Approximation algorithms and hardness results for labeled connectivity problems

Let G=(V,E) be a connected multigraph, whose edges are associated with labels specified by an integer-valued function ℒ:E→ℕ. In addition, each label ℓ∈ℕ has a non-negative cost c(ℓ). The minimum label spanning tree problem (MinLST) asks to find a spanning tree in G that minimizes the overall cost of the labels used by its edges. Equivalently, we aim at finding a minimum cost subset of labels I⊆ℕ such that the edge set {e∈E:ℒ(e)∈I} forms a connected subgraph spanning all vertices. Similarly, in the minimum label s – t path problem (MinLP) the goal is to identify an s–t path minimizing the combined cost of its labels. The main contributions of this paper are improved approximation algorithms and hardness results for MinLST and MinLP.     

试论西方人力资源管理思维方式的沿革——从线性思维到复杂思维

从古希腊到近代,西方社会在对人的管理思想方面,其间虽不乏系统的、有机的思想,但线性思维方式一直居于统治地位。今天,复杂性思维方式已逐渐融入西方企业人力资源管理理论与实践之中,而这一切,均与同时代自然科学思维方式密切相关。     

On the computational complexity of bridgecard

Bridgecard is a classical trick-taking game utilizing a standard 52-card deck, in which four players in two competing partnerships attempt to “win” each round, i.e. trick. Existing theories and analysis have already attempted to show correlations between system designs and other technical issues with parts of the game, specifically the “Bidding” phase, but this paper will be the first to attempt to initiate a theoretical study on this game by formulating it into an optimization problem. This paper will provide both an analysis of the computational complexity of the problem, and propose exact, as well as, approximation algorithms.     

The use of edge-directions and linear programming to enumerate vertices

Given a list of vectors that contains directions of the edges of a given polytope ℘ and the availability of an algorithm that solves linear programs over ℘, we describe a method for enumerating the vertices of ℘; in particular, the method is adaptable to polytopes which are presented as (linear) projections of polytopes having linear inequality representation. Polynomial complexity bounds under both the real and the binary computation models are derived when the dimension of the polytope is fixed and the given LP algorithm is polynomial. Dedicated to Professor Frank K. Hwang on the occasion of his sixty fifth birthday. Supported in part by a grant from ISF—the Israel Science Foundation, by a VPR grant at the Technion and by the Fund for the Promotion of Research at the Technion.     

成分数据的多元回归建模方法研究

在社会、经济、技术等许多领域的数据分析中,成分数据(compositional data)是一种应用十分广泛的数据类型,可以被用来反映诸如投资结构、产业结构、居民消费结构等问题.将成分数据的logratio变换方法与偏最小二乘路径分析相结合,提出在因变量是成分数据,而与之相关的若干个自变量也都是成分数据的情况下,建立了多元线性回归模型的方法.该建模方法可以满足成分数据的定和约束,克服成分数据中完全多重共线性对建模的不良影响,并且突出成分数据主题含义在建模中的作用和意义.作为案例,应用所提出的方法,采用北京市三类产业的投资、GDP以及就业的结构数据,建立了三者之间的回归模型,进一步说明了多元成分数据回归建模的工作过程及其应用价值.     

Minimization of maximum lateness under linear deterioration

This paper considers a single-machine scheduling problem to minimize the maximum lateness. The processing time of each job is a linear function of the time when the job starts processing. This problem is known to be -hard in the literature. In this paper, we design a branch-and-bound algorithm for deriving exact solutions by incorporating several properties concerning dominance relations and lower bounds. These properties produce synergic effects in accelerating the solution finding process such that the algorithm can solve problems of 100 jobs within 1 min on average. To compose approximate solutions, we revise a heuristic algorithm available in the literature and propose several hybrid variants. Numerical results evince that the proposed approaches are very effective in successfully reporting optimal solutions for most of the test cases.     

Note on the hardness of generalized connectivity

Let G be a nontrivial connected graph of order n and let k be an integer with 2??k??n. For a set S of k vertices of G, let ??(S) denote the maximum number ? of edge-disjoint trees T ₁,T ₂,??,T _? in G such that V(T _i )??V(T _j )=S for every pair i,j of distinct integers with 1??i,j???. Chartrand et al. generalized the concept of connectivity as follows: The k-connectivity, denoted by ?? _k (G), of G is defined by ?? _k (G)=min{??(S)}, where the minimum is taken over all k-subsets S of V(G). Thus ?? ₂(G)=??(G), where ??(G) is the connectivity of G, for which there are polynomial-time algorithms to solve it. This paper mainly focus on the complexity of determining the generalized connectivity of a graph. At first, we obtain that for two fixed positive integers k ₁ and k ₂, given a graph G and a k ₁-subset S of V(G), the problem of deciding whether G contains k ₂ internally disjoint trees connecting S can be solved by a polynomial-time algorithm. Then, we show that when k ₁ is a fixed integer of at least 4, but k ₂ is not a fixed integer, the problem turns out to be NP-complete. On the other hand, when k ₂ is a fixed integer of at least 2, but k ₁ is not a fixed integer, we show that the problem also becomes NP-complete.     

A production planning system based on linear programming

This paper describes the production planning system developed for the chemicals division of the Boliden Company Ltd., Sweden. The major elements of the production planning system are a linear programming model, a cost model, a scheduling program and a program to forecast the economic outcome. A special organization was established to implement the plans.     

A linear programming based heuristic algorithm for charge and discharge scheduling of electric vehicles in a building energy management system

Electric vehicles (EVs) are becoming an attractive alternative to gasoline vehicles owing to the increase of greenhouse gas emissions and gasoline prices. EVs are also expected to function as battery storages for stabilizing large fluctuations in the power grid through the vehicle-to-grid power system, which requires smart charge and discharge scheduling algorithms. In this paper, we develop a linear programming based heuristic algorithm on a time–space network model for charge and discharge scheduling of EVs. We also develop an improved two-stage heuristic algorithm to cope with uncertain demands and departure times of EVs, and evaluate the effect of the smart charge and discharge scheduling of EVs on a peak load reduction in a building energy management system.     

Performance evaluation based on multiple attributes with nonparametric frontiers

Performance rating and comparison of a group of entities is frequently based on the values of several attributes. Such evaluations are often complicated by the absence of a natural or obvious way to weight the importance of the individual dimensions of the performance. This paper proposes a framework based on nonparametric frontiers to rate and classify entities described by multiple performance attributes into ‘performers’ and ‘underperformers’. The method is equivalent to Data Envelopment Analysis (DEA) with entities defined only by outputs. In the spirit of DEA, the weights for each attribute are selected to maximize each entity’s performance score. This approach, however, results in a new linear program that is more direct and intuitive than traditional DEA formulations. The model can be easily understood and interpreted by practitioners since it conforms better to the practice of evaluating and comparing performance using standard specifications. We illustrate the model’s use with two examples. The first evaluates the performance of employees. The second is an application in manufacturing where multiple quality attributes are used to assess and compare performance of different manufacturing processes.     

基于GLM的贝叶斯变量与模型选择

针对非正态响应的部分因子试验,当筛选试验所涉及的因子数目较大时,提出了基于广义线性模型(generalized linear models,GLM)的贝叶斯变量与模型选择方法.首先,针对模型参数的不确定性,选择了经验贝叶斯先验.其次,在广义线性模型的线性预测器中对每个变量设置了二元变量指示器,并建立起变量指示器与模型指示器之间的转换关系.然后,利用变量指示器与模型指示器的后验概率来识别显著性因子与选择最佳模型.最后,以实际的工业案例说明此方法能够有效地识别非正态响应部分因子试验的显著性因子.     

预算报酬方案和线性报酬方案的一个比较分析

在代理理论的框架下 ,分析比较企业实务中最为常见的两种报酬方案 :预算报酬方案和线性报酬方案 .通过建立一个具体模型进行定量模拟分析 ,探讨影响企业报酬方案的激励成本的主要因素 .根据模拟的数值结果 ,具体描述了企业应该如何根据其业绩评价信息系统的质量来选择和设计报酬激励方案 ,以较低的成本达到预定的控制和激励目标     

Error-correcting codes based on partial linear maps of finite-dimensional vector spaces

Journal of Combinatorial Optimization - The determination of bounds on the size of codes with given minimum distance is an important problem in the coding theory. In this paper, we construct codes...     

Top management team diversity and high performance: An integrative approach based on upper echelons and complexity theory

This paper analyses Top Management Team (TMT) composition diversity as an antecedent of firm performance in accordance with a recent paradigm based on Complexity Theory. Research into TMT diversity is commonly seen as a double-edged sword because inconclusive results have been achieved in prior studies. This controversy has reinforced the call to employ a more appropriate methodology by moving beyond the reliance on multiple regression analysis and towards the use of fuzzy-set qualitative comparative analysis. The study provides various TMT diversity configurations that lead to high performance. The study therefore contributes towards the TMT diversity literature by utilising asymmetric testing to advance in the understanding of the diversity of TMT attributes as an antecedent of high firm outcome. The paradigm currently facing TMT internal complexity is doubly relevant for managers, to ascertain the best TMT diversity compositions to achieve the best strategic goal and thereby the highest firm outcome, and for new research avenues in the demographic literature, to obtain richer insights from TMT data, which might provide additional information on the complex relations established within these TMTs.     

The ambivalent effect of complexity on firm performance: A study of the global service provider industry

Prior literature is ambivalent about whether organizational complexity has positive or negative effects on firm performance. Using rich data on global service providers, we explore this ambivalence by disentangling performance consequences of different types of organizational complexity. We show that complexity arising from the coordination of different services and operations negatively influences profit margins through increased coordination costs, whereas complexity coming from the sophistication of particular services may positively influence margins through informational advantages. We also investigate the moderating effects of process commoditization and client-specific investments. Our findings point to critical performance dilemmas facing global service providers in a highly competitive industry, and they help better differentiate performance effects of complexity at different organizational levels.     

On linear bilevel problems with multiple objectives at the lower level

Bilevel programming problems provide a framework to deal with decision processes involving two decision makers with a hierarchical structure. They are characterized by the existence of two optimization problems in which the constraint region of the upper level problem is implicitly determined by the lower level optimization problem. This paper focuses on bilevel problems for which the lower level problem is a linear multiobjective program and constraints at both levels define polyhedra. This bilevel problem is reformulated as an optimization problem over a nonconvex region given by a union of faces of the polyhedron defined by all constraints. This reformulation is obtained when dealing with efficient solutions as well as weakly efficient solutions for the lower level problem. Assuming that the upper level objective function is quasiconcave, then an extreme point exists which solves the problem. An exact and a metaheuristic algorithm are developed and their performance is analyzed and compared.     

Unacceptable Solutions and the Hybrid Discriminant Model

A new family of linear programming (LP) discriminant models, the hybrid discriminant model, was recently presented with claims that it avoids all the problems of its predecessor LP models. However, this note shows that it does not avoid unacceptable solutions.     

Mathematical Programming Formulations for the Discriminant Problem: An Old Dog Does New Tricks*

In recent years, much research has been done on the application of mathematical programming (MP) techniques to the discriminant problem. While promising results have been obtained, many of these techniques are plagued by a number of problems associated with the model formulation including unbounded, improper, and unacceptable solutions as well as solution instability under linear transformation of the data. In attempting to solve these problems, numerous formulations have been proposec involving additional variables and/or normalization constraints. While effective, these models can also become quite complex. In this paper we demonstrate that a simple, well-known special case of Hand's [13] original formulation provides an implicit normalization which avoids the problems for which various complicated remedies have been devised. While other researchers have made use of this formulation, its properties have not previously been fully recognized.