list out the application of assignment problem
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Abstract
This paper presents a review pertaining to assignment problem within the education domain, besides looking into the applications of the present research trend, developments, and publications. Assignment problem arises in diverse situations, where one needs to determine an optimal way to assign subjects to subjects in the best possible way. With that, this paper classified assignment problems into two, which are timetabling problem and allocation problem. The timetabling problem is further classified into examination, course, and school timetabling problems, while the allocation problem is divided into student-project allocation, new student allocation, and space allocation problems. Furthermore, the constraints, which are of hard and soft constraints, involved in the said problems are briefly elaborated. In addition, this paper presents various approaches to address various types of assignment problem. Moreover, direction and potential paths of problem solving based on the latest trend of approaches are also highlighted. As such, this review summarizes and records a comprehensive survey regarding assignment problem within education domain, which enhances one’s understanding concerning the varied types of assignment problems, along with various approaches that serve as solution.
1. Introduction
Problems related to assignment arise in a range of fields, for example, healthcare, transportation, education, and sports. In fact, this is a well-studied topic in combinatorial optimization problems under optimization or operations research branches. Besides, problem regarding assignment is an important subject that has been employed to solve many problems worldwide [1]. This problem has been commonly encountered in many educational activities all over the world. Within the education domain, this review classified the assignment problem into two: timetabling problem and allocation problem.
Assignment problem refers to the analysis on how to assign objects to objects in the best possible way (optimal way) [2, 3]. The two components of assignment problem are the assignments and the objective function. The assignment signifies underlying combinatorial structure, while the objective function reflects the desires to be optimized as much as possible. Nonetheless, the question is, “how to carry out an assignment with optimal objective, and at the same time, fulfilling all the related constraints?” In order to address the question, several diverse methods have been proposed [1, 2], such as the exact method [4], the heuristics method [5], the local search-based [6], the population search-based [7], and the hybrid algorithm [8].
The aim of looking into assignment problem is to discover an assignment among two or more sets of elements, which could minimize the total cost of all matched pairs. Relying on the specific structure of the matched sets and the cost function form, the allocation problems can be categorised into quadratic, bottleneck, linear, and multidimensional groups [9]. Hence, every assignment problem has a table or matrix. Normally, the rows are comprised of objects or people to assign, while the columns consist of the things or tasks to be assigned. Meanwhile, the numbers in the table refer to the costs related to every particular assignment. With that, this study presents a review of assignment problem within educational activities, where the problems were classified into timetabling and allocation problems. In fact, studies within this area have commonly displayed substantial progress with diverse methodologies.
The organization of this paper is given as follows: Section 2 discusses the definition and the mathematical formulation of general assignment problem. Next, the types of assignment problem within the education domain, along with their approaches, are presented in Section 3. In fact, this section is divided into subsections that elaborate in detail the two types of problem: (i) timetabling problem and (ii) allocation problem. Finally, the conclusion, future direction, and potential path of solution approach are presented in Section 4.
2. Definition and Mathematical Formulation of General Assignment Problem
The general aim of assignment problem is to optimize the allocation of resources to demand points where both resources and demand point share equal number [1]. The problem, hence, can be mathematically presented as follows:
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