Unit ii-3-am
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The document discusses an assignment problem where there are 5 machines that each need to be assigned to 1 of 5 jobs. It provides the mathematical formulation and explains how to use the Hungarian method to determine the optimal assignment that minimizes total cost. Specifically, it involves creating a cost matrix, reducing costs by subtracting row and column minimums to find a matrix with all zeros, and using lines to cover the zeros and identify the optimal assignment. Some applications of assignment problems are also listed such as assigning salespeople to territories or vehicles to routes.
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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.
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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.
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This document discusses operational research and assignment techniques. It begins by defining operational research as a scientific approach to problem solving aimed at reducing costs. It then provides examples of how operational research is used in various sectors like transportation, healthcare, and banking. The document outlines the characteristics and limitations of operational research. It proceeds to define assignment techniques as a way to allocate jobs and resources in the lowest cost manner. The remainder of the document details the specific steps involved in solving an assignment problem using a matrix-based approach to find an optimal solution.
Algorithm for Hungarian Method of Assignment
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.
Assignment model
The assignment problem is a special case of transportation problem in which the objective is to assign ‘m’ jobs or workers to ‘n’ machines such that the cost incurred is minimized.
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The document discusses several assignment problems involving allocating jobs or tasks to machines, employees, clerks or cities in an optimal way to minimize time, cost or maximize returns. Specific problems include assigning 5 jobs to 5 machines to minimize total time, assigning jobs to machines to maximize total returns, assigning 4 jobs to 3 staff to minimize total time, assigning clerks to tasks where some assignments are prohibited, and finding the optimal tour for a salesman to visit 5 cities while minimizing total distance traveled. Solutions to these assignment problems are to be found using techniques like the assignment algorithm, Hungarian method, column reduction, row reduction and prohibiting certain assignments.
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The document discusses the assignment problem and various methods to solve it. The assignment problem involves assigning jobs to workers or other resources in an optimal way according to certain criteria like minimizing time or cost. The Hungarian assignment method is described as a multi-step algorithm to find the optimal assignment between jobs and workers/resources. It involves creating a cost matrix and performing row and column reductions to arrive at a matrix with zeros that indicates the optimal assignment. The document also briefly discusses handling unbalanced and constrained assignment problems.
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Assignment problem method
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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.
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The assignment problem is a special case of transportation problem in which the objective is to assign ‘m’ jobs or workers to ‘n’ machines such that the cost incurred is minimized.
Hungarian algorithm
Hungarian Algorithm which is used in optimizing the assignment problems are simply described using a working example.
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The document discusses the assignment problem and various methods to solve it. The assignment problem involves assigning jobs to workers or other resources in an optimal way according to certain criteria like minimizing time or cost. The Hungarian assignment method is described as a multi-step algorithm to find the optimal assignment between jobs and workers/resources. It involves creating a cost matrix and performing row and column reductions to arrive at a matrix with zeros that indicates the optimal assignment. The document also briefly discusses handling unbalanced and constrained assignment problems.
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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.
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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.
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The document discusses the assignment problem and provides examples of solving it using different methods. It can be summarized as:
1) The assignment problem involves allocating tasks or jobs to workers or machines in the most efficient way, often to minimize costs. It has special characteristics as each job can only be assigned to one worker.
2) The document provides examples of solving assignment problems using methods like the least cost method, stepping stone method, and the Hungarian method.
3) It also discusses how to model assignment problems as transportation problems and how to solve maximization versions by converting to minimization problems.
Hungarian Method
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.
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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.
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The document discusses different methods to solve assignment problems including enumeration, integer programming, transportation, and Hungarian methods. It provides examples of balanced and unbalanced minimization and maximization problems. The Hungarian method is described as having steps like row and column deduction, assigning zeros, and tick marking to find the optimal assignment with the minimum cost or maximum profit. A sample problem demonstrates converting a profit matrix to a relative cost matrix and using the Hungarian method to find the optimal solution.
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My name is Niraj Thapa. I have compiled Assignment Chapter including SM, PM & Exam Questions of AMA.
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Assignment problem
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.
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AMA_Assignment Theory notes
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.
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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.
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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.
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This is a special type of LPP in which the objective function is to find the optimum allocation of a number of tasks (jobs) to an equal number of facilities (persons). Here we make the assumption that each person can perform each job but with varying degree of efficiency. For example, a departmental head may have 4 persons available for assignment and 4 jobs to fill. Then his interest is to find the best assignment which will be in the best interest of the department.
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Assignment Poblems
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.
Assignment problem
The document discusses the assignment problem and provides examples of solving it using different methods. It can be summarized as:
1) The assignment problem involves allocating tasks or jobs to workers or machines in the most efficient way, often to minimize costs. It has special characteristics as each job can only be assigned to one worker.
2) The document provides examples of solving assignment problems using methods like the least cost method, stepping stone method, and the Hungarian method.
3) It also discusses how to model assignment problems as transportation problems and how to solve maximization versions by converting to minimization problems.
Hungarian Method
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.
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The document describes an assignment problem involving assigning tasks to employees at Big Bazaar to maximize total effectiveness. It provides an example of assigning 5 tasks (Research, Selling, Advertising, Customer Service, Managing Budget) to 5 employees (Rohit, Raj, Nikhat, Amar, Kumal) based on their effectiveness levels for each task. The optimal assignment achieved a total effectiveness of 300. It also examines whether assigning the Advertising task to Amar was correct, which it determined was correct as it maximized total effectiveness. A second example involves scheduling seminars at TCS to minimize the number of employees unable to attend. The optimal schedule assigns seminars on specific days with a total of 70 employees unable to attend at least one
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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.
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The document discusses different methods to solve assignment problems including enumeration, integer programming, transportation, and Hungarian methods. It provides examples of balanced and unbalanced minimization and maximization problems. The Hungarian method is described as having steps like row and column deduction, assigning zeros, and tick marking to find the optimal assignment with the minimum cost or maximum profit. A sample problem demonstrates converting a profit matrix to a relative cost matrix and using the Hungarian method to find the optimal solution.
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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.
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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.
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2. The solution involves drawing the projections of the points A and B, determining the true length (TL) of the line AB, and locating its traces by extending the projections.
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2. The elevation of the line measures 78 mm. The true length of the line and the inclination of the line to the horizontal plane must be found. The traces of the line must also be located.
3. The steps involve drawing the projections, locating the points P' and Q', drawing the inclined line using the given angle, measuring the true length and inclination angle, and determining the traces.
AMA_Assignment Theory notes
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.
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The document discusses various topics related to assembly modeling including assembly modelling, interference checking, tolerance analysis, and mass property calculations. It describes assembly modeling concepts such as different assembly approaches (bottom-up, top-down), mating conditions (coincident, concentric, etc.), and assembly planning considerations (part dependencies, assembly order). Tolerance analysis methods like worst case arithmetic, worst case statistical and Monte Carlo simulation are summarized. Mass property calculations of parts like mass, center of gravity, and moments of inertia are also covered. Finally, mechanism simulation and interference checking are introduced.
99995327.ppt
The document discusses different techniques for clipping lines and polygons to a viewing window or clipping region.
It describes line clipping algorithms like Cohen-Sutherland that use outcodes to quickly reject lines outside the clipping region or clip lines intersecting the boundary. It also discusses the midpoint subdivision algorithm for line clipping.
For polygon clipping, it explains the Sutherland-Hodgeman algorithm which clips polygons against each window edge one by one, dividing the polygon into smaller clipped polygons inside the viewing region.
matrices_and_loops.pptx
An array is a fixed size sequence of elements of the same type. It allows direct access to elements by their index position. Arrays can store multiple values in an organized way and are a fundamental abstract data type. The document then provides algorithms for matrix addition, subtraction, and multiplication using two-dimensional arrays. It also discusses sparse matrices and different types of control statements like if/else, loops (while, do-while, for), and nested structures.
CIM 15ME62 Module-3
This document provides an overview of line balancing methods and computerized line balancing. It discusses traditional line balancing methods like the largest candidate rule, Kilbridge and Wester method, and ranked positional weights method. It also describes computerized line balancing algorithms like COMSOAL that use heuristics and random selection to explore solutions. The COMSOAL method is explained through an example where work elements are assigned to stations while meeting precedence and cycle time constraints.
Undecidable Problems and Approximation Algorithms
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.
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22d2optimalassemblylinebalancing222 110829065724-phpapp02
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Vam
numerical on vogel's approximation method for finding the initial solution to a transportation model problem
Simplex method maximisation
The document summarizes the simplex method for solving linear programming problems involving maximization. It involves 12 steps: 1) Formulating the LPP, 2) Introducing slack, surplus and artificial variables, 3) Formulating the initial basic solution, 4) Constructing the initial simplex table, 5) Checking for positive elements in the Cj-Zj row, 6) Identifying the incoming basic variable, 7) Choosing the incoming basic variable if multiple positives exist, 8) Identifying the outgoing basic variable, 9) Constructing the next simplex table using row operations, 10) Completing the new simplex table, 11) Repeating steps 5-10, and 12) Terminating when the
Project networks
A publisher has contracted an author to produce a textbook. The production process involves the author submitting a manuscript and files, editing, sample page and cover design, artwork, formatting, and printing. The critical path through the network is the author submitting the manuscript, editing, formatting, artwork approval, plate production, and binding, taking 17 weeks total to complete the project.
Or flowchart
This flowchart outlines an optimization process to find an optimal solution. It starts with finding an initial basic solution, then checks if that solution is optimal. If it is optimal, that solution is the final answer. If not, the process seeks a better solution to try and find the optimal one.
Strategic management model
The document outlines a strategic management model that includes four main stages: strategic intent, formulation, implementation, and evaluation. It involves analyzing internal and external environments to determine a vision, mission, goals and objectives. Strategies are then formulated, implemented through resource allocation and structure, and evaluated for effectiveness with feedback into reformulation.
Maximisation problem
The document presents a linear programming problem to determine the optimal production mix for two products (P1 and P2) that maximizes profit. The products have different processing times and resource requirements on milling and drilling machines, which have limited weekly hours. The problem is formulated as a linear program to maximize total profit subject to the machine hour constraints. Slack variables are introduced and the problem is solved using the simplex method to find the optimal production levels of 50 units of P1 and 20 units of P2, yielding maximum profit of Rs. 20,500.
Lpp numerical
an LPP problem asked in aktu mba exam in 2008 (operations research) formulated, and solved using simplex method
Lpp numerical solved
a linear programming problem asked in aktu mba exam of operations research in 2008, formulated, and solved using graphical method
Lpp formulation
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.
Lp formulation
This document formulates a linear programming problem to determine the optimal production quantities of Products P1 and P2 given machine time and contribution margin constraints. Product P1 takes 4 hours on machine M1 and 2 hours on M2, while Product P2 takes 2 hours on M1 and 4 hours on M2. The objective is to maximize total contribution by choosing the quantities x1 and x2 subject to the 60 hours available on M1, 48 hours on M2, and non-negativity constraints.
Graphical method
The document describes a production problem involving two products (P1 and P2) that are manufactured using two machines (M1 and M2). P1 requires 4 hours on M1 and 2 hours on M2, while P2 requires 2 hours on M1 and 4 hours on M2. The goal is to determine the optimal quantities of P1 and P2 to maximize total contribution, given 60 hours available on M1 and 48 hours on M2. This problem is modeled as a linear programming problem and graphically solved by plotting the constraint lines and finding their intersection point.
Games
The document contains information about game theory including pure strategies, mixed strategies, and solving games. It provides examples of games represented as payoff matrices and discusses applying the principles of dominance, algebraic methods for 2x2 games, graphical methods for 2xn and mx2 games, and linear programming for mxn games. It also includes an example analyzing a 6x6 game modeling the Allied invasion of Normandy in WWII.
Game theory
Four teams will participate in a game involving selecting strategies of A or B. The aim is to score the maximum dividends. Scoring is based on the number of As and Bs selected. The document then explains the Prisoner's Dilemma game theory concept where two prisoners can either cooperate or betray each other, and discusses why rational individuals may not cooperate even if it is in their best interest to do so.
Dual formulation example
The document discusses how to formulate the dual of a primal linear programming problem. It provides 10 steps for converting a primal maximization problem into a dual minimization problem. As an example, it formulates the dual of the primal problem: Maximize z = -5x1 + 2x2 subject to x1 - x2 ≥ 2 and 2x1 + 3x2 ≤ 5, with non-negativity constraints. The dual is formulated as: Minimize z = -2y1 + 5y2 subject to -y1 + 2y2 ≥ -5 and y1 + 3y2 ≥ 2, with non-negativity constraints on the dual variables y1 and y2.
Decision tree solved
A finance manager is considering drilling a well on their property. Based on past data, there is a 70% chance of finding water at 20 meters depth, and a 20% chance of finding water between 20-25 meters if no water is found at 20 meters. The costs to drill are Rs.500 per meter plus Rs.15,000 to buy water externally if the well is not drilled. The optimal decision tree strategy is to first drill to 20 meters, and if no water, then drill further to 25 meters, resulting in an expected cost of Rs. 11,350.
Decision theory numerical
The grocer must decide how many cases of milk to stock for tomorrow's demand. Each case sold yields a profit of Rs.3, but unsold cases at the end of the day lose Rs.5. Historical demand data shows the number of cases demanded and the probability of each quantity. The optimal decision can be determined by calculating the expected monetary value (EMV) of stocking different quantities of milk based on the probabilities and outcomes. The expected profit for the grocer if they stock the quantity with the highest EMV is Rs.47.7.
Crashing
project management. crashing a network. finding optimum duration and optimum cost of project. operations research (OR)
Assignment model problems
A fast food chain wants to build four new stores and received bids from six construction companies. The document shows the bid amounts in a table and describes using the Hungarian method to determine the optimal assignment of companies to stores that minimizes the total cost. The method involves reducing the table through successive steps to reveal a unique solution with no remaining zeros. The result assigns each store to a single construction company to minimize the total cost for building all four stores.
Minimisation problem
a minimisation linear programming problem (LPP), solved using simplex method (operations research: OR)
Operations research
Operations research (OR) is a tool used to increase the effectiveness of managerial decisions. It can help with profit maximization, production management like determining optimal product mix and scheduling, financial management, marketing management, and personnel management. Some common OR models include linear programming, transportation, assignment, and sequencing problems. OR uses mathematical techniques like linear programming, decision theory, game theory, queuing theory, simulation, network analysis, and inventory models.
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QU本科学位证成绩单【微信95270640】《皇后大学毕业证书原版制作QU成绩单》【Q微信95270640】《仿制QU毕业证成绩单皇后大学学位证书pdf电子图》，A.为什么留学生需要操作留信认证?
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Unit ii-3-am
- 3. • Suppose there are 5 machines and 5 jobs to be performed. • 1 machine can do only 1 job at a time. • How the machines should be assigned to the jobs? • Given – the cost of performing a job on a machine. • An Assignment Problem (AP) is always square. • The assignment is done on a one-to-one matching basis.
- 4. • Only one allocation is possible in a given row or column. • The AP is inherently degenerate, as the assignment is done on a one-to-one matching basis. (In the above 5 machine 5 job problem, there would be 25 cells, but allocation can be made only in 5 cells, whereas 9 cells should be allocated.) • Total number of assignments possible = n!
- 6. Hungarian Method Machine X Y Z Job A 25 31 35 B 15 20 24 C 22 19 17 • Machine opportunity and job opportunity cost to be determined. • The minimum element of a particular row or column to be subtracted from all elements of that row or column.
- 7. Machine X Y Z Job A 25 31 35 B 15 20 24 C 22 19 17
- 8. Machine X Y Z Job A 25 31 35 B 15 20 24 C 22 19 17
- 9. Machine X Y Z Job A 25-25 31-25 35-25 B 15-15 20-15 24-15 C 22-17 19-17 17-17
- 10. Machine X Y Z Job A 0 6 10 B 0 5 9 C 5 2 0 Job Opportunity Cost 1st Reduced Cost Matrix
- 11. Machine X Y Z Job A 0 6 10 B 0 5 9 C 5 2 0
- 12. Machine X Y Z Job A 0 4 10 B 0 3 9 C 5 0 0 Machine Opportunity Cost 2nd Reduced Cost (Total Opportunity Cost) Matrix
- 13. 0 4 10 0 3 9 5 0 0 • Optimal assignment is that assignment where total opportunity cost is zero. • We draw horizontal and vertical lines so as to cross all the zero elements using the minimum number of lines.
- 14. 0 4 10 0 3 9 5 0 0 • Optimal assignment is that assignment where total opportunity cost is zero. • We draw horizontal and vertical lines so as to cross all the zero elements using the minimum number of lines. • If the minimum number of lines required to do so is equal to the number of rows or columns, then optimum allocation is possible.
- 15. 0 4 10 0 3 9 5 0 0 • Optimal assignment is that assignment where total opportunity cost is zero. • We draw horizontal and vertical lines so as to cross all the zero elements using the minimum number of lines. • If the minimum number of lines required to do so is equal to the number of rows or columns, then optimum allocation is possible. • In this case it is not possible.
- 16. 0 4 10 0 3 9 5 0 0 • We identify the minimum element not covered by lines.
- 17. 0 4 10 0 3 9 5 0 0 • We identify the minimum element not covered by lines. • In this case it is 3.
- 18. 0 4 10 0 3 9 5 0 0 • We subtract it from…
- 19. Assignment Model: Applications • Assign salespeople to sales territories. • Assign vehicles to routes. • Assign accountants to client accounts. • Assign contracts to bidders through systematic evaluation of bids from competing suppliers. • Assign naval vessels to patrol sectors. • Schedule teachers to classes.
- 20. Assignment Model: Applications • Matching men to machines according to pieces produced per hour by each individual on each machine. • Matching teams to projects by the expected cost of each team to accomplish each project.