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How to Solve Assignment Problem Questions Quiz by Proceeding in a Step Wise and Logical Manner?

“The assignment problem can be referred to as a very basic optimization based problem, used frequently in the field of mathematics!”

Here you require getting hold of matching weights in a weighted graph, having two divisions. In each problem different agents as well as different tasks are present. An agent will be assigned to a task. This task will incur some costs; the cost will be dependent on the combination of the agent and task.

If you are wondering about how to solve assignment problem questions quiz, then you do not need to worry too much, as the internet will provide most of your answers.

Assigning agents

The different tasks that are required to be performed, will incur some costs. One agent will be assigned to complete one task here. This is done in such a manner, so that the total cost of that assignment gets minimized.

If you find that the numbers of tasks or agents are equal in number, then the total costs incurred will be equal to the sum of the cost for each agent. This kind of problem is also given the name of Linear Programming Problem or LPP.

Algorithms used

The Hungarian algorithm method is one of the best methods developed for solving assignment problems.

  • The auction algorithm is also in use nowadays.
  • The different assignment problems can be referred to as a really special case of transportation problem.

Both of these can be solved by use of simplex algorithm. However, these special cases have special methods to solve problems more efficiently.

If the number of agents present is too large in number, then randomization method can be used. You will know how to solve assignment problem questions quiz by going through more articles on the internet.

Hungarian technique

You need to firstly consider an objective function having minimization type. You then need to follow the steps mentioned below.

  • Firstly, you require locating the cost element of smallest value in each of the rows of the table. You can begin your operation from the first row. The element having the smallest value will then get subtracted from the elements present in the row. The end result will be at least one zero value present in each row of the newly constructed table.
  • After the construction of the table has been completed, you have to inspect the columns of the table. Beginning with the first column, you have to get hold of the cost element in each of the columns. A similar method of subtracting the smallest element from each column is then done. Therefore, a zero value is now present in the columns.
  • After these things have been done, the assignments of values for the new table is done.

Row and column examination

The different rows are inspected one by one until you find the row having just one zero. The assignment of value is done to this zero and a square symbol is put around it. In the column, the other zeroes are cancelled out. This is because; they will not be used for making assignments anymore in that column. Similar steps are then performed for the rows too.

The idea of “how to solve assignment problem questions quiz”, will now come really easily and fast for you. These steps get repeated till all zeroes present get cancelled out. In the end, if the number of zeroes being marked is equal to the number of rows or columns, then the optimal solution has been achieved.

Covering zeroes

During the next step, the least number of lines required for covering all the zeroes in the matrix are drawn. You need to mark all those rows which do not have any assigned value.

After this, the columns which contain zeroes in the marked rows are also marked. Assignment is now given to the columns. These steps keep getting repeated until you do not have any more rows or columns. After this has been done, lines are drawn which pass through both unmarked rows and marked columns.

If no solution exists for the problem, then in a square matrix, then the zeroes will be covered by lines which are less in number compared to size of matrix.

Final steps for solving

If the number of lines that you have drawn, equals to the number of rows in the matrix, then it is the optimum solution, if that is not the case, you have to work further. You have to make a selection among all uncovered elements. This selected element will then be added to t6h element lying in the intersection of two lines. You will now have a matrix for all fresh assignments.

All steps that were taken before, needs to be taken again. You need to continue the steps until number of rows or columns become equal and you have solved your assignment problem.

Problem example

If you are thinking hard about how to solve assignment problem questions quiz, and have not really understood how things work in it, then you need examples. When you have viewed examples of such problems, everything will become clear to you. As mentioned earlier, these problems have agents and tasks.

Suppose in a taxi firm there are some taxis or agents and some customers or tasks. Based on this data, it is understood that costs involved in picking up a customer will be dependent on time taken by a taxi to reach pickup points. Solution to this problem would be a customer-taxi combination incurring least cost.

Resource allocation

The assignment problem can be referred to as a very special kind of LPP. The resources here are allocated on a one to one basis. Everything gets allocated on course of these problems in such a way that profit is maximized and manufacturing cost gets minimized.

The assignment model provides a really simple approach in solving these problems. When you are facing a quiz on assignment problems, you will find that these problems eventually make you better prepared for tackling real life situations.

Understanding a model

It is very important for you to understand assignment models before you set about solving different actual problems. All your doubts and queries regarding how to solve assignment problem questions quiz, will be solved once you have understanding of standard models. If you find that there are n numbers of facilities available and n number of jobs, then you must understand that you require n assignments.

You have to make these assignments in such a manner that costs incurred per job are least in amount. This is actually the essence of assignment problems.

Aim of solving problem

You will find that the most important aim of solving assignments problems is to get hold of an assignment among different sets of elements. Classification of assignments is made in groups such as bottleneck, linear, quadratic etc. It is therefore mandatory for assignment problems to have tables. Numbers are inputted into these tables to show different costs. Most of these assignment problems, are usually of two types, either time table fixing or allocation problems. A lot of progress has been made in this sector and many different methods are being used for solving these assignment problems.

Approach to be taken

The solution to timetabling and assignment problem are varied in nature. We will show you all methods available for solving these problems. It is then up to you to choose a method that you understand and apply well. When you are watching out for “how to solve assignment problem questions quiz”, you should try out all methods before zeroing in to one.

You have to understand that choosing a suitable method will increase your chances of getting positive results greatly. For allocation problems especially, we have provided you with heuristic as well as Meta heuristic ways, hybrid techniques.

Time tabling problems

In these problems, information about particular events to occur is provided. With the help of such information, resources are allocated. A number of events, can be assigned to a limited number of time slots by use of methods provided by us.

Without assignment, it is really challenging to allot such time slots. Lots of different factors are required to be taken into consideration when you do these assignments. Four parameters including set of times, resources, meetings and constraints are needed to be considered here. All these constraints are needed to be satisfied.

Finding optimal way to solve problems

There exists different time table based problems, including school timetable, examination timetable etc. there are two types of constraints too, including soft and hard constraints. You will find that we provide with summaries as well as surveys regarding assignments. Having a good idea about how to solve assignment problem questions quiz, will really help you perform better in tests.

We provide you with all kinds of approaches, in a systematic manner for you to ace these quizzes. You can always gain access to our website and look up for means to solve all assignment problems. After going through our guide solving such problems will be a piece of cake for you.

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