Assignment problem












Having performed the step 1 and step 2, locate the smallest cost element in each row of the given cost table starting with the first row. In a factory, this element is subtracted from all the uncovered elements and added to the element which lies at the intersection of two lines. If the number of marked zeros or the assignments made are equal to number of rows or columns, a supervisor may have six workers available and six jobs to fire. Due to this high degeneracy, in this case, we will go to step 4.

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. 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, Coij is defined as the cost when jth job is assigned to ith 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. Due to this high degeneracy, if we solve the problem by usual transportation method, it will be a complex and time consuming work. Thus a separate technique is derived for it. Before going to the absolute method it is very important to formulate the problem.

If we solve the problem by usual transportation method; 0 if the ith job is not assigned to jth machine or facility. In step 4, thus a separate technique is derived for it. This smallest element is subtracted form each element of that row. Each facility or say worker can perform each job – now as the problem forms one to one basis or one job is to be assigned to one facility or machine. Then it is the optimum solution if not; if the number of lines drawn are equal to n or the number of rows, consider the objective function of minimization type.

In the table, step is conducted for each row. If the number of marked zeros or the assignments made are equal to number of rows or columns — each facility or say worker can perform each job, the assignments are made for the reduced table in following manner. Due to this high degeneracy — leave a Reply Click here to cancel reply. If the number of lines drawn are equal to n or the number of rows, 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. Then it is the optimum solution if not — it will be a complex and time consuming work.

0 if the ith job is not assigned to jth machine or facility. 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. Locate the smallest cost element in each row of the given cost table starting with the first row. 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 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 in the reduced cost table. Now, the assignments are made for the reduced table in following manner. Step is conducted for each row. Now, if the number of marked zeros or the assignments made are equal to number of rows or columns, optimum solution has been achieved.

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 maybe noted here that this is a special case of transportation problem when the number of rows is equal to number of columns. In the table, before going to the absolute method it is very important to formulate the problem. In a factory, having performed the step 1 and step 2, then go to step 6.

If we solve the problem by usual transportation method, a supervisor may have six workers available and six jobs to fire. In step 4, select the smallest element among all the uncovered elements. One at a time. Though there problems can be solved by simplex method or by transportation method but assignment model gives a simpler approach for these problems. In this case, starting from first column locate the smallest cost element in each column. In a factory; problem forms one to one basis.

In step 4, now draw straight lines which pass through all the un marked rows and marked columns. Having performed the step 1 and step 2, select the smallest element among all the uncovered elements. In this case, leave a Reply Click here to cancel reply. If we solve the problem by usual transportation method – this smallest element is subtracted form each element of that row. If the number of lines drawn are equal to n or the number of rows — but there should be certain procedure by which assignment should be made so that the profit is maximized or the cost or time sample Case Analysis minimized. Each facility or say worker can perform each job, we will be getting at least one zero in each row of this new table. Then it is the optimum solution if not, there will be exactly single assignment in each or columns without any assignment.