DIVIDE ROW MINIMA AND SUBTRACT COLUMN MINIMA TECHNIQUE FOR SOLVING ASSIGNMENT PROBLEMS (original) (raw)
Related papers
IOP Publishing, 2021
The assignment problems (AP) are an important part of linear programming problems (LPP) that deal with the allocation of different resources for different activities based on one to one. The assignment problem is established in a variety positions when decision makers need to determine the optimal allocation and this means assigning only one task to one person to achieve maximum profits or imports or achieve less time or less cost based on the type of problem. In this work, a new technique has been provided to find an optimal solution for the assignment problems of maximization objective function. Comparing the proposed technique results with the Hungarian method indicates that the new technique has easier and less steps to find the optimal solution and thus the time is reduced and the effort is largely reduced.
A Comparative Analysis of Assignment Problem
Assignment problems arise in different situation where we have to find an optimal way to assign n-objects to mother objects in an injective fashion. The assignment problems are a well studied topic in combinatorial optimization. These problems find numerous application in production planning, telecommunication VLSI design, economic etc. The assignment problems is a special case of Transportation problem. Depending on the objective we want to optimize, we obtain the typical assignment problems. Assignment problem is an important subject discussed in real physical world we endeavor in this paper to introduce a new approach to assignment problem namely, matrix ones assignment method or MOA-method for solving wide range of problem. An example using matrix ones assignment methods and the existing Hungarian method have been solved and compared it graphically. Also some of the variations and some special cases in assignment problem and its applications have been discussed in the paper.
A NEW APPROACH TO SOLVE AN UNBALANCED ASSIGNMENT PROBLEM
In this paper I have proposed a new approach to solve an unbalanced assignment problem (UBAP). This approach includes two parts. First is to obtain an initial basic feasible solution (IBFS) and second part is to test optimality of an IBFS. I have proposed two new methods Row Penalty Assignment Method (RPAM) and Column Penalty Assignment Method (CPAM) to obtain an IBFS of an UBAP. Also I have proposed a new method Non-basic Smallest Effectiveness Method (NBSEM) to test optimality of an IBFS. We can solve an assignment problem of maximization type using this new approach in opposite sense. By this new approach, we achieve the goal with less number of computations and steps. Further we illustrate the new approach by suitable examples. INTRODUCTION The assignment problem is a special case of the transportation problem where the resources are being allocated to the activities on a one-to-one basis. Thus, each resource (e.g. an employee, machine or time slot) is to be assigned uniquely to a particular activity (e.g. a task, site or event). In assignment problems, supply in each row represents the availability of a resource such as a man, machine, vehicle, product, salesman, etc. and demand in each column represents different activities to be performed such as jobs, routes, factories, areas, etc. for each of which only one man or vehicle or product or salesman respectively is required. Entries in the square being costs, times or distances. The assignment method is a special linear programming technique for solving problems like choosing the right man for the right job when more than one choice is possible and when each man can perform all of the jobs. The ultimate objective is to assign a number of tasks to an equal number of facilities at minimum cost (or maximum profit) or some other specific goal. Let there be 'm' resources and 'n' activities. Let c ij be the effectiveness (in terms of cost, profit, time, etc.) of assigning resource i to activity j (i = 1, 2, …., m; j = 1, 2,…., n). Let x ij = 0, if resource i is not assigned to activity j and x ij = 1, if resource i is assigned to activity j. Then the objective is to determine x ij 's that will optimize the total effectiveness (Z) satisfying all the resource constraints and activity constraints. 1. Mathematical Formulation Let number of rows = m and number of columns = n. If m = n then an AP is said to be BAP otherwise it is said to be UBAP. A) Case 1: If m < n then mathematically the UBAP can be stated as follows:
Two New Effective Methods to Find the Optimal Solution for the Assignment Problems
2020
Assignment problem (AP) is one of the main optimization problems, itis a private type of transportation problem (TP) in which every origin must have the ability to meet the request of any destination, i.e. any worker must be able to perform any job. The assignment problem is used to find one for one among a group of workers each of whom specializes for a specific job among a set of jobs, the main goal is to reduce gross cost (or reduce gross time) according to user requirements. This paper introduces two new methods (Al-Saeedi's 1st M. and Al-Saeedi's 2nd M.) to find a solution to the assignment problem. Moreover, some numerical examples were given to compare the results of the solution of the two new methods with the result of the solution of the Hungarian method. The two new methods are a systematic procedure, simple to apply and with minimal time and effort when using. The numerical experiment indicates that the two new methods are effective and promising.
Finding an Optimal Solution of Assignment Problem
YMER Digital
Assignment model comes under the class of linear programming model which is the most used techniques of operations research, which looks alike with transportation model with an objective function of minimizing the time or cost of manufacturing the products by allocating one job to one machine or one machine to one job or one destination to one origin or one origin to one destination only. In this paper, we represent linear mathematical formulation of Assignment problem and solved using Lingo Software. Keyword: Resource Allocation, Optimization Problem, Lingo Software, Assignment problem.
A New Diagonal Optimal Approach for Assignment Problem
Different situations give rise to the assignment problem, where we must discover an optimal way to assign 'n' objects to 'm' in an bijective function. We have, in this research, propose the possibility of solving exactly the Linear Assignment Problem with a method that would be more efficient than the Hungarian method of exact solution. This method is based on applying a series of pairwise interchanges of assignments to a starting heuristically generated feasible solution, wherein each pairwise interchange is guaranteed to improve the objective function value of the feasible solution.It seems that our algorithm finds the optimal solution which is the same as one found by the Hungarian method, but in much simpler. 7980 M. Khalid et al.
Ones Assignment Method for Solving Assignment Problems
Assignment problem is an important subject discussed in real physical world. We endeavor in this paper to introduce a new approach to assignment problem namely, ones assignment method, for solving a wide rang of such problems. This method offers significant advantages over similar methods, in the process, first we define the assignment matrix, then by using determinant representation we obtain a reduced matrix which has at least one 1 in each row and columns. Then by using the new method, we obtain an optimal solution for assignment problem by assigning ones to each row and each column. The new method is based on creating some ones in the assignment matrix and then try to find a complete assignment to there ones. The proposed method is a systematic procedure, easy to apply and can be utilized for all types of assignment problem with maximize or minimize objective functions. At the end, this method is illustrated with some numerical examples.
Permutation-Matrix Approach to Optimal Assignment Design
2021
The paper presents a new iterative approach to solving Linear Assignment problems (LAP) and finding a perfect matching in a weighted bipartite graph iteratively. For that, a new permutation-matrix model of optimal linear assignment is proposed, which allows recursively finding solutions on a set of augmenting paths built based on the current matching. The results can be combined with other methods for solving a LAP such as the Hungarian Algorithm and minimal cost method in order to find an optimum faster.
A New Method for Finding an Optimal Solution of Assignment Problem
International Journal for Research in Applied Science & Engineering Technology (IJRASET), 2022
In this paper a new method is proposed for finding an optimal solution of a wide range of assignment problems, directly. A numerical illustration is established and the optimality of the result yielded by this method is also checked. The most attractive feature of this method is that it requires very simple arithmetical and logical calculations. The method is illustrated through an example.
A new method to solve assignment models
Applied Mathematical Sciences, 2017
Assignment models is one of topics of operations research. It consists of assigning a specific (person or worker) to a specific (task or job) assuming that there are the number of persons equal to the number of tasks available. The optimal result is to assignment one person to one job, contrast to the transportation models the source is connected to one or more of destination. The most common method to solve assignment models is the Hungarian method. In this paper introduced another method to solve assignment models by use the graph in the general formula directly. The edges are represented the cost of assigning person to task, the nods are represented the tasks and persons. The solution will be by choosing the minimum cost (edge) from the costs (edges) and delete the selected edge as well as nodes associated with the edge, then delete all other edges associated with the nodes. Repeat the process until all workers are assigned to each tasks and be the solution is the optimal solution.