Varying routes to the top: identifying different strategies in the MBA marketplace

The market for MBA degrees is changing rapidly. As this market tends to maturity,an increase in the number of universities offering these degrees is evident, andalso in the different formats in which these degrees are offered. In thisincreasingly crowded marketplace, there exist two main sources of informationthat buyers (students as well as prospective employers of MBA students) can useto assess the products on offer—whether or not a Business school/MBAprogramme is accredited, and also the position of the school in availablerankings, a number of which are regularly published. Playing ‘the rankingsgame’ is one that occupies the time and effort of many MBA directorsglobally, as they all try to edge their way upwards in order to attract more andbetter students. The problem with an ordinal ranking, though, is that itsuggests too readily that it is based upon a unidimensional measure. We use thedata behind one of these rankings, that of the Financial Times top 100,full-time MBA programmes in 2008, in order to explore to what extent schools areusing different routes to try to improve their rankings. Using a variety ofmultivariate statistical tools, we base our analysis on the three underlyingfactors of alumni career progress, diversity, and idea generation. What emergesis a clearer picture of the extent to which programmes that are ranked veryclosely do, in fact, base their success on very different routes to the top.     

Sparse approximate solution of fitting surface to scattered points by MLASSO model

The goal of this paper is to achieve a computational model and corresponding efficient algorithm for obtaining a sparse representation of the fitting surface to the given scattered data. The basic idea of the model is to utilize the principal shift invariant(PSI) space and the l_1 norm minimization. In order to obtain different sparsity of the approximation solution, the problem is represented as a multilevel LASSO(MLASSO)model with different regularization parameters. The MLASSO model can be solved efficiently by the alternating direction method of multipliers. Numerical experiments indicate that compared to the AGLASSO model and the basic MBA algorithm, the MLASSO model can provide an acceptable compromise between the minimization of the data mismatch term and the sparsity of the solution. Moreover, the solution by the MLASSO model can reflect the regions of the underlying surface where high gradients occur.     

A STOCHASTIC MOVING BALLS APPROXIMATION METHOD OVER A SMOOTH INEQUALITY CONSTRAINT

We consider the problem of minimizing the average of a large number of smooth component functions over one smooth inequality constraint. We propose and analyze a stochastic Moving Balls Approximation (SMBA) method. Like stochastic gradient (SG) methods, the SMBA method's iteration cost is independent of the number of component functions and by exploiting the smoothness of the constraint function, our method can be easily implemented. Theoretical and computational properties of SMBA are studied, and convergence results are established. Numerical experiments indicate that our algorithm dramatically outperforms the existing Moving Balls Approximation algorithm (MBA) for the structure of our problem.     

A proposal for a hybrid meta-strategy for combinatorial optimization problems

In this paper, we propose an algorithm named BDS (Bound-Driven Search) that combines features of exact and approximate methods. The proposed procedure may be seen as a local search algorithm that systematically explores (in a branch-and bound sense) the most promising nodes, thus preventing solutions from being reevaluated. Additionally, it can be regarded as an exact method as it may be able to guarantee that the solution found is optimal. We present the application of this new algorithm to a specific problem domain: the permutation flow shop scheduling problem with makespan objective. The subsequent computational experiments are encouraging, as the algorithm is able to yield exact or near exact solutions to most instances of the problem. Furthermore, the algorithm outperforms one of the best state-of-the-art algorithms for the problem.     

Approximation algorithms for combinatorial fractional programming problems

We are concerned with a combinatorial optimization problem which has the ratio of two linear functions as the objective function. This type of problems can be solved by an algorithm that uses an auxiliary problem with a parametrized linear objective function. Because of its combinatorial nature, however, it is often difficult to solve the auxiliary problem exactly. In this paper, we propose an algorithm which assumes that the auxiliary problems are solved only approximately, and prove that it gives an approximate solution to the original problem, of which the accuracy is at least as good as that of approximate solutions to the auxiliary problems. It is also shown that the time complexity is bounded by the square of the computation time of the approximate algorithm for the auxiliary problem. As an example of the proposed algorithm, we present a fully polynomial time approximation scheme for the fractional 0–1 knapsack problem.     

MBA项目评价与改进系统的反馈动态复杂性分析

中国MBA教育的评价与改进是当前MBA教育发展的瓶颈,为了寻求提升MBA教育质量的有效方法,用系统动力学流率基本入树建模法构建了MBA教育的SD模型.通过用极小基模生成集法对模型中的反馈环进行分析,找到系统基模.在MBA教育SD模型中存在两个增长上限基模和一个舍本逐末基模.根据学习型组织理论:找到管理系统中的基模并用系统思考的方法正确处理基模,是保障系统运行的重要方法.但是,对于一个象MBA教育项目这样的典型动态复杂系统,发现其中所有的基模往往非常困难.本文提供了一个迅速并准确找到复杂系统中全部基模的方法,即极小基模生成集法.不论我们面临的动态系统有多么复杂,都可以使用该方法来分析其中的反馈环结构.构造SD流率基本入树模型,运用该方法进行反馈动态分析,提出了改进中国MBA教育的管理策略.     

带投资约束且p不确定的推广p-中位问题

p-中位问题是设施选址中的一个经典模型,在交通、物流等领域有着广泛应用．在经典p-中位问题的基础上提出一种p不确定的推广p-中位问题,并且加上总投资约束,使得此推广模型更加实用．针对此推广模型,提出三种启发式算法：简单启发式算法、变邻域搜索算法和改进的遗传算法．数值实验结果表明变邻域搜索算法和改进的遗传算法在求解此推广模型时是有效的．     

An effective heuristic algorithm to minimise stack shuffles in selecting steel slabs from the slab yard for heating and rolling

Steel production is a multi-stage process. A slab yard serves as a buffer between the continuous casting stage and the steel rolling stage. Steel slabs are stored in stacks in the yard. Shuffling is needed when picking up a slab for heating and rolling, if it is not in the top position of a stack. This paper studies the problem of selecting appropriate slabs in the yard for a given rolling schedule so as to minimise the total shuffling cost. The study uses the hot strip rolling mill in Shanghai Baoshan Iron and Steel Complex as an application background. We propose a new heuristic algorithm to solve the problem. This is a two-phase algorithm that first generates an initial feasible solution and then improves it using local search. The new algorithm is compared with the algorithm in use on randomly generated test problems and on real data. Experimental results show that the proposed algorithm yields significant better solutions. The average improvement over the old algorithm is 15%.     

求解无容量设施选址问题的拉格朗日蝙蝠算法

无容量设施选址问题(Uncapacitated Facility Location Problem,UFLP)是一类经典的组合优化问题,被证明是一种NP-hard问题,易于描述却难于求解.首先根据UFLP的数学模型及其具体特征,重新设计了蝙蝠算法的操作算子,给出了求解UFLP的蝙蝠算法.其次构建出三种可行化方法,并将其与求解UFLP的蝙蝠算法和拉格朗日松弛算法相结合,设计了求解该问题的拉格朗日蝙蝠算法.最后通过仿真实例和与其他算法进行比较的方式,验证了该混合算法用来求解UFLP的可行性,是解决离散型问题的一种有效方式.     

An iterated local search algorithm based on nonlinear programming for the irregular strip packing problem

The irregular strip packing problem is a combinatorial optimization problem that requires to place a given set of two-dimensional polygons within a rectangular container so that no polygon overlaps with other polygons or protrudes from the container, where each polygon is not necessarily convex. The container has a fixed width, while its length can change so that all polygons are placed in it. The objective is to find a layout of the set of polygons that minimizes the length of the container.We propose an algorithm that separates overlapping polygons based on nonlinear programming, and an algorithm that swaps two polygons in a layout so as to find their new positions in the layout with the least overlap. We incorporate these algorithms as components into an iterated local search algorithm for the overlap minimization problem and then develop an algorithm for the irregular strip packing problem using the iterated local search algorithm. Computational comparisons on representative instances disclose that our algorithm is competitive with other existing algorithms. Moreover, our algorithm updates several best known results.     

A BRANCH BOUND METHOD FOR SUBSET SUM PROBLEM

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基于迭代投影的梯度硬阈值追踪算法

梯度硬阈值追踪算法是求解稀疏优化问题的有效算法之一.考虑到算法中投影对最优解的影响,提出一种比贪婪策略更好的投影算法是很有必要的.针对一般的稀疏约束优化问题,利用整数规划提出一种迭代投影策略,将梯度投影算法中的投影作为一个子问题求解.通过迭代求解该子问题得到投影的指标集,并以此继续求解原问题,以提高梯度硬阈值追踪算法的计算效果.证明了算法的收敛性,并通过数值实例验证了算法的有效性.     

The balanced linear programming problem

The Balanced Linear Programming Problem (BLPP) arises in situations which require equitable distribution of a scarce resource. The BLPP can be transformed to the standard form of the linear programming problem by introducing 2∥N∥ + 2 additional variables and 2∥N∥ additional constraints. This transformation is not desirable from the computational point of view for larger values of ∥N∥ as it increases the problem size substantially. It is also undesirable from a theoretical perspective as it might affect the special structure of the constraint matrix. In this paper, we develop an algorithm for the BLPP which does not require problem enlargement. The algorithm is based on the relationship between the BLPP and the minimax linear programming problem, and solving the latter problem parametrically. Our algorithm, in essence, performs steps that are similar to those performed in the parametric simplex method with parametric right hand side. We then adapt our algorithm for the network flow problem and this specialized algorithm can be applied on the network directly without maintaining the simplex tableau.     

Mapping the structure of MBA programmes: a comparative study of the structure of accredited AMBA programmes in the United Kingdom

This paper reports on an application a multivariate analysis technique called Co-Plot. It replicates a study conducted among leading MBA programmes in the United States using the same technique; a statistical method especially suited for this type of analysis where there are samples with relatively few observations (business schools) and large numbers of variables (subject modules, core and elective). Using Co-Plot the paper presents a mapping of the structure of 32 Association of Masters of Business Administration (AMBA) accredited MBA programmes in the United Kingdom and compares the characteristics of the resultant groupings of MBA programmes and the relationship between group membership. The patterns of core and elective modules offered by the selected MBA programmes are then compared with the rankings of UK business schools. The research shows that in the UK, unlike in the US, the clustering is not as strong and clear. Five groups/clusters of schools are identified together with four main clusters of core and electives modules offered. Differentiation is only significant when the electives modules are taken into account unlike the US where differentiation is evident between programmes with the core modules.     

Adaptive scheme of discretization for one semiiterative method in solving ill-posed problems

We consider a new algorithm to solving a linear ill-posed problem with operators of finite smoothness. The algorithm uses a semiiterative method for the regularization of the original problem in combination with an adaptive strategy of discretization. For the operators, the algorithm achieves the optimal order of accuracy. Moreover, it is more economical in the sense of the amount of used discrete information as compared with standard methods.     

An integer-programming-based heuristic for the balanced loading problem

This paper presents an efficient heuristic algorithm for the one-dimensional loading problem in which the goal is to pack homogeneous blocks of given length and weight in a container in such a way that the center of gravity of the packed blocks is as close to a target point as possible. The proposed algorithm is based on the approximation of this problem as a knapsack problem. This algorithm has the same computational complexity but a better worst-case performance than the algorithm recently proposed by Amiouny et al. [Oper. Res. 40 (1992) 238]. Moreover, the computational results also show that, in general, it performs better on randomly generated problems.     

Shortest path in the presence of obstacles: An application to ocean shipping

This paper presents the problem of determining the estimated time of arrival (ETA) at the destination port for a ship located at sea. This problem is formulated as a shortest path problem with obstacles, where the obstacles are modelled by polygons representing the coastlines. An efficient solution algorithm is proposed to solve the problem. Instead of generating a complete visibility graph and solving the problem as an ordinary shortest path problem, the algorithm constructs arcs to the ship node during the solution process only when needed. This greatly enhances the algorithmic performance. Computational results based on test problems from an actual dry-bulk shipping operation are provided. The proposed algorithm is implemented in a decision support system for the planning of ship operations and it has successfully been applied on several real life problems.     

带损伤弹性反问题的数值分析

考虑一类由椭圆性方程和热传导方程共同来刻画的准静态弹性模型,通过给定观测值来反演边界的牵引力.首先构造一个凸目标泛函,并引入Tikhonov正则化方法,使之极小化得到一个稳定的近似解.再用有限元离散求解,导出误差估计.最后,用数值例子说明算法的可行性和有效性.     

Optimal compactification of a floorplan and its relation to other optimization problems-a dynamic programming approach

We examine an algorithm for the compactification of an arrangement of rectangles in the plane as it is used for floorplans in the automated design of electronic circuits (also called sizing of floorplans). We reformulate this problem as a multistage decision problem and show that the algorithm is in fact the optimal solution obtained by the backward induction procedure of dynamic programing. The model allows generalisations to non-geometrical applications in scheduling and reliability.     

An all-linear programming relaxation algorithm for optimizing over the efficient set

The problem (P) of optimizing a linear function over the efficient set of a multiple objective linear program has many important applications in multiple criteria decision making. Since the efficient set is in general a nonconvex set, problem (P) can be classified as a global optimization problem. Perhaps due to its inherent difficulty, it appears that no precisely-delineated implementable algorithm exists for solving problem (P) globally. In this paper a relaxation algorithm is presented for finding a globally optimal solution for problem (P). The algorithm finds an exact optimal solution to the problem after a finite number of iterations. A detailed discussion is included of how to implement the algorithm using only linear programming methods. Convergence of the algorithm is proven, and a sample problem is solved.Research supported by a grant from the College of Business Administration, University of Florida, Gainesville, Florida, U.S.A.