Assignment problem - Wikipedia

 

assignment problem in operations research

This paper presents a new algorithm for solving the assignment problem. The algorithm is based on a scheme of relaxing the given problem into a series of simple network flow (transportation) problems for each of which an optimal solution can be easily moomentis.gq by: The Assignment Problem: Suppose we have n resources to which we want to assign to n tasks on a one-to-one basis. Suppose also that we know the cost of assigning a given resource to a given task. We wish to find an optimal assignment–one which minimizes total cost. Assignment Problems:SOLUTION OF AN ASSIGNMENT PROBLEM Operations Research Formal sciences Mathematics Formal Sciences Statistics.


Assignment problem: Hungarian method 3 – Operations-Research-Wiki


Assignment problem is a special type of linear programming problem which deals with the allocation of the various resources to the various activities on one to one basis. It does it in such a way that the cost or time involved in the process is minimum and profit or sale is maximum. Though there problems can be solved by simplex method or by transportation method but assignment model gives a simpler approach for these problems. In a factory, a supervisor may have six workers available and six jobs to fire.

He will have to take decision regarding which job should be given to which worker. Problem forms one to one basis. This is an assignment problem. Suppose there are n facilitates and n jobs it is clear that in this case, there will be n assignments. Each facility or say worker can perform each job, one at a time. But there should be certain procedure by which assignment should be made so that the profit is maximized or the cost or time is minimized. In the table, Co ij is defined as the cost when j th job is assigned to i th worker.

It maybe noted here that this is a special case of transportation problem when the number of rows is equal to number of columns. Any basic feasible solution of an Assignment problem consists 2n — 1 variables of which the n — 1 variables are zero, n is number of jobs or number of facilities.

Due to this high degeneracy, if we solve the problem by usual transportation method, it will be a complex and time consuming work, assignment problem in operations research. Thus a separate technique is derived for it. Before going to the absolute method it is very important to formulate the problem. Now as the problem forms one to one basis or one job is to be assigned to one facility or machine.

Consider the objective function of minimization type, assignment problem in operations research. Following steps are involved in solving this Assignment problem.

Locate the smallest cost element in each row of the given cost table starting with the first row, assignment problem in operations research. Now, this smallest element is subtracted form each element of that row. So, we will be getting at least one zero in each row of this new assignment problem in operations research. Having constructed the table as by step-1 take the columns of the table.

Starting from first column locate the smallest cost element in each column. Now subtract this smallest element from each element of that column.

Having performed the step 1 and step 2, we will be getting at least one zero in each column assignment problem in operations research the reduced cost table. Step is conducted for each row. Nowassignment is made to this single zero by putting the square around it and at the same time, all other zeros in the corresponding rows are crossed out x step is conducted for each column. Now, if the number of marked zeros or the assignments made are equal to number of rows or columns, optimum solution has been achieved.

There will be exactly single assignment in each or columns without any assignment. In this case, we will go to step 4. At this stage, draw the minimum number of lines horizontal and vertical necessary to cover all zeros in the matrix obtained in step 3, Following procedure is adopted:.

In step 4, if the number of lines drawn are equal to n or the number of rows, then it is the optimum solution if not, then go to step 6. Select the smallest element among all the uncovered elements. Now, this element is subtracted from all the uncovered elements and added to the element which lies at the intersection of two lines.

This is the matrix for fresh assignments. Repeat the procedure from step 3 until the number of assignments becomes equal to the number of rows or number of columns. You must be logged in to post a comment, assignment problem in operations research. Checking for Optimality Transportation Problem. Leave a Reply Click here to cancel reply.

 

Assignment Problem in Linear Programming : Introduction and Assignment Model

 

assignment problem in operations research

 

This paper presents a new algorithm for solving the assignment problem. The algorithm is based on a scheme of relaxing the given problem into a series of simple network flow (transportation) problems for each of which an optimal solution can be easily moomentis.gq by: Meaning of Assignment Problem 2. Definition of Assignment Problem 3. Mathematical Formulation 4. Hungarian Method 5. Variations. Meaning of Assignment Problem: An assignment problem is a particular case of transportation problem where the objective is to assign a number of resources to an equal number of activities so as to minimise total cost. Assignment Problems:SOLUTION OF AN ASSIGNMENT PROBLEM Operations Research Formal sciences Mathematics Formal Sciences Statistics.