Question selection responding to information on customers from heterogeneous populations to select offers that maximize expected profit

The advent of Internet broking pages allows customers to ‘apply’ to a number of different companies at one time, leading to multiple offers made to a customer. The saturated condition of the personal financial products has led to falling ‘take’ rates. Financial institutions are trying to increase the ‘take’ rates of their personal financial products. Applicants for credit will have to provide information for risk assessment, which can be used to assess the probability of a customer accepting an offer. Interactive channels such as the Internet and telephone allow questions that are asked to depend on previous answers. The questions selected need to provide information to assess the probability of acceptance of a particular variant of financial product. In this paper, we investigate a model to predict the best offer to extend next to a customer based on the response for the questions, as well as the question selection itself.     

Hemivariational inequality approach to constrained problems for star-shaped admissible sets

The hemivariational inequality approach is applied to establish the existence of solutions to a large class of nonconvex constrained problems in a reflexive Banach space. The admissible sets are supposed to be star-shaped with respect to a ball. Due to a discontinuity property of the Clarke directional differential related to the corresponding distance functions, the proposed method permits one to attain the solution without passing to zero with the penalization parameter. Some applications to nonconvex constrained variational problems illustrate the theory.     

Modelling ship operational reliability over a mission under regular inspections

A ship is required to operate for a fixed mission period. Should a critical item of equipment fail at sea, the ship is subject to a costly event with potentially high risk to ship and crew. Given warning of a pending defect, the ship can try to return to port under its own power and thus attempt to avoid an at sea failure. Defects which lead to a failure are detected by inspection, and the task is to select the appropriate frequency of inspection to balance the number of occasions that a ship fails at sea and the number of preventive inspection based returns to port during a mission to correct a defect. The modelling entails using the delay time concept. Expressions are established for the expected number of preventive and failure returns over a mission, and an example given of a cost based balance to select an optimal inspection period. Although addressing ship reliability, the model has relevance to the mission reliability of any repairable equipment with remote main repair facilities.     

快递企业航空货运网络的构建

快递业竞争激烈,构建高效合理的航空货运网络是快递企业提高竞争力的重要手段。“枢纽—辐射”式航空货运网络是整合航空快递资源、提高航空快递资源利用效率、提高快递企业竞争力的有效模式。本文以降低航空快递网络成本、加快航空快递处理时间为目标,从航空快递网络枢纽的选取、指派关系的确定、枢纽个数的选择三个方面研究了航空快递网络模型建立问题,选用遗传算法求解不同枢纽个数下航空快递网络的运输成本,并据此进行枢纽的选取,运用重力模型法进行指派关系的确定,在此基础上运用超效率DEA模型确定枢纽个数。接着,以包含17个节点的顺丰航空快递网络的规划为例,对本文所提出的模型和算法进行了验证,验证结果证实了模型的合理性。本文的研究为快递企业构建航空货运网络提供了科学实用的方法,该方法的使用可以降低航空货运成本,提高效率,从而提高快递企业的竞争力。     

The Design of Routes,Service Frequencies,and Schedules for a Municipal Bus Undertaking: A Case Study

This paper describes a case study of the reorganization of a municipal bus undertaking. The terms of reference were to consider reorganizing the route structure, to advise on frequencies to operate on the chosen routes, to compile timetables, and to design bus schedules so that the recommended system could be implemented with the minimum number of active buses. Theoretically, all of these variables can interact and one global model should be used to optimize the entire system simultaneously. In practice, the components of this problem had to be uncoupled and tackled separately. An heuristic model designed to provide a "good" route network was developed. Service frequencies were allocated to routes so that a measure of service to passengers was maximized. Bus timetables were compiled using conventional methods and a linear programming model used to assign individual buses to journeys. A new scheme based on the recommendations of the study has been implemented. It is expected that it will reduce the annual operating deficit by [pound]35,000 without appreciably decreasing the overall level of service offered.     

Algebra at the Turn of the Century

At the turn of the century it seems to be appropriate to pause and to try to envision future possibilities. We want to discuss the prospects of algebra. To look into the future requires an understanding of the past, the longstanding aims, but also the difficulties which have been encountered. We are going to review part of the history of algebra in order to outline its present state. It is important to notice the missed opportunities and to analyze the reasons. To recognize the present possibilities requires to be aware of the tools which now are available and which may not yet have been used in an optimal way. We urge the reader to focus attention to the need for algebraic considerations in all parts of mathematics but also outside of mathematics. Of course, a view back should also strengthen the interest in classical open problems which now may be feasible to attack.This is a the written version of a lecture presented at the National Conference on Algebra VII, held in Beijing Normal University, October 1999.     

A multivariate adaptive regression splines cutting plane approach for solving a two-stage stochastic programming fleet assignment model

The fleet assignment model assigns a fleet of aircraft types to the scheduled flight legs in an airline timetable published six to twelve weeks prior to the departure of the aircraft. The objective is to maximize profit. While costs associated with assigning a particular fleet type to a leg are easy to estimate, the revenues are based upon demand, which is realized close to departure. The uncertainty in demand makes it challenging to assign the right type of aircraft to each flight leg based on forecasts taken six to twelve weeks prior to departure. Therefore, in this paper, a two-stage stochastic programming framework has been developed to model the uncertainty in demand, along with the Boeing concept of demand driven dispatch to reallocate aircraft closer to the departure of the aircraft. Traditionally, two-stage stochastic programming problems are solved using the L-shaped method. Due to the slow convergence of the L-shaped method, a novel multivariate adaptive regression splines cutting plane method has been developed. The results obtained from our approach are compared to that of the L-shaped method, and the value of demand-driven dispatch is estimated.     

Singularity of the “swallow-tail” type and the glass-glass transition in a system of collapsing hard spheres

In the mode-coupling approximation, we consider the transition to the glass state in a system of collapsing hard spheres (a system with the hard-core potential to which a repulsive step is added). We propose an approximation for the structure factor of the system, which we use to construct the phase diagram of the transition to the glass state. We show that there exists a maximum on the liquid-glass curve corresponding to the reentrant transition to the glass state in the system. In the framework of the proposed model, we consider bifurcations of solutions of the equations describing the transition to the glass state and show that there exist bifurcations of the “swallow-tail” type corresponding to the glass-glass transition.     

Rhombus filtrations and Rauzy algebras

Peach introduced rhombal algebras associated to quivers given by tilings of the plane by rhombi. We develop general techniques to analyze rhombal algebras, including a filtration by what we call rhombus modules. We introduce a way to relate the infinite-dimensional rhombal algebra corresponding to a complete tiling of the plane to finite-dimensional algebras corresponding to finite portions of the tiling. Throughout, we apply our general techniques to the special case of the Rauzy tiling, which is built in stages reflecting an underlying self-similarity. Exploiting this self-similar structure allows us to uncover interesting features of the associated finite-dimensional algebras, including some of the tree classes in the stable Auslander-Reiten quiver.     

Superized Troesch complexes and cohomology for strict polynomial superfunctors

We adapt a construction due to Troesch to the category of strict polynomial superfunctors in order to construct complexes of injective objects whose cohomology is isomorphic to Frobenius twists of the (super)symmetric power functors. We apply these complexes to construct injective resolutions of the even and odd Frobenius twist functors, to investigate the structure of the Yoneda algebra of the Frobenius twist functor, and to compute other extension groups between strict polynomial superfunctors. By an equivalence of categories, this also provides cohomology calculations in the category of left modules over Schur superalgebras.     

The utility of returns to scale in DEA programming: An analysis of Michigan rural hospitals

In 1984, Banker, Charnes, and Cooper introduced the capability of using data envelopment analysis to assess increasing, decreasing, or constant returns to scale. This analysis would appear to make an important contribution to the health care field because of the regulatory environment within which the industry exists and the competition among hospitals for additional services and capacity. In many states, hospitals must submit a “certificate of need” to prove eligibility to add capacity or services. Agency administrators at the state level should analyze each hospital's production performance to determine the effectiveness of resource utilization. Residents of a state where hospitals are regulated need to know the effectiveness of agencies in allowing resources to be properly allocated to hospitals. Returns to scale analysis can help provide answers to these concerns. We examine Michigan rural hospitals and propose a simple, yet logical procedure for evaluating returns to scale for technically inefficient hospitals.     

Asymptotic behavior of continuous stochastic games

Summary The aim of this paper is to analyze the asymptotic behavior of the value functions of a continuous stochastic game as the number of stages grows to infinity or the discount factor approaches 1. After the setup of the problem we prove that, in both cases, the extrema of the value functions converge to the same limits. The convergence of the value functions is then obtained from the unicity of the solution of a functional problem and it is thus possible to design hypotheses that assure the convergence to a constant. This allows to assign a value to an undiscounted infinite-stage stochastic game in several senses and to show that optimal strategies are available for both players. Furthermore the boundedness of the remainders of the value function after removing the principal terms is analyzed, with appropriate hypotheses, and related to the existence of solutions of a Howard's type functional equation. This allows to show that for an infinite-stage undiscounted stochastic game optimal stationary strategies exist at least if this functional equation has some solution.     

Mathematical programming modeling of the Response Time Variability Problem

The Response Time Variability Problem (RTVP) is a scheduling problem that has recently been defined in the literature. The RTVP has a broad range of real-life applications from manufacturing to services and information technology. A previous study developed a position exchange heuristic to apply to initial sequences for the RTVP, and a MILP (Mixed Integer Linear Programming) to obtain optimal solutions with a practical limit of 25 units to be scheduled. This paper aims to improve the best mathematical programming model developed thus far in order to solve larger instances up to 40 units to optimality. The contribution of this paper is 4-fold: (i) larger instances can be solved to optimality by the off the shelf standard software; (ii) the new optimal solutions of the RTVP can be used to compare the results of heuristic procedures; (iii) the importance of modeling is demonstrated, as well as the huge impact that reformulation, redundant constraints and the elimination of symmetries have on the efficiency of MILPs is clearly established; finally (iv) a challenge to develop a customized optimization algorithm to rival the MILP solution efficiency for the RTVP is put forward.     

财政支农专项转移支付制度制定:矫正工商资本下乡异化行为

制定怎样的财政支农专项转移支付制度才能正确引导与矫正工商资本下乡行为？为了探索出能够有效矫正工商资本下乡异化行为的财政制度,文章采用动态博弈的方法剖析工商资本下乡企业的行为。经深入研究发现,国家财政支付制度的实施成效取决于分配制度(“勉励”还是“嘉奖”)及工商资本下乡企业的发展阶段。随着企业的逐渐壮大,在政策机制中融入“嘉奖”制度较事后的“勉励”制度,对于发展农业提升企业利益与反哺农民改善民生的两种行为,可更好的引导工商资本下乡正确与合理的分配资金。     

The relevance of DEA benchmarking information and the Least-Distance Measure

Efficiency analysis is performed not only to estimate the current level of efficiency, but also to provide information on how to remove inefficiency, that is, to obtain benchmarking information. Data Envelopment Analysis (DEA) was developed in order to satisfy both objectives and the strength of its benchmarking analysis gives DEA a unique advantage over other methodologies of efficiency analysis. This study proposes the use of the Least-Distance Measure in order to obtain the shortest projection from the evaluated Decision Making Unit (DMU) to the strongly efficient production frontier, thus allowing an inefficient DMU to find the easiest way to improve its efficiency. In addition to producing reasonable benchmarking information, the proposed model provides efficiency values which satisfy the general requirements that every well-defined efficiency measure should meet.     

煤层注水非线性渗流方程的解析解及应用

本文运用流体力学,多孔介质流体动力学,渗流理论等理论知识,结合实验室和现场试验,从理论上对煤层注水预湿煤体机理进行了研究.分析了煤层注水过程,建立起了煤层注水的数学模型;对煤层注水的边界条件进行了描述.由于描述煤层注水的方程组为非线性的,为简化它们,利用了因次分析理论,引入了注水压力,渗透速度,煤水份增加量等无因次量.之后讨论了其解析和近似解.另外:结合实际煤层注水的科研项目,说明了该理论指导煤层注水及设计的作用和重要性.     

Effects of imprecise weighting in hierarchical preference programming

Preference programming is a general term for multi-criteria decision analytical approaches allowing incomplete preference information. In the PAIRS method, interval judgments are assigned to weight ratios between attributes to model imprecision in multi-attribute value trees. This paper studies the effects of a hierarchical model structure on the overall imprecision, as the form of the hierarchy also affects the form of imprecision that can be assigned to the model. The aim is to find out good procedural practices for reducing overall imprecision descending inherently from the model structure. The study provides simulation results about the ability of various weighting schemes to identify dominated alternatives, which are discussed with respect to other issues related to the weighting process. According to the results, a hierarchical model is structurally somewhat more unable to identify dominances than a corresponding nonhierarchical model, but its cognitive advantages often cancel out this. The results also suggest paying reasonable attention to the precision of the lower level judgments and to identifying possible correlations between the criteria.     

Quasiconformal extensions to space of Weierstrass-Enneper lifts

The Ahlfors-Weill extension of a conformal mapping of the disk is generalized to the Weierstrass-Enneper lift of a harmonic mapping of the disk to a minimal surface, producing homeomorphic and quasiconformal extensions to space. The extension is defined through the family of best Möbius approximations to the lift applied to a bundle of euclidean circles orthogonal to the disk. Extension of the planar harmonic map is also obtained subject to additional assumptions on the dilatation. The hypotheses involve bounds on a generalized Schwarzian derivative for harmonic mappings in terms of the hyperbolic metric of the disk and the Gaussian curvature of the minimal surface. Hyperbolic convexity plays a crucial role.     

Misclassification rates,critical values and size of the design in measurement systems capability studies

Measurement systems capability analysis aims to test if the variability of a measurement system is small relative to the variability of a monitored process. At present some open questions are related both to the interpretation of the critical values of the indices typically used by practitioners to assess the capability of a gauge and to the choice of the size of the experimental design to test the repeatability and the reproducibility of the measurement process. In this paper, starting from the misclassification rates of a measurement system, we present a solution to these issues. Copyright © 2009 John Wiley & Sons, Ltd.     

Local limit theorems for multiplicative free convolutions

This paper describes the quality of convergence to an infinitely divisible law relative to free multiplicative convolution. We show that convergence in distribution for products of identically distributed and infinitesimal free random variables implies superconvergence of their probability densities to the density of the limit law. Superconvergence to the marginal law of free multiplicative Brownian motion at a specified time is also studied. In the unitary case, the superconvergence to free Brownian motion and that to the Haar measure are shown to be uniform over the entire unit circle, implying further a free entropic limit theorem and a universality result for unitary free Lévy processes. Finally, the method of proofs on the positive half-line gives rise to a new multiplicative Boolean to free Bercovici–Pata bijection.