 In today's session we are going to discuss regarding the decision making under certainty solution by the assignment problem. Let's start with the learning outcome. Here at the end of the session student will be able to formulate the particular business problem or any kind of problem in any industry in a linear programming for the optimal assigning the jobs and finally along with that he is going to determine the schedule of job assignment with the minimum cost or the time involved in the process along with the maximum the profit or the sale. Now let's start with the assignment problem. What is assignment problem? Assignment problem is nothing else. It is a familiar with the transportation linear programming problem. Here there is allocation of various resources or you can say jobs to the various activities or the workers one to one basis. The main goal or you can say the intention of the assignment problem is to minimize the cost or the time involved in the process or you can say the manufacturing along with the maximizing the profit or the sale. You should keep in mind the intention is what to see the your production cost or the production or processing cost should be minimized and the time required to complete that particular production or the manufacturing of that particular product is to be minimum along with the maximizing the profit or the sale. Now let me take the example. Because there is a factory there are six workers available and the six jobs. Now there is a challenging to the you can say the in charge to make a decision regarding the which job should be assigned to which worker. So that the cost and the time required for the completion of the particular job is minimum and the maximum output or you can say maximum production should be there so that it will help to have the maximum profit or you can say the selling. Suppose there are M facilities and N jobs facilities may means you can take the example of labor or the worker and N jobs you can say there are activities for each particular job there will be N assignments. Each facilities or the say the worker will have one job at a time here the assignment should be in such a way that profit is maximized or the cost of the time is minimized here this is a single assignment prep problem pay off table here you observe that there are N number of workers along with the M number of particular jobs and the each workers to the each job the particular cost or the time required are been defined that is a CO 11, CO 12, see these are the CO 11, CO 12, CO 13, all these are the pay off for the each respective work to the each picture respective jobs. Here you should keep in mind the particular assignment problems are divided in two ways or you can say two types one is a balanced type of assignment problem second is an unbalanced type of assignment problem. How to finalize whether the given problem or the obtained industrial or you can say the business problem which is converted into the linear programming is a balanced type or unbalanced type for that there is a simple criteria that the number of row should be equal to number of volume at that time we can say that particular problem is a balanced type means what here suppose I define that in this particular table only three workers are there and three jobs are there I am considering only three workers and three jobs then your pay off table will be of matrix three by three that is what this is here the number of rows are equal to number of columns suppose the this pay off table if I consider there are four number of workers and only three number of jobs then your matrix will be of that will be of you can say the four into three here the number of rows are not equal to number of columns in such a case it is called as unbalanced type of assignment problem to overcome that we have to go for the addition of a particular dummy row or dummy column as per the requirement which is necessary to convert that unbalanced assignment problem to the balance one problem once you convert you can start to use solve that particular problem and you can define the schedule of the assignment the particular job to particular worker here this is a hangarance assignment method which is used to solve or which is used to schedule the particular assignment of the job to the particular worker the first step is what row reduction in the row reduction means what yeah yeah one two three are the rows that are the workers and the job one job to these are the columns as we know your row reduction means what in each row we have to see the minimum cost or minimum pay off yeah they are said locate the smallest cost element in each row after locating that you have to separate it with the each element of that respective room in this step that is the first step row reduction you will get that in each row there will be at least one zero second step is called as a column reduction in this after whatever the table is obtained after the row reduction in that the column wise is observed in the column again the smallest element is selected and that smallest element is subtracted with the particular respective column so that there will be a each at least one zero in each column after step one and two that is row reduction in the column reduction you will get that at least there is one zero in each row as well as one zero in each column the step three have to get after getting the row reduction and the column reduction table draw the minimum number of horizontal or vertical lines as per the requirement and cover the zero element by the box if the number of box drawn is equal to the number of a particular row or column the solution is obtained that is optimal solution if not we have to go for the step four here in step four we have to select the element which is uncovered by the vertical line as well as a horizontal line means what the cell which is not covered by the horizontal or vertical line that cells should be seen in that overall cells we have to select the smallest one that smallest one should be again should be subtracted with the each uncovered elements and along with itself also after that that cell should be added with the cell where there is an intersection of horizontal line as well as vertical line means we have to add that to that particular cell and the cost element which only line are passing there is no any intersection of the horizontal and the vertical line it should be kept as it is after that repeat this step three and four until we get the optimal solution after getting the optimal solution we have to finalize and we have to schedule the particular assignment of the jobs or the resource to the particular machine or the workers this is the steps should be carried for the solving the assignment problem with the hangarians method so it is called as hangarian assignment method let us select the correct answer for the questions hope so you have selected the correct answer I will show the answer these are the references for the today's session thank you