First and foremost, it is important to define what the assignment model is. So, this is a specific application of a linear programming problem (commonly referred to as LPP) the main goal of which is to assign a task to a group of individuals. There can be only one assignment, or there can be several different ones. In case of the latter, the main aim is typically to complete them in such a way that the overall cost is minimized. Thus, it can be said that the assignment model is a special application of linear programming. When you get a linear programming assignment, one of the main priorities is to find the most suitable solution, as well as consider how possible it would be to make it cost-effective. Speaking about assignment problems can be of two types: balanced and unbalanced. Balanced assignment problems usually consist of a square matrix while non-balanced assignments consist of a non-square matrix. This aspect should be taken into account when you get down to work on the task your teacher has assigned to you.
Most common methods to solve the assignment model
There are four most commonly used methods to solve the assignment model. They are as follows:
- Integer programming method. This is a rather lengthy method which is why solving the assignment model using it can be quite tricky. What is more, you will get n+n equalities and nxn decision variables. As a result, you’ll end up with 8 equalities and 16 variables even for a 4x4 matrix problem.
- Transportation methods. This is another time-consuming method. However, what is even more significant is that it will be a square matrix when this method is used. Furthermore, the solution will most likely degenerate.
- Enumeration method. This is one of the simplest methods to use. However, errors are something to be expected when using this method. Another important detail to mention when choosing the enumeration method is that the optimal solution is typically the one where one can provide minimum cost.
- Hungarian method. It is called so because it was developed by two Hungarian mathematicians. Sometimes it is also referred to as Flood’s technique or reduced matrix method. If you want to use this method, make sure that the following two conditions are present: square matrix; your problem should deal with minimization.
Taking everything into account, a lot depends on the exact details of your linear programming task. When you are trying to complete such an assignment, attention to detail is crucial. Your teacher may tell you which method to use, or you may need to choose it on your own. Sometimes having a proper sample on hand helps as you will have an example to follow right in front of you. Don’t forget that the main objective of the assignment model is to allocate different resources to various activities on one to one basis. By doing so, it becomes possible to minimize the cost and the time spent, as well as maximize the profits. This is what you should keep in mind every time you are working on your linear programming task. You need to find a way to save some money by delivering excellent results. Completing such tasks calls for a lot of preparation. Allocate as much time as possible and conduct a proper research study. It may take a while until you find a solution that meets all your demands. Yet, the better you are at it, the easier it will get. What is more, finding solutions to similar problems will become a part of your daily routine should you consider building a career in this field. Therefore, you have an actual chance of helping your company minimize the costs and boost the profit which is a win for everybody.