Mathematical Models for Studying the Value of Motivational Leadership in Teams

Mathematical models are presented for studying the value of leadership in a team where the members interact with each other. The models are based on a leader’s role of motivating each team member to perform closer to his/her maximum ability. These models include controllable parameters whose values reflect the amount of task interdependence among the workers as well as the motivational skill and variability in the skill of the leader. Confirming results—such as the fact that the skill level of the leader is a critical factor in the expected performance of the team—establish credibility in the models. Mathematical analysis and computer simulations are used to provide new managerial insights into the value of the leader—such as the fact that the skill of the leader can be more important than controlling the amount of interdependence among the team members and that having a choice of multiple leaders with no particular motivating skill is beneficial to the performance of small teams but not to large teams.Daniel Solow received a B.S. in Mathematics from Carnegie-Mellon, an M.S. in Operations Research from the University of California at Berkeley, and a Ph. D. in Operations Research from Stanford University. He has been a professor at Case Western Reserve University since 1978. His research interests include complex systems, discrete, linear, and nonlinear optimization. He has also developed systematic methods for teaching mathematical proofs, computer programming, and operations research.Sandy Kristin Piderit is an assistant professor of organizational behavior at the Weatherhead School of Management at Case Western Reserve University, and earned her Ph.D. from the University of Michigan. She studies the roles of relationships among coworkers on their performance and satisfaction with their work environments, and has published studies in the Academy of Management Review, the Journal of Management Studies, and Management Science.Apostolos Burnetas received a Diploma in Electrical Engineering from National Technical University in Athens, Greece, and an M.B.A. and Ph.D. in Operations Research from Rutgers University. He has been at the Department of Operations at Case Western Reserve University and is currently an Associate Professor at the Department of Mathematics at the University of Athens. His research interests include stochastic models and optimization, complex systems, and applications in queueing systems, supply chain and the interface of operations with finance.Chartchai Leenawong received a B.S. in Mathematics from Chulalongkorn University in Bangkok, an M.S. in Computer Science from the Asian Institute of Technology in Bangkok, and a Ph.D. in Operations Research from Case Western Reserve University. His research interests include mathematical modeling of complex systems as applied to business organizations. He has been a professor at King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand since 2002.     

A formal analysis of the model management literature

This paper presents an extensive bibliography of the archival material on model management, and an analysis of that material. It argues that the three general approaches to model management can be observed, called here the data-model analogy, knowledge-based and model-representation approaches. For the period 1970 to 1989, 57 journals were exhaustively searched for articles dealing with model management; 152 articles were identified. An informal analysis shows that model creation and execution have been the major model management functions addressed by research, and that mathematical programming and simulation have been the dominant model areas. Applications have addressed the extremes of Operations Research models, namely policy and strategy at one extreme and operations at the other, with many applications in accounting and finance also prevalent. A formal analysis using factor analysis shows that research in model management has moved away from speculation and focus on certain limited aspects of the subject towards the practical implementation of model management systems. Further, a regression model shows that the model-representation approach has tended to yield implemented systems, whereas the data-model analogy approach has not. Directions for future research and development are suggested.     

Scheduling farm operations

Scheduling operations on a farm is considered depending on the available men and machinery and on the influence of the weather on materials (moisture content). A simulation model with a heuristic strategy for selecting operations at each moment of decision based on the state of the system and a linear programming model are used in the grain harvest to demonstrate the influence of the models on the resulting variable costs (overtime, drying of wet grain and timeliness losses of wheat and straw) and the influence of input data (weather, attributes of material and number of workable hours) on those costs. The lower costs found with simplified input (hourly, daily, weekly data) in simulation is continued with the linear programming model due to its deviation from the real workable time constraints and decision variables. Such a tendency suggests that LP-models usual in agricultural planning are too simple.     

Duality in inexact fractional programming with set-inclusive constraints

This paper extends the fractional programming problem with set-inclusive constraints studied earlier by replacing every coefficient vector in the objective function with a convex set. A dual is formulated, and well-known duality results are established. A numerical example illustrates the dual strategy to obtain the value of the initial problem.The research of the first author was conducted while he was on sabbatical at the Department of Operations Research, Stanford University, Stanford, California. The financial assistance of the International Council for Exchange of Scholars is gratefully acknowledged. The author is grateful to the Department of Operations Research at Stanford for the use of its research facilities.     

农机配套服务的系统分析和协调优化模型研究

在界定农机配套服务的基础上,首先系统分析了农机配套服务的影响因素,以黑龙江垦区51个农场近10年农机和粮食产量等数据为例,采用相关分析、建立最优模型等方法知目前黑龙江垦区农机配套比与粮食单产相关系数的绝对值存在逐年减少趋势.再以七星农场近10年数据为例知小型农机具配套比与粮食产量相关性最密切,而利用建立最优回归模型揭示大中型拖拉机配套农机具对粮食产量起到显著作用.最后建立和分析农机配套服务的协调优化模型,确定了决策变量的满足条件,为推进农机配套服务具有重要意义.     

Modeling partial harvesting in intensive shrimp culture: A network-flow approach

Despite the promising laboratory results and theoretical arguments on the potential of partial harvesting in enhancing the productivity and profitability of intensive shrimp growout facilities, the implementation of partial harvesting in practical operation is rather difficult due to its complex nature. In this paper, we developed a practical model of partial harvesting using the network-flow approach so that it can be readily implemented and solved in MS EXCEL. We demonstrated the use of this spreadsheet model with data from a commercial shrimp farm in Hawaii. The results indicate that the model is capable of identifying the efficient harvest policy as well as assessing the viability of partial harvesting under a variety of managerial conditions and objectives.     

MULTISPECIES EXPLOITATION WITH EVOLUTIONARY SWITCHING OF HARVESTING STRATEGIES

In this paper, we propose a bioeconomic model which describes a fishery in which each of two noninteracting species is harvested by a given group of fishers during a defined time period. Then the Fishing Regulatory Authority allows each fisher to reconsider the harvesting decision at fixed (discrete) periods of time. The model derives from an Italian fisheries management experience in the Northern Adriatic Sea, where this kind of “self‐adjusting” fishing policy has been proposed to regulate harvesting of two shellfish species. The proposed dynamic model assumes the form of a hybrid system, as the natural growth functions of the two species (in continuous time) are coupled with a discrete time adaptive system that regulates how agents switch from one harvesting strategy to the other period by period according to an evolutionary mechanism based on profit comparison. In order to obtain some insights into the basic mechanisms of the system, some relevant benchmark cases are analyzed before tackling (mainly numerically) the complete hybrid model. Our results suggest that, for proper sets of parameters, this kind of myopic and adaptive self‐regulation may ensure a virtuous trade‐off between profit maximization and resource conservation, driven by cost externalities and market pressure.     

Combining a path method and parametric linear programming for the computation of competitive equilibria

A path-following philosophy (continuation method, global Newton method) is used to compute equilibria for piecewise linear economies while taking advantage of the linear structure of the model. The existence of a path leading through certain faces of a polyhedral set to an equilibrium point is demonstrated. Computational experience is reported which indicates that this method is promising for models dealing with many commodities and relatively few consumers.Most of this paper has been extracted from the author's doctoral dissertation for the Department of Operations Research at Stanford University; the author would like to express indebtedness to his advisor, R. Wilson. Major revisions were made while the author was at Bell Laboratories in Whippany, New Jersey.     

运筹学教学与数学建模

根据从事《运筹学》教学的体会 ,论述了运筹学教学与数学建模教育的关系 ,并介绍了教学的一些做法     

Dynamic graphs and continuous Boolean networks,II: Large-scale organic structures

In this paper, we propose a new method for constructing large-scale dynamic graphs. The procedure is based on the notion of graph entanglement, and involves “organic” operations such as self-replication and random mutations. Graphs obtained in this manner are globally asymptotically stable, and the simulation of their dynamics requires only a modest computational effort. As a result, they provide a suitable mathematical framework for studying the behavior of large-scale continuous Boolean networks.     

Mathematical morphology on bipolar fuzzy sets: general algebraic framework

In many domains of information processing, bipolarity is a core feature to be considered: positive information represents what is possible or preferred, while negative information represents what is forbidden or surely false. If the information is moreover endowed with vagueness and imprecision, as is the case for instance in spatial information processing, then bipolar fuzzy sets constitute an appropriate knowledge representation framework. In this paper, we focus on mathematical morphology as a tool to handle such information and reason on it. Applying mathematical morphology to bipolar fuzzy sets requires defining an appropriate lattice. We extend previous work based on specific partial orderings to any partial ordering leading to a complete lattice. We address the case of algebraic operations and of operations based on a structuring element, and show that they have good properties for any partial ordering, and that they can be useful for processing in particular spatial information, but also other types of bipolar information such as preferences and constraints. Particular cases using Pareto and lexicographic orderings are illustrated. Operations derived from fuzzy bipolar erosion and dilation are proposed as well.     

On the use of conditional expectation in portfolio selection problems

Annals of Operations Research - In this paper, we examine the use of conditional expectation, either to reduce the dimensionality of large-scale portfolio problems or to propose alternative...     

Fuzzy理论在工程环境灾害预测中的应用

针对矿山大型排土场所出现的滑坡等工程环境灾害的预测与防治问题,着重探讨排土场边坡失稳破坏预测问题.文中采用Fuzzy数学中的Fuzzy概率测度理论建立理论预测分析模型,并对大型排土场边坡失稳破坏的Fuzzy概率测度进行具体的预测分析,所获结果与已有的经典分析方法所获理论结果一致.针对矿山大型排土场所出现的滑坡等工程环境灾害防治问题,提出了具体的防治技术措施.     

An interview with Laurens de Haan

Laurens de Haan was born January 15, 1937 in Rotterdam, The Netherlands. He graduated 1966 in mathematics and received a doctoral degree in 1970 from the University of Amsterdam, while working at the Mathematical center CWI in Amsterdam. Since 1973 he was Professor for probability and mathematical statistics at the Econometric Institute of the Economic Faculty at the Erasmus University Rotterdam, where he retired 1998. Since 2008 he is part-time professor at the Department of Econometrics and Operations Research of Tilburg University. Laurens de Haan has been active in research throughout his career. He has published more than 110 scientific papers. Among other distinctions, he was elected IMS fellow for his seminal contributions to extreme value theory in 1977, and he was appointed Honorary Doctor of the University of Lisbon in 2000.     

On the Optimal Three-tier Multimedia Streaming Services

In this paper, we provide a mathematical model for the streaming media provider seeking a minimum cost while fulfilled the requirements assumed by a three-tier framework. The proposed model involves a linear cost function subjected to fuzzy relational equations, where the algebraic operations employed are the max-min operations.     

Globalization, social development, and operations research: an exploration of strategies for success

This paper argues that in today’s world order, policy-making takes precedence over analytical and technical models that have historically formed the mainstay of Operations Research. The structural and human dimensions of this transition is discussed in the form of six Policy Imperatives aimed at the creation of a world order that makes it more humane and less vulnerable to failure. It is proposed that though OR occupies a prominent role in developmental initiatives, in order for its successful implementation in meeting social goals, the context in which it is invoked must be conducive to social transformation. An earlier version of this paper was presented at the International Conference on Operations Research for Development (ICORD) held December 27–30, 2002 at Anna University, Chennai. The author would like to acknowledge the helpful comments of anonymous reviewers. He would also like to thank Professor K.S.P. Rao of Anna University for his gracious assistance.     

Reassessing operations research in Finland

At the beginning of 1980 the Finnish Operations Research Society (FORS) established a working group (OTSA) headed by Y. Seppälä. The aim was to analyse R.L. Ackoff's and others' criticism of operations research in order to make improvement proposals for the Finnish operations research. The final report of this working group was completed in December 1981.Within this project an analysis was made of opinions of members of the Finnish Operations Research Society concerning their own work and role. It was found to be a drawback that the Finnish operations research has been too much concerned with well defined problems, neglecting truly challenging ‘wicked’ problems. Accordingly, the main recommendation of the group is that besides operations researchers concerned with well structured problems we should also train systems analysts to deal essentially with poorly defined problems.This article will provide a profile of the Finnish operations researchers as reflected in the survey. An analysis of the crisis in operations research will be given as well as a portrayal of the roles for operations researcher and systems analyst. The paper concludes by presenting various working methods of systems analysts on the basis of the final report by the OTSA group.     

The Development of a Mathematical Model of the Operations of a National Glass Manufacturer

In this paper, a mathematical model of the entire operations of a national glass manufacturer is developed. This includes the float glass manufacture, distribution, storage operations and the technical considerations dictated by the plant as well as the operating procedures. The model is initially for a planning year, and is generated from a ‘monthly model’. This monthly model interconnects with other monthly models primarily via stock flows. The mathematical model is formulated in a unique way that allows certain production aspects to be modelled using a ‘pseudo-continuous’ time frame, rather than a discrete one. The generation of the overall model (as a mixed integer linear programming problem) and its solution is also discussed.     

Cost Optimized Design for the Local Wind Turbine Grid of an Onshore Wind Farm

Annals of Operations Research - This document analyses the problem of designing a minimum cost local wind turbine grid (or LWTG) for an onshore wind farm. The LWTG is responsible for adding up the...