) It uses the principle that the optimal solution does not change if a constant is subtracted from rows/columns with a total cost of zero.
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.
The document defines linear programming and its key components. It explains that linear programming is a mathematical optimization technique used to allocate limited resources to achieve the best outcome, such as maximizing profit or minimizing costs. The document outlines the basic steps of the simplex method for solving linear programming problems and provides an example to illustrate determining the maximum value of a linear function given a set of constraints. It also discusses other applications of linear programming in fields like engineering, manufacturing, energy, and transportation for optimization.
The document discusses the stable marriage problem and its solution using the Gale-Shapley algorithm. The stable marriage problem aims to match pairs of men and women for marriage such that there are no two people who would both rather be matched with each other over their assigned partners. The Gale-Shapley algorithm solves this problem by having the men and women iteratively propose to their preferred partners until all pairs are in stable marriages. An example with 5 men and 5 women ranked by their preferences is provided to illustrate the algorithm's steps.
Undecidable Problems and Approximation AlgorithmsMuthu Vinayagam
The document discusses algorithm limitations and approximation algorithms. It begins by explaining that some problems have no algorithms or cannot be solved in polynomial time. It then discusses different algorithm bounds and how to derive lower bounds through techniques like decision trees. The document also covers NP-complete problems, approximation algorithms for problems like traveling salesman, and techniques like branch and bound. It provides examples of approximation algorithms that provide near-optimal solutions when an optimal solution is impossible or inefficient to find.
This document discusses the Hungarian method for solving assignment problems. It begins by explaining the assignment problem and providing an example with 2 machines and 2 operators. It then describes the Hungarian method, which finds the optimal assignment in polynomial time. The method is explained through a 4x4 example, with the key steps being: 1) row and column reductions, 2) finding a complete assignment or using adjustments to enable it. The document also notes the method works for balanced or minimization problems, and how maximization problems can be converted. It concludes by providing a professor-subject example and walking through applying the Hungarian method to find the optimal assignment.
Divide and conquer is an algorithm design paradigm where a problem is broken into smaller subproblems, those subproblems are solved independently, and then their results are combined to solve the original problem. Some examples of algorithms that use this approach are merge sort, quicksort, and matrix multiplication algorithms like Strassen's algorithm. The greedy method works in stages, making locally optimal choices at each step in the hope of finding a global optimum. It is used for problems like job sequencing with deadlines and the knapsack problem. Minimum cost spanning trees find subgraphs of connected graphs that include all vertices using a minimum number of edges.
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 discusses different methods for minimizing Boolean functions, including algebraic manipulation, tabular methods, and Karnaugh maps. The tabular method involves grouping minterms based on their binary representations and combining terms that differ by one bit. Karnaugh maps provide a visual way to group adjacent minterms and identify prime implicants to find a minimized expression. Both methods aim to cover all minterms with the fewest prime implicants.
A brief study on linear programming solving methodsMayurjyotiNeog
This document summarizes linear programming and two methods for solving linear programming problems: the graphical method and the simplex method. It outlines the key components of linear programming problems including decision variables, objective functions, and constraints. It then describes the steps of the graphical method and simplex method in solving linear programming problems. The graphical method involves plotting the feasible region and objective function on a graph to find the optimal point. The simplex method uses an algebraic table approach to iteratively find the optimal solution.
Semelhante a Muzammil irshad.pptxhdududududiufufufufu (20)
End-to-end pipeline agility - Berlin Buzzwords 2024Lars Albertsson
We describe how we achieve high change agility in data engineering by eliminating the fear of breaking downstream data pipelines through end-to-end pipeline testing, and by using schema metaprogramming to safely eliminate boilerplate involved in changes that affect whole pipelines.
A quick poll on agility in changing pipelines from end to end indicated a huge span in capabilities. For the question "How long time does it take for all downstream pipelines to be adapted to an upstream change," the median response was 6 months, but some respondents could do it in less than a day. When quantitative data engineering differences between the best and worst are measured, the span is often 100x-1000x, sometimes even more.
A long time ago, we suffered at Spotify from fear of changing pipelines due to not knowing what the impact might be downstream. We made plans for a technical solution to test pipelines end-to-end to mitigate that fear, but the effort failed for cultural reasons. We eventually solved this challenge, but in a different context. In this presentation we will describe how we test full pipelines effectively by manipulating workflow orchestration, which enables us to make changes in pipelines without fear of breaking downstream.
Making schema changes that affect many jobs also involves a lot of toil and boilerplate. Using schema-on-read mitigates some of it, but has drawbacks since it makes it more difficult to detect errors early. We will describe how we have rejected this tradeoff by applying schema metaprogramming, eliminating boilerplate but keeping the protection of static typing, thereby further improving agility to quickly modify data pipelines without fear.
Learn SQL from basic queries to Advance queriesmanishkhaire30
Dive into the world of data analysis with our comprehensive guide on mastering SQL! This presentation offers a practical approach to learning SQL, focusing on real-world applications and hands-on practice. Whether you're a beginner or looking to sharpen your skills, this guide provides the tools you need to extract, analyze, and interpret data effectively.
Key Highlights:
Foundations of SQL: Understand the basics of SQL, including data retrieval, filtering, and aggregation.
Advanced Queries: Learn to craft complex queries to uncover deep insights from your data.
Data Trends and Patterns: Discover how to identify and interpret trends and patterns in your datasets.
Practical Examples: Follow step-by-step examples to apply SQL techniques in real-world scenarios.
Actionable Insights: Gain the skills to derive actionable insights that drive informed decision-making.
Join us on this journey to enhance your data analysis capabilities and unlock the full potential of SQL. Perfect for data enthusiasts, analysts, and anyone eager to harness the power of data!
#DataAnalysis #SQL #LearningSQL #DataInsights #DataScience #Analytics
Analysis insight about a Flyball dog competition team's performanceroli9797
Insight of my analysis about a Flyball dog competition team's last year performance. Find more: https://github.com/rolandnagy-ds/flyball_race_analysis/tree/main
Open Source Contributions to Postgres: The Basics POSETTE 2024ElizabethGarrettChri
Postgres is the most advanced open-source database in the world and it's supported by a community, not a single company. So how does this work? How does code actually get into Postgres? I recently had a patch submitted and committed and I want to share what I learned in that process. I’ll give you an overview of Postgres versions and how the underlying project codebase functions. I’ll also show you the process for submitting a patch and getting that tested and committed.
Orchestrating the Future: Navigating Today's Data Workflow Challenges with Ai...Kaxil Naik
Navigating today's data landscape isn't just about managing workflows; it's about strategically propelling your business forward. Apache Airflow has stood out as the benchmark in this arena, driving data orchestration forward since its early days. As we dive into the complexities of our current data-rich environment, where the sheer volume of information and its timely, accurate processing are crucial for AI and ML applications, the role of Airflow has never been more critical.
In my journey as the Senior Engineering Director and a pivotal member of Apache Airflow's Project Management Committee (PMC), I've witnessed Airflow transform data handling, making agility and insight the norm in an ever-evolving digital space. At Astronomer, our collaboration with leading AI & ML teams worldwide has not only tested but also proven Airflow's mettle in delivering data reliably and efficiently—data that now powers not just insights but core business functions.
This session is a deep dive into the essence of Airflow's success. We'll trace its evolution from a budding project to the backbone of data orchestration it is today, constantly adapting to meet the next wave of data challenges, including those brought on by Generative AI. It's this forward-thinking adaptability that keeps Airflow at the forefront of innovation, ready for whatever comes next.
The ever-growing demands of AI and ML applications have ushered in an era where sophisticated data management isn't a luxury—it's a necessity. Airflow's innate flexibility and scalability are what makes it indispensable in managing the intricate workflows of today, especially those involving Large Language Models (LLMs).
This talk isn't just a rundown of Airflow's features; it's about harnessing these capabilities to turn your data workflows into a strategic asset. Together, we'll explore how Airflow remains at the cutting edge of data orchestration, ensuring your organization is not just keeping pace but setting the pace in a data-driven future.
Session in https://budapestdata.hu/2024/04/kaxil-naik-astronomer-io/ | https://dataml24.sessionize.com/session/667627
STATATHON: Unleashing the Power of Statistics in a 48-Hour Knowledge Extravag...sameer shah
"Join us for STATATHON, a dynamic 2-day event dedicated to exploring statistical knowledge and its real-world applications. From theory to practice, participants engage in intensive learning sessions, workshops, and challenges, fostering a deeper understanding of statistical methodologies and their significance in various fields."
Build applications with generative AI on Google CloudMárton Kodok
We will explore Vertex AI - Model Garden powered experiences, we are going to learn more about the integration of these generative AI APIs. We are going to see in action what the Gemini family of generative models are for developers to build and deploy AI-driven applications. Vertex AI includes a suite of foundation models, these are referred to as the PaLM and Gemini family of generative ai models, and they come in different versions. We are going to cover how to use via API to: - execute prompts in text and chat - cover multimodal use cases with image prompts. - finetune and distill to improve knowledge domains - run function calls with foundation models to optimize them for specific tasks. At the end of the session, developers will understand how to innovate with generative AI and develop apps using the generative ai industry trends.
1. Submitted by: MUZAMMIL IRSHAD
Enrollment no.: 72215601723
Branch/Sem: BBA 2nd Sem
Section: B
ASSIGNMENT PROBLEM
2. WHAT IS ASSIGNMENT PROBLEM?
• It involves assignment of people to pro jobs to machines, workers to jobs and teachers to classes etc.,
while minimizing the total assignment costs.
• One of the important characteristics of assignment problem is that only one job (or worker) is assigned to
one machine (or project). An assignment problem is a special type of linear programming problem where
the objective is to minimize the cost or time of completing a number of jobs by a number of persons.
• This method was developed by D. Kon Hungarian mathematician and is there known as the Hungarian
method of assignment problem.
• In order to use this method, one needs to know only the cost of making all the possible assignments.
• Each assignment problem has a matrix (table) associated with it. Normally, the objects (or people) one
wishes to assign are expressed in rows, whereas the columns represent the tasks (or things) assigned to
them.
• The number in the table would then be the costs associated with each particular assignment.
3. HUNGARIAN METHOD
• Top Banner The Hungarian method is a computational optimization technique that addresses
the assignment problem in polynomial time and foreshadows following primal-dual alternatives.
In 1955, Harold Kuhn used the term “Hungarian method” to honour two Hungarian
mathematicians, Dénes Kőnig and Jenő Egerváry. Let’s go through the steps of the Hungarian
method with the help of a solved example..
HUNGARIAN METHOD TO SOLVE ASSIGNMENT PROBLEMS
• The Hungarian method is a simple way to solve assignment problems. Let us first discuss
the assignment problems before moving on to learning the Hungarian method
4. HUNGARIAN METHOD STEPS
• Check to see if the number of rows and columns are equal; if they are, the assignment problem is considered to be balanced. Then go to step 1. If it is not balanced, it should be balanced before the algorithm is
applied.
• Step 1 – In the given cost matrix, subtract the least cost element of each row from all the entries in that row. Make sure that each row has at least one zero.
• Step 2 – In the resultant cost matrix produced in step 1, subtract the least cost element in each column from all the components in that column, ensuring that each column contains at least one zero.
• Step 3 – Assign zeros Analyse the rows one by one until you find a row with precisely one unmarked zero. Encircle this lonely unmarked zero and assign it a task. All other zeros in the column of this circular zero
should be crossed out because they will not be used in any future assignments. Continue in this manner until you’ve gone through all of the rows.Examine the columns one by one until you find one with precisely
one unmarked zero. Encircle this single unmarked zero and cross any other zero in its row to make an assignment to it. Continue until you’ve gone through all of the columns.
• Step 4 – Perform the Optimal TestThe present assignment is optimal if each row and column has exactly one encircled zero.The present assignment is not optimal if at least one row or column is missing an
assignment (i.e., if at least one row or column is missing one encircled zero). Continue to step 5. Subtract the least cost element from all the entries in each column of the final cost matrix created in step 1 and
ensure that each column has at least one zero.
• Step 5 – Draw the least number of straight lines to cover all of the zeros as follows:(a) Highlight the rows that aren’t assigned.(b) Label the columns with zeros in marked rows (if they haven’t already been
marked).(c) Highlight the rows that have assignments in indicated columns (if they haven’t previously been marked). (d) Continue with (b) and (c) until no further marking is needed.(f) Simply draw the lines
through all rows and columns that are not marked. If the number of these lines equals the order of the matrix, then the solution is optimal; otherwise, it is not..
• Step 6 – Find the lowest cost factor that is not covered by the straight lines. Subtract this least-cost component from all the uncovered elements and add it to all the elements that are at the intersection of these
straight lines, but leave the rest of the elements alone.
• Step 7 – Continue with steps 1 – 6 until you’ve found the highest suitable assignment
5.
6. TYPE OF ASSIGNMENT PROBLEM
Balanced Assignment Problem:
• Balanced Assignment Problem is an assignment problem where the number of facilities is equal
to the number of jobs.
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.
Dummy Job/Facility:
• A dummy job or facility is an imaginary job/facility with zero cost or time introduced to make an
unbalanced assignment problem balanced.
Infeasible Assignment:
An Infeasible Assignment occurs in the cell (i, j) of the assignment cost matrix if ith person is
unable to perform jth job. It is sometimes possible that a particular person is incapable of doing certain
work or a specific job cannot be performed on a particular machine. The solution of the assignment
problem should take into account these restrictions so that the infeasible assignments can be avoided.
This can be achieved by assigning a very high cost to the cells where assignments are prohibited.
7. UNBALANCED ASSIGNMENT PROBLEMS
• 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. The dummy rows or columns will contain all costs elements
as zeroes. The Hungarian method may be used to solve the problem.
8.
9. RESTRICTION IN ASSIGNMENT
• It is sometimes possible that a particular person is incapable of doing certain work
or a specific job cannot be performed on a particular machine. The solution of the
assignment problem should take into account these restrictions so that the
restricted (infeasible) assignment can be avoided. This can be achieved by assigning
a very high cost (say ∞ or M)to the cells where assignments are prohibited, thereby
restricting the entry of this pair of job-machine or resource-activity into the final
solution.
10.
11. TRAVELLING SALESMAN MODEL
Given a set of cities and distances between every pair of cities, the problem is
to find the shortest possible route that visits every city exactly once and
returns to the starting point.
Note the difference between Hamiltonian Cycle and TSP. The Hamiltonian
cycle problem is to find if there exists a tour that visits every city exactly
once. Here we know that Hamiltonian Tour exists (because the graph is
complete) and in fact, many such tours exist, the problem is to find a
minimum weight Hamiltonian Cycle.