The balanced academic curriculum problem revisited

The Balanced Academic Curriculum Problem (BACP) consists in assigning courses to teaching terms satisfying prerequisites and balancing the credit course load within each term. The BACP is part of the CSPLib with three benchmark instances, but its formulation is simpler than the problem solved in practice by universities. In this article, we introduce a generalized version of the problem that takes different curricula and professor preferences into account, and we provide a set of real-life problem instances arisen at University of Udine. Since the existing formulation based on a min–max objective function does not balance effectively the credit load for the new instances, we also propose alternative objective functions. Whereas all the CSPLib instances are efficiently solved with Integer Linear Programming (ILP) state-of-the-art solvers, our new set of real-life instances turns out to be much more challenging and still intractable for ILP solvers. Therefore, we have designed, implemented, and analyzed heuristics based on local search. We have collected computational results on all the new instances with the proposed approaches and assessed the quality of solutions with respect to the lower bounds found by ILP on a relaxed and decomposed problem. Results show that a selected heuristic finds solutions of quality at 9%–60% distance from the lower bound. We make all data publicly available, in order to stimulate further research on this problem.     

排课问题分组优化决策中的CourseRank

时间表(T im etab ling)问题是NP-完全的,因此很难寻求一个有效的整体优化算法.分组作为重要的优化策略,可以将课程按优先等级逐次分组,每组再采用组合优化方法.通常认为课程的规模是优先等级的决定性因素.然而选课的模式允许学生在一定的范围内选择课程,这就使得课程的关联关系更复杂.该文将课程的关联关系描述为一个M arkov链,进而给出了课程优先度(CourseR ank)的概念.通过对清华大学2002年度学生选课数据的分析和计算,结果表明课程的规模仍然是重要的因素,但并不完全是决定性的.     

A classification of assembly line balancing problems

Assembly lines are special flow-line production systems which are of great importance in the industrial production of high quantity standardized commodities. Recently, assembly lines even gained importance in low volume production of customized products (mass-customization). Due to high capital requirements when installing or redesigning a line, its configuration planning is of great relevance for practitioners. Accordingly, this attracted attention of many researchers, who tried to support real-world configuration planning by suited optimization models (assembly line balancing problems). In spite of the enormous academic effort in assembly line balancing, there remains a considerable gap between requirements of real configuration problems and the status of research. To ease communication between researchers and practitioners, we provide a classification scheme of assembly line balancing. This is a valuable step in identifying remaining research challenges which might contribute to closing the gap.     

Predictive factors of students’ motivation to succeed in introductory mathematics courses: evidence from higher education in the UAE

The purpose of the study is to examine whether there is a significant relationship between students’ motivation to succeed in introductory mathematics courses offered by universities in the United Arab Emirates (UAE) as the dependent variable of the research and another five independent variables including cognitive mathematics self-concept, affective mathematics self-concept, extrinsic motivation as expectations of future career and income, students’ age and the number of mathematics courses taken by students. The rationale of the study is based on the significance of mathematics achievements for students and academic institutions in particular, as well as for the society in general. The study is designed based on a quantitative research methodology and a sample of 685 students participated in completing a survey questionnaire. The sample is drawn from students who were registered in different introductory mathematics courses at four academic institutions of higher education in the UAE. The quantitative correlation analysis among students’ motivation, cognitive mathematics self-concept, affective mathematics self-concept, extrinsic motivation, students’ age and the number of mathematics courses taken by students reveals theoretically consistent interrelationships. The quantitative multiple regression analysis indicates that the five independent variables explain 71.3% of the variation in students’ motivation to succeed in introductory mathematics courses.     

Implementation of goal programmingin long-range resource planning in university management

This paper presents a resource allocation model via Goal Programming (GP) in a long-range planning horizon in university management. In the proposed model, the introduction of new courses in the academic units and the allocation of available budget within the academic units as well as the forecast of the budget which is actually needed for better academic performance are taken into consideration. An illustrative example is presented to expound the model     

非参数秩检验在宿舍因素对学风影响中的应用

学风建设是大学教育教学管理中的重要环节,对学生的学习成绩、顺利毕业和就业等都有至关重要的影响。宿舍是学生学习和生活的重要场所,本文应用非参数统计秩检验和中位数检验研究了宿舍对学生学业成绩的影响,得到目前大学宿舍因素对学生学业成绩的影响高度显著,进而建议高等学校应加强学生宿舍管理,把宿舍作为学风建设的重要环节。     

A Hierarchical Goal-Programming Approach to Reverse Resource Allocation in Institutions of Higher Learning

As universities react to severe financial pressures, there is a danger that too much emphasis will be placed on ‘balancing the budget’ at the expense of the academic goals of the institution. Therefore, the overall objective of this paper is to design and implement a model for reducing the operating budgets of the academic units of a university, while reflecting the diverse goals of the academic community. It recognizes that faculty, department chairmen and deans should share the responsibility of ‘reverse’ resource allocations or budget reductions. The model utilizes a goal-programming approach to reflect the multiple-phased model to allow for some degree of decentralization of decision making.The model is applied to a small private university. The solution to the model reveals the distribution of budget reductions among the schools and within the departments. A survey of potential users reveals a definite preference for the model results over the actual budget procedure.     

Balancing sparse Hamiltonian eigenproblems

Balancing a matrix by a simple and accurate similarity transformation can improve the speed and accuracy of numerical methods for computing eigenvalues. We describe balancing strategies for a large and sparse Hamiltonian matrix H.It is first shown how to permute H to irreducible form while retaining its structure. This form can be used to decompose the Hamiltonian eigenproblem into smaller-sized problems. Next, we discuss the computation of a symplectic scaling matrix D so that the norm of D⁻¹HD is reduced. The considered scaling algorithm is solely based on matrix-vector products and thus particularly suitable if the elements of H are not explicitly given. The merits of balancing for eigenvalue computations are illustrated by several practically relevant examples.     

分布式数据流处理系统管理中负载均衡问题建模与求解

对分布式数据流处理系统管理中,处理节点负载均衡问题进行了研究。阐述了分布式数据流处理系统的运行机理以及节点负载不均衡的成因,并提出了对系统负载均衡调整的优化方案;对提出的优化方案建立模型,并对模型的适用条件进行理论分析;然后采用蚁群算法对模型进行求解,并针对分布式数据流处理系统实时性的需求对算法进行改进;最后用实验证明本文所建立的模型及其求解方法对于解决分布式数据流处理系统管理中节点负载均衡问题的有效性。     

The mixed and multi model line balancing problem: a comparison

The balancing problem deals with the assignment of tasks to work stations. We can distinguish two approaches in the literature on the mixed model line balancing problem, that both transform this problem into a single model line balancing problem. These approaches use combined precedence diagrams and adjusted task processing times, respectively.An experiment was carried out to compare several heuristics based on the combined precedence diagram. A new optimisation method has been developed. The results indicate that the position of common tasks in the precedence diagram of the different models has a significant effect on both the CPU time and the unequal distribution of the total work content of single models among work stations. Moreover, good solutions with respect to the number of required stations go together with long CPU times. For several instances, we decreased the CPU times considerably without deteriorating the performance of the methods, by using a reversed combined precedence diagram.     

学生学习成绩相关性的研究

从大学生学习成绩出发,应用广义线性回归模型研究了学生学年间成绩的相关性,揭示了大学一年级,尤其是一年级的二学期是影响学生后期学习的关键阶段.进一步应用聚类分析,得到学生成绩在大学一年级就已经埋下了两极分化的隐患,应用判别分析得出了两极分化的关键课程.该结论为教育教学和学生管理提供决策依据.     

The generalized balanced academic curriculum problem with heterogeneous classes

We propose an extension of the Generalized Balanced Academic Curriculum Problem (GBACP), a relevant planning problem arising in many universities. The problem consists of assigning courses to teaching terms and years, satisfying a set of precedence constraints and balancing students’ load among terms. Differently from the original GBACP formulation, in our case, the same course can be assigned to different years for different curricula (i.e., the predetermined sets of courses from which a student can choose), leading to a more complex solution space. The problem is tackled by both Integer Programming (IP) methods and combinations of metaheuristics based on local search. The experimental analysis shows that the best results are obtained by means of a two-stage metaheuristic that first computes a solution for the underlying GBACP and then refines it by searching in the extended solution space.     

Preservice Teachers' Use of Multiple Representations In Solving Arithmetic Mean Problems

The development of preservice teachers' views of various mathematical concepts involves building a repertoire of flexible representations of the concepts they teach. In this study, science and mathematics preservice teachers (n = 19) were asked to solve graphical and numerical problems involving the arithmetic mean and to provide two different solutions for each problem. Background information about the preservice teachers was obtained, including subject area specialty, type of statistics courses previously taken, type of science laboratory courses previously taken, and prior experience with real data outside the classroom. In solving the problems, some participants presented two different methods: algorithmic computation and balancing deviations about the mean. A significant difference was found between science and mathematics preservice teachers in the use of balancing deviations to solve the problems but not in the use of the computational algorithm.     

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??In this paper, the multivariate linear statistical method is applied to research the undergraduate grades of students from the school of mathematics in Hefei University of Technology, and explore the impact on the later achievement by the early stage of achievement from all undergraduate courses. First, we get the main components from the previous courses by principal component analysis, then construct a linear regression model between the later achievement and main components by the stepwise regression method. Next, a linear regression model between the later achievement and the early stage of achievement from all undergraduate courses is constructed by Adaptive-Lasso method. Finally, comparative analysis is performed for the result of the above models. The research shows that the principal component regression model based on the Adaptive-Lasso method can well fit the later achievement, and give a reasonable explanation for the later academic performance.     

Measurement of students’ mathematics motivation and self-concept at institutions of higher education: evidence of reliability and validity

ABSTRACT

The study aims at proposing a quantitative instrument tailored to measure the level of mathematics motivation and self-concept of students in mathematics courses at academic institutions of higher education. The significance of this study stems from its endeavour to measure mathematics motivation and self-concept of students in courses of mathematics at academic institutions of higher education which ultimately contributes to the success of students, academic institutions and societies. A quantitative research methodology has been employed in this study in which a 55-item survey instrument has been tailored and piloted. The results of factor analysis indicate that the instrument’s items loaded into mathematics motivational factors and mathematics self-concept factors. The cumulative percentage explained by mathematics motivational factors is 55.3% and the cumulative percentage explained by mathematics self-concept factors is 53.2%. The factors of mathematics motivation and mathematics self-concept explain the majority of variance in the dataset. The findings of validity and reliability tests show that 35 items measure mathematics motivation through four subscales which include importance and necessity of mathematics; perception of success in mathematics; enjoyment of mathematics; and expectations of future career and income. The other 20 items measure mathematics self-concept through two subscales which include cognitive mathematics self-concept and affective mathematics self-concept.     

Heuristics and lower bounds for the simple assembly line balancing problem type 1: Overview,computational tests and improvements

Assigning tasks to work stations is an essential problem which needs to be addressed in an assembly line design. The most basic model is called simple assembly line balancing problem type 1 (SALBP-1). We provide a survey on 12 heuristics and 9 lower bounds for this model and test them on a traditional and a lately-published benchmark dataset. The present paper focuses on algorithms published before 2011.     

Mathematical tasks,study approaches,and course grades in undergraduate mathematics: a year-by-year analysis

Students approach learning in different ways, depending on the experienced learning situation. A deep approach is geared toward long-term retention and conceptual change while a surface approach focuses on quickly acquiring knowledge for immediate use. These approaches ultimately affect the students’ academic outcomes. This study takes a cross-sectional look at the approaches to learning used by students from courses across all four years of undergraduate mathematics and analyses how these relate to the students’ grades. We find that deep learning correlates with grade in the first year and not in the upper years. Surficial learning has no correlation with grades in the first year and a strong negative correlation with grades in the upper years. Using Bloom's taxonomy, we argue that the nature of the tasks given to students is fundamentally different in lower and upper year courses. We find that first-year courses emphasize tasks that require only low-level cognitive processes. Upper year courses require higher level processes but, surprisingly, have a simultaneous greater emphasis on recall and understanding. These observations explain the differences in correlations between approaches to learning and course grades. We conclude with some concerns about the disconnect between first year and upper year mathematics courses and the effect this may have on students.     

An empirical method for assessing the research relevance gap

There has been much debate on the relevance to firms of the academic research produced by business schools. However, what has not received as much attention is how the relevance of the research to businesses should be measured in a systematic and empirical way. We develop a systematic method to test for the relevance of academic research to businesses. Our method models as a vector autoregressive process the interests of the academic and practitioner communities in some new topic, as expressed by the number of articles published in the academic and the practitioner literature on that topic per calendar quarter, and then studies Granger causality between the academic and practitioner interest processes. This method can be used by academics to empirically demonstrate the impact of their intellectual contributions on practitioners and thence on the business world. We employ our approach to two relatively new and important topics, Real Options and Economic Value Added.     

Models and Algorithms for Carsharing Systems and Related Problems

In a Carsharing System, a fleet of cars is distributed at specified stations in an urban area, users can take and return cars at any time and station. For operating such a system in a satisfactory way, the stations have to keep a good ratio between the total number of places and the number of cars in each station, in order to refuse as few customer requests as possible. In this work, we propose to model the resulting problem of balancing the load of the stations as a General Pickup and Delivery Problem. As problems of this type are known to be hard, we discuss possible heuristic approaches both for the static (offline) and the dynamic (online) version of the problem, and give approximation results for special cases.     

A branch and bound algorithm for determining locations of long-term care facilities

This paper focuses on the problem of determining locations for long-term care facilities with the objective of balancing the numbers of patients assigned to the facilities. We present a branch and bound algorithm by developing dominance properties, a lower bounding scheme and a heuristic algorithm for obtaining an upper bound for the problem. For evaluation of the suggested branch and bound algorithm, computational experiments are performed on a number of test problems. Results of the experiments show that the suggested algorithm gives optimal solutions of problems of practical sizes in a reasonable amount of computation time.