Effort estimates through project complexity

This paper reports the results obtained from use of project complexity parameters in modeling effort estimates. It highlights the attention that complexity has recently received in the project management area. After considering that traditional knowledge has consistently proved to be prone to failure when put into practice on actual projects, the paper endorses the belief that there is a need for more open-minded and novel approaches to project management. With a view to providing some insight into the opportunities that integrate complexity concepts into model building offers, we extend the work previously undertaken on the complexity dimension in project management. We do so analyzing the results obtained with classical linear models and artificial neural networks when complexity is considered as another managerial parameter. For that purpose, we have used the International Software Benchmarking Standards Group data set. The results obtained proved the benefits of integrating the complexity of the projects at hand into the models. They also addressed the need of a complex system, such as artificial neural networks, to capture the fine nuances of the complex systems to be modeled, the projects.     

Cycling in proofs and feasibility

There is a common perception by which small numbers are considered more concrete and large numbers more abstract. A mathematical formalization of this idea was introduced by Parikh (1971) through an inconsistent theory of feasible numbers in which addition and multiplication are as usual but for which some very large number is defined to be not feasible. Parikh shows that sufficiently short proofs in this theory can only prove true statements of arithmetic. We pursue these topics in light of logical flow graphs of proofs (Buss, 1991) and show that Parikh's lower bound for concrete consistency reflects the presence of cycles in the logical graphs of short proofs of feasibility of large numbers. We discuss two concrete constructions which show the bound to be optimal and bring out the dynamical aspect of formal proofs. For this paper the concept of feasible numbers has two roles, as an idea with its own life and as a vehicle for exploring general principles on the dynamics and geometry of proofs. Cycles can be seen as a measure of how complicated a proof can be. We prove that short proofs must have cycles.

     

Cycling in linear complementarity problems

A bound for the minimum length of a cycle in Lemke's Algorithm is derived. An example illustrates that this bound is sharp, and that the fewest number of variables is seven.     

Teacher Mentoring as a Community Effort

This article presents the findings from a study of a mentoring program for novice mathematics and science teachers, which was provided by their teacher education program. This study reports the findings of interviews with novice math and science teachers, their mentors, and the mentoring program administrators to explore stakeholder perceptions of mentoring support. Findings suggest the importance of using multiple mentoring strategies to develop, support, and retain high‐quality math and science teachers in the teaching profession. This study contributes to what is known about the role that teacher education programs may play in mentoring novice math and science teachers who have graduated from their programs.     

The Determination of Total Research Effort

The reasons for endeavouring to estimate the appropriate total research expenditure in a manufacturing industry are outlined. Three techniques are discussed using an analytical, a comparative and a synthetic approach respectively. It is pointed out that the guidance given by these three techniques differs substantially in particular situations and that more studies are needed as to the relative value of the three solutions. It is suggested that an individual company should be spending about one-fifth of its future capital requirements on R. & D. The R. & D. expenditure of the U.K. should be about 4 per cent of the gross national product.     

No Cycling in the Graphs!

A variety of results on the problem of destroying all cycles in a graph by removing sets of vertices of minimum cardinality are presented.     

变捕捞努力量收获模型控制

利用微分包含给出了努力量可变的收获模型,基于生存理论和求解线性规划给出了将单种群数量控制在某范围的方法.最后对于常用的Logistic模型,证明只要控制努力量就可以将种群数量控制在指定范围内.     

Effort Games and the Price of Myopia

We consider Effort Games, a game‐theoretic model of cooperation in open environments, which is a variant of the principal‐agent problem from economic theory. In our multiagent domain, a common project depends on various tasks; carrying out certain subsets of the tasks completes the project successfully, while carrying out other subsets does not. The probability of carrying out a task is higher when the agent in charge of it exerts effort, at a certain cost for that agent. A central authority, called the principal, attempts to incentivize agents to exert effort, but can only reward agents based on the success of the entire project. We model this domain as a normal form game, where the payoffs for each strategy profile are defined based on the different probabilities of carrying out each task and on the boolean function that defines which task subsets complete the project, and which do not. We view this boolean function as a simple coalitional game, and call this game the underlying coalitional game. We suggest the Price of Myopia (PoM) as a measure of the influence the model of rationality has on the minimal payments the principal has to make in order to motivate the agents in such a domain to exert effort. We consider the computational complexity of testing whether exerting effort is a dominant strategy for an agent, and of finding a reward strategy for this domain, using either a dominant strategy equilibrium or using iterated elimination of dominated strategies. We show these problems are generally #P‐hard, and that they are at least as computationally hard as calculating the Banzhaf power index in the underlying coalitional game. We also show that in a certain restricted domain, where the underlying coalitional game is a weighted voting game with certain properties, it is possible to solve all of the above problems in polynomial time. We give bounds on PoM in weighted voting effort games, and provide simulation results regarding PoM in another restricted class of effort games, namely effort games played over Series‐Parallel Graphs (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Models for Allocating Police Preventive Patrol Effort

This paper develops models that maximize the expected number of occasions per unit of time that a police patrol unit enters a street segment during the time that a crime is visible. Constraints are added that insure a minimum patrol coverage to all streets. The successive visits from street-to-street form a Markov chain. The solution that maximizes the objective function gives a stochastic decision rule which is used with Monte Carlo techniques to generate a random patrol schedule. The problem is posed with one car and several cars patrolling the same region.     

A Collaborative Effort to Improve University Engineering Instruction

This study focused on the instructional development of an assistant professor of environmental engineering in collaboration with science education and higher education faculty members. One semester of data was collected in the assistant professor's environmental engineering laboratory class as he endeavored to address his teaching goals. Data collection included pre and post interviews with the assistant professor, students, and program coordinator, and collection of course documents, such as the course syllabus and assignments. In addition, all of the classroom sessions were observed and videotaped, and a midsemester video stimulated‐recall interview was conducted. Results show the assistant professor made growth in the areas of questioning strategies, “think time” for students, increased class participation, and the implementation of a student‐designed field research project. Implications include that new professors can benefit from peer faculty support, and they and their students can benefit when the new professors recognize the complementary nature of research and teaching.     

需求依赖销售努力库存系统的随机比较

研究需求依赖销售努力库存系统中需求不确定性对系统最优订货量、利润和销售努力的影响.对一般需求模型给出期望利润关于订货量和努力水平为联合凹的充分条件,证明期望利润函数的超模性质.对加乘需求模型证明系统最优利润和最优努力水平都可由一类与需求分布有关的广义TTT变换来表示.通过引入定义在不同支撑分布集合上一阶、二阶和三阶随机占优,得到广义TTT变换之差与二阶和三阶随机占优之间的关系式,建立了比较库存系统最优利润或努力水平的理论基础.在一阶和二阶随机占优意义下对加乘需求模型得到比较系统最优利润和努力水平的充分条件或充分必要条件.进一步,证明存在一类需求分布当系统关键比(或市场价格)足够大时系统最优利润和努力水平随需求可变性的增加而增加.最后给出几个数值例子验证了研究结果.     

Effort associated with a class of random optimization methods

When differentiability is not assumed random procedures can be successfully used to estimate the extreme values of a given function. For a class of such algorithms we treat the problem of estimating the mean effort.Research partially supported by CNPq-Brazil.     

Measuring Stiffness

Many problems have been proposed for the testing and evaluation of mathematical software for the solution of the initial value problem for a system of ordinary differential equations. The stiffness of a given problem is of great significance for testing, but the concept is at best somewhat vague and the few quantitative measures of stiffness being used are of limited value. A relatively precise and quantitative way is proposed to answer the questions: How does the stiffness vary in the course of the integration of a given problem? Is a given problem A stiffer than a given problem B, and if so, by how much?     

需求与销售努力相关下混合渠道供应链协调研究

建立了由一个制造商和一个分销商组成的混合渠道供应链模型,考虑了产品需求量与分销商的销售努力相关时,混合渠道供应链中分销商的订货量、销售努力的契约协调问题。并通过改进的收入共享契约使混合渠道供应链达到了分销商订货量和销售努力的同时协调。并进行了算例分析,比较了传统渠道供应链及混合渠道供应链以及供应链成员的利润变化情况,分析结果表明在一定契约参数条件下,制造商增加电子渠道对供应链及供应链成员都是有益的。     

销售努力及双市场化期权下的三级供应链协调

本文针对需求随机且受到零售商销售努力影响的情况,研究了由制造商、分销商和零售商组成的三级供应链的协调问题。文章首先用双期权契约对三级供应链进行协调,即在制造商和分销商以及分销商和零售商之间都采用期权契约,发现在零售商独自承担努力成本的情况下仅通过双期权契约无法协调供应链。因此在双期权契约的基础上加入了努力成本共担契约,发现当期权价格满足某种线性关系以及零售商努力成本按特定比例分摊时,联合双期权契约和努力成本共担契约能顺利协调供应链。在此基础上,文章还引入了期权的市场化定价规则,研究了期权采用市场化定价规则对供应链协调产生的影响,研究表明,引入期权市场化定价规则增加了供应链协调需要满足的条件,降低了协调的可能性,且协调状态下的期权价格受到市场因素如利率、价格波动率等的影响。最后,文章给出了期权市场化定价规则下供应链协调的条件以及参数变化对协调的影响。     

奖惩机制下考虑销售努力的闭环供应链协调

以一个制造商和一个零售商组成的闭环供应链为研究对象,考虑在政府的奖惩机制下需求同时受销售价格和销售努力影响的供应链协调问题.首先,在集中决策下,研究了供应链系统的最优决策,并给出了均衡解存在的条件和奖惩力度所满足的范围;在分散决策下,重点分析了奖惩力度以及销售努力对供应链双方决策的影响.其次,使用特许经营契约能够使供应链达到协调.最后,给出了数值算例和仿真分析.     

生鲜供应链中保鲜努力投入及订货定价研究

结合生鲜损耗严重和过度保鲜双重背景,本文在区分保质期和实际有效供货时长的基础上,比较研究了由单一零售商与单一供应商构成的二级生鲜供应链中,两个主体合作与否及主导主体变化对供应链保鲜努力水平和定价的影响机制。研究表明,集中式供应链中,保鲜努力投入随新鲜度(价格)敏感性增强(减弱)而增加,而随有效供货时长增加呈倒U型;供应链的总利润也随新鲜度(价格)敏感性增强(减弱)或有效供货时长上升而增加。分散式供应链中,随新鲜度的敏感性增强,保鲜努力和总利润增加;随价格的敏感性增强,保鲜努力增加而总利润减小;而随有效供货时长上升,保鲜努力先增大后减小,总利润增加。分散式供应链存有搭便车的机会,但因有效供货时长占保质期比例不同,自身投入保鲜努力可能比搭便车更有利。