Choosing the Operational Research Programme for B.I.S.R.A

This paper examines some important problems in the evaluation and selection of research projects, with particular reference to operational research projects in a central industry research organization. A method for project evaluation is suggested which provides data suitable for use in a powerful and flexible formal procedure for project selection. In evaluating a project, the assessment of resource requirements is based on a probabilistic network plan of the project, and the estimates of benefits are derived from the marginal effects on the industry of performing or not performing the project, using discounted cash flow techniques. The procedure for project selection chooses not only the projects to be undertaken, but also the team sizes that should be used. A wide variety of constraints can be imposed on the system to reflect different aspects of management policy or other special factors. The procedures described have been implemented, and have proved well worth while.     

Kronecker representation and decompositional analysis of closed queueing networks with phase-type service distributions and arbitrary buffer sizes

Two approximative fixed-point iterative methods based on decomposition for closed queueing networks with Coxian service distributions and arbitrary buffer sizes are extended to include phase-type service distributions. The irreducible Markov chain associated with each subnetwork in the respective decompositions is represented hierarchically using Kronecker products. The two methods are implemented in a software tool capable of computing the steady-state probability vector of each subnetwork by a multilevel method at each fixed-point iteration and are compared with other methods for accuracy and efficiency. Numerical results indicate that there is a niche filled by the two approximative methods. The authors thank Jean-Michel Fourneau for pointing out Marie’s method and Brouwer’s fixed-point theorem. The first author gratefully acknowledges grant TüBA-GEBİP from the Turkish Academy of Sciences.     

TWO NOVEL GRADIENT METHODS WITH OPTIMAL STEP SIZES

In this work we introduce two new Barzilai and Borwein-like steps sizes for the classical gradient method for strictly convex quadratic optimization problems.The proposed step sizes employ second-order information in order to obtain faster gradient-type methods.Both step sizes are derived from two unconstrained optimization models that involve approximate information of the Hessian of the objective function.A convergence analysis of the proposed algorithm is provided.Some numerical experiments are performed in order to compare the efficiency and effectiveness of the proposed methods with similar methods in the literature.Experimentally,it is observed that our proposals accelerate the gradient method at nearly no extra computational cost,which makes our proposal a good alternative to solve large-scale problems.     

基于工期-成本综合效用最大的关键链项目缓冲确定

为提高关键链中工期和成本的综合效用,研究一种基于关键链工期和成本进行双目标优化的缓冲确定方法。首先,该方法考虑项目不同工序间工期和成本之间的关系,并基于工期和成本的风险暴露度确定权重,解决不同工序间工期和成本偏好难以量化的问题;其次,根据权重多效用函数对工期和成本进行归一化处理,并确定综合效用最大情况下不同工序的最佳工期;最后基于尾部集中法确定项目缓冲。通过蒙特卡洛模拟实验,将此方法提取缓冲后的项目实际综合效用与传统方法进行比较。比较结果显示,该方法极大地提高项目中工期和成本的综合效用,并且对项目工期和成本均形成更有效的保护。     

基于系统双重风险共担的多项目鼓缓冲设置研究

为了提高关键链多项目缓冲管理的效率,首次提出了一种基于多项目双重风险共担的鼓缓冲设置方法。新方法从系统角度分析了多项目不同层级的风险共担作用,以同时落在在子项目关键链和多项目系统关键链上的系统关键活动工期占比为切入点对缓冲进行分层管理,抽取部分项目缓冲集中到系统层面,同时综合考虑风险独立因子以及鼓活动有效产出影响指数对鼓缓冲进行了定量设置。仿真结果表明,本文方法在多项目按时完工率、项目缓冲平均消耗率、系统关键链上鼓活动平均延误百分比、多项目系统总工期和成本这几个绩效方面的表现更优,提高了多项目系统的风险应对能力。     

Determination of critical chain project buffer based on information flow interactions

It has been well accepted in the literature that co-dependency between project activity durations is caused by resource tightness and network complexity. However, we show that information flow interaction between activities is the key factor for it. Based on whether there exist spliced relationships between activities, we introduce the concept of rework safety time. We propose a method to compute the rework safety time using the information output and input time factors, rework probability matrix, and rework impact matrix. We achieve the optimization of the critical chain sequencing via the design structure matrix so that the dependency between activities is reduced. The project buffer is then determined by the tail concentration method based on the optimized chain. The empirical results show that, as opposed to the traditional RSEM method, our approach improves the project buffer consumption rate, shortens project duration, reduces project cost, and increases project on-time completion rate.     

基于容错机制的关键链项目缓冲差别监控研究

关键链项目缓冲监控绩效受活动自身和活动执行主体特性的双重影响,项目经理应根据不同执行主体对活动进行差别监控,而现有缓冲监控研究未充分考虑活动执行主体异质性。首先,结合网络复杂度和风险感知等活动自身因素以及综合信任度等执行主体层面因素对缓冲进行分配;其次,引入容错机制对不同活动触发点进行差别设置,并将缓冲监控分为信任型和监督型两类监控模式;最后,根据活动缓冲消耗对不同活动进行差别动态监控。蒙特卡洛模拟结果表明,本文方法能够有效降低错误预警,保证项目按计划执行并实现对项目的综合优化。     

A comparison of the String Gradient Weighted Moving Finite Element method and a Parabolic Moving Mesh Partial Differential Equation method for solutions of partial differential equations

We compare numerical experiments from the String Gradient Weighted Moving Finite Element method and a Parabolic Moving Mesh Partial Differential Equation method, applied to three benchmark problems based on two different partial differential equations. Both methods are described in detail and we highlight some strengths and weaknesses of each method via the numerical comparisons. The two equations used in the benchmark problems are the viscous Burgers’ equation and the porous medium equation, both in one dimension. Simulations are made for the two methods for: a) a travelling wave solution for the viscous Burgers’ equation, b) the Barenblatt selfsimilar analytical solution of the porous medium equation, and c) a waiting-time solution for the porous medium equation. Simulations are carried out for varying mesh sizes, and the numerical solutions are compared by computing errors in two ways. In the case of an analytic solution being available, the errors in the numerical solutions are computed directly from the analytic solution. In the case of no availability of an analytic solution, an approximation to the error is computed using a very fine mesh numerical solution as the reference solution.     

A Chart for Evaluating Product Research and Development Projects

A method of evaluating research and development projects is described. The method is based on the use of an evaluation chart. The main purpose of the chart is to calculate a project score which is a measure of a selected evaluation criterion. A method of constructing a chart is illustrated using a project index as the evaluation criterion. The chart contains a list of twelve questions, the answers to which are assumed to be the main determinants of the variables in the formula of the index. Each question is followed by a set of answers from which a choice is to be made, and underneath each answer is a numerical score. The numerical scores are logarithmic functions of the answers to which they relate, and when added together give a project score which is a logarithmic function of the index. Various methods of using the chart, and a suggested evaluation procedure, are also described.     

A combined splitting—cross entropy method for rare-event probability estimation of queueing networks

We present a fast algorithm for the efficient estimation of rare-event (buffer overflow) probabilities in queueing networks. Our algorithm presents a combined version of two well known methods: the splitting and the cross-entropy (CE) method. We call the new method SPLITCE. In this method, the optimal change of measure (importance sampling) is determined adaptively by using the CE method. Simulation results for a single queue and queueing networks of the ATM-type are presented. Our numerical results demonstrate higher efficiency of the proposed method as compared to the original splitting and CE methods. In particular, for a single server queue example we demonstrate numerically that both the splitting and the SPLITCE methods can handle our buffer overflow example problems with both light and heavy tails efficiently. Further research must show the full potential of the proposed method.     

Probabilistic Networks and R & D Portfolio Selection

Mathematical programming methods have been suggested and used as an aid to R & D project portfolio selection. One of the main criticisms of the use of such models is that the stochastic nature of the problem has been largely ignored. This paper presents a method which takes into account the stochastic nature of resource requirements and project benefits, using a combination of probabilistic networks, simulation and mathematical programming. A case study based on data from an industrial R & D laboratory is presented and compared with the use of expected value methods. The results of the study indicate that in this particular case the deterministic linear programming solution is robust.     

EPC项目关键链缓冲区设置模型研究

为有效解决EPC项目关键链缓冲区时间估计不够准确而影响项目进度计划编制与控制的问题,在分析现有关键链缓冲区设置方面研究成果及其存在不足基础上,首先采用探索性因子分析法,通过文献归纳、问卷设计与数据采集、数据处理与分析,进行了EPC项目缓冲区设置影响因素发掘与提取,提取出了21项EPC项目缓冲区设置关键影响因素;其次建立了基于影响因素权重及其对不同工序影响程度的工序综合权重计算模型,同时引入工序位置权重及工序作业时间风险弹性系数,构建了项目缓冲区及输入缓冲区定量确定模型;最后以某EPC项目为例进行了应用研究,论证了关键链缓冲区设置模型的准确性与可操作性,为EPC项目缓冲区设置提供了借鉴。     

Consistent multiple testing for change points

The change point problem for independent normal means is considered as a multiple testing problem. Two stepwise methods are considered. Namely, the binary segmentation method of Vostrikova (1981) [7] and the maximum residual down method of Cohen et al. (2009) [5]. Both of these methods are shown to be consistent. Consistent here means that as sample sizes tend to infinity, the probability of making an error (false rejection or false acceptance) tends to zero.     

Forcing Linearity on Greedy Codes

Described in this paper are two different methods of forcing greedy codesto be linear over arbitrary finite fields. Both methods are generalizationsof the binary B-greedy codes as well as the triangular greedycodes over arbitrary fields. One method generalizes to arbitrary orderingsover arbitrary finite fields while the other method generalizes theB-greedy codes to linear codes over arbitrary finite fields.Examples of the first method are computed for triangular greedy codes. Theseexamples give codes similar to triangular codes from B-orderings.Both methods are shown to be substantially different.     

Dynamic monitoring and control of software project effort based on an effort buffer

The improvement to the monitoring and control efficiency of software project effort is a challenge for project management research. We propose to overcome this challenge through the use of a model for the buffer determination and monitoring of software project effort. This software project effort buffer was originally determined on the basis of a risk management factor analysis with total consideration for project managers’ risk preference. The effort buffer was next allocated to different stages according to the buffer allocation cardinal. An effort deviation monitoring and control model was then established based on the grey prediction model, including the establishment of a deviation monitoring and control model, a simulation test of the accuracy and the deviation prediction algorithm flow chart. The method system was eventually applied to an actual project and compared with the actual project data. The results show that the relative error test accuracy of the proposed model is qualified according to the test standard of the grey model, signifying that it could be used for the prediction of effort deviation and decision-making. The proposed model could use the dynamic control system to monitor and control software project effort in an effective manner.     

B-splines methods with redefined basis functions for solving fourth order parabolic partial differential equations

In this work, we discuss two methods for solving a fourth order parabolic partial differential equation. In Method-I, we decompose the given equation into a system of second order equations and solve them by using cubic B-spline method with redefined basis functions. In Method-II, the equation is solved directly by applying quintic B-spline method with redefined basis functions. Stability of these methods have been discussed. Both methods are unconditionally stable. These methods are tested on four examples. The computed results are compared wherever possible with those already available in literature. We have developed Method-I for fourth order non homogeneous parabolic partial differential equation from which we can obtain displacement and bending moment both simultaneously, while Method-II gives only displacement. The results show that the derived methods are easily implemented and approximate the exact solution very well.     

On the choice of step size in subgradient optimization

This paper recommends some procedures for the selection of step sizes in the context of subgradient optimization. The first of these procedures is developed in detail in this study and is a theoretically convergent scheme. This method has two phases, the first phase is designed to accelerate the solution procedure towards an optimal solution, while the second phase helps to close in on an optimal solution. A second technique recommended is a simple-minded scheme which, although not theoretically convergent, seems to be computationally very efficient. These two methods are shown to compare favorably with Held, Wolfe and Crowder's scheme for prescribing step sizes. We also suggest some modifications of the latter scheme to make it computationally more efficient.     

Second-order,loosely coupled methods for fluid-poroelastic material interaction

This work focuses on modeling the interaction between an incompressible, viscous fluid and a poroviscoelastic material. The fluid flow is described using the time-dependent Stokes equations, and the poroelastic material using the Biot model. The viscoelasticity is incorporated in the equations using a linear Kelvin–Voigt model. We introduce two novel, noniterative, partitioned numerical schemes for the coupled problem. The first method uses the second-order backward differentiation formula (BDF2) for implicit integration, while treating the interface terms explicitly using a second-order extrapolation formula. The second method is the Crank–Nicolson and Leap-Frog (CNLF) method, where the Crank–Nicolson method is used to implicitly advance the solution in time, while the coupling terms are explicitly approximated by the Leap-Frog integration. We show that the BDF2 method is unconditionally stable and uniformly stable in time, while the CNLF method is stable under a CFL condition. Both schemes are validated using numerical simulations. Second-order convergence in time is observed for both methods. Simulations over a longer period of time show that the errors in the solution remain bounded. Cases when the structure is poroviscoelastic and poroelastic are included in numerical examples.     

Managing Cost Overrun Risk in Project Funding Allocation

This paper discusses decision making of project funding allocation under uncertain project costs. Because project costs are uncertain and funding allocations may not necessarily match the costs required, each project is inherently subject to a cost overrun risk (COR). In this paper, a model is proposed in which project cost is treated as a factor with a probability density function. The decision maker then allocates the total funding to the projects while minimizing a weighted sum of mean and variance of the COR of the project portfolio. Some properties of project COR are derived and interpreted. Optimal funding allocation, in relationship to factors such as various project sizes and riskiness, project interdependency, and the decision maker’s risk preference, is analyzed. The proposed funding allocation model can be integrated with project selection decision-making and provides a basis for more effective project control.     

Tests of Parameters of Several Gamma Distributions with Inequality Restrictions

Gamma distribution is one of the most used methods of modeling lifetime data. However, testing homogeneity of parameters of m 3 gamma distributions against order restrictions is almost non-existent in the current literature. We propose two methods to this end: one uses quadratic forms involving ratios of cumulants as test statistic and the other is a stepwise procedure which uses Fisher's method of combining p-values when shape parameters are equal but unknown. Both procedures allow use of arbitrary sample sizes of m populations. Test of the inequality restrictions as a null hypothesis against unrestricted alternatives is also considered. A Monte Carlo study of power at various alternatives shows that both methods are competitive when they are applicable.