Research On The Solution And Application Of An Unbalance Assignment Problem

Assignment problem is a classic problem in operational research about linear programming.In practical life and production arrangement,the assignment problem of different kinds of unbalanced styles,which came into being on the basis of production management,is the keystone for the present research.The thesis firstly talks about a balance assignment problem in practical application. Build the mathematics model of the balance assignment problem,and then offer solutions to the problems.Among these solutions,Hungarian algorithm is widely used.Hungarian algorithm is a very simple but efficient way to solve assignment problems.The origin of Hungarian algorithm,its application,the solution model as well as its principle will be introduced in this article.To the unbalanced assignment problem,after building its mathematics model,the article introduces the method that changes the unbalanced assignment problem into balanced assignment problem.There are two situations in the unbalanced assignment problem:one is that the number of personnel is smaller than the number of assignment;another is on the contrary.In practical assignment work, frequently,we will be faced with a problem whether a person has the qualification to undertake a task.Therefore,the article builds an assignment mathematics model,which means the personnel will be restricted by the amount of task.About the solution to the "personnel more than assignment" apportionment problem,the article not only points out the localization of Adding rows with zeroes,also offers a better method--- Adding rows with small value and its detailed situations.What's more,the article also presents a new method,that is,adding rows with ordered small value.Based on this method and Hungarian algorithm,the article offers a solution to the multi-objectives decision problem---personnel with ability restriction and personnel fewer than assignment".This means that assignment problem with qualification restriction can be transformed into the traditional assignmaent problem.On the other hand, the article advises solving the "personnel more than assignment" assignment problem with Hungarian algorithm.Considering the colligated evaluation and improvement,the article gives more conditions about "assignment problem with qualification restriction" and strengthens the mathematics model of the unbalanced assignment problem.First,build the mathematics model of qualification restriction,then explain why a person has the qualification to undertake a certain task,and state the full conditions for the mathematics model of qualification restriction.In the last part,in order to prove the practicability and validity of the new method,the thesis gives the example of numerical value to explain how to solve problems with adding rows with ordered small value.At the same time,the author points out the limitation of the thesis and that there is a lot to be improved.