Evaluating the water sector in Italy through a two stage method using the conditional robust nonparametric frontier and multivariate adaptive regression splines

The aim of this paper is to assess the efficiency of the integrated water service in Italy in recent years, through a robust and flexible methodology. This paper, from a methodological point of view, enhances a ”two stage” method, based on ideas suggested by Florens and Simar (2005), which estimates the efficiency frontier through conditional robust models and bypasses, at the same time, the choice of a specific functional form in the second stage; the MARS (Multivariate Adaptive Regression splines) method, in fact, provides for approximate production function using linear splines without any assumption of a functional form.Applying this specific two stage method, despite poor assumptions of the production function form, we provide an estimate for the Italian water companies; we have found spatial and dimensional patterns, especially in metropolitan vs. low density areas.     

Electronic service matching: Failure of incentive compatibility in Vickrey auctions

We consider pricing schemes for matching customers and providers on double-sided markets for electronic services. While existing second-best solutions are incentive compatible, the associated payment functions are difficult to implement in real-world settings. Based on the Vickrey–Clarke–Groves (VCG) and the $k$-pricing mechanism, we propose two straightforward payment schemes that offer a practical alternative to the second-best solution. Our experiments provide evidence that the VCG payments fail to implement incentive compatibility. This failure is due to the interdependency of the participants’ utilities.     

Directional distances and their robust versions: Computational and testing issues

Directional distance functions provide very flexible tools for investigating the performance of Decision Making Units (DMUs). Their flexibility relies on their ability to handle undesirable outputs and to account for non-discretionary inputs and/or outputs by fixing zero values in some elements of the directional vector.  and  indicate how the statistical properties of Farrell–Debreu type of radial efficiency measures can be transferred to directional distances. Moreover, robust versions of these distances are also available, for conditional and unconditional measures. B?din, Daraio, and Simar (2012) have shown how conditional radial distances are useful to investigate the effect of environmental factors on the production process. In this paper we develop the operational aspects for computing conditional and unconditional directional distances and their robust versions, in particular when some of the elements of the directional vector are fixed at zero. After that, we show how the approach of B?din et al. (2012) can be adapted in a directional distance framework, including bandwidth selection and two-stage regression of conditional efficiency scores. Finally, we suggest a procedure, based on bootstrap techniques, for testing the significance of environmental factors on directional efficiency scores. The procedure is illustrated through simulated and real data.     

A robust nonparametric approach to evaluate and explain the performance of mutual funds

The topic of the measurement of mutual funds’ performance is receiving an increasing interest both from an applied and a theoretical perspective. Beside the traditional financial literature, a growing body of studies has started to apply the tools of frontier analysis for benchmarking comparisons in portfolio analysis. Our paper contributes to this literature proposing a robust nonparametric approach for analysing mutual funds. It is based on the concept of order-m frontier [Cazals, C., Florens, J.P., Simar, L., 2002. Nonparametric frontier estimation: A robust approach. Journal of Econometrics 106, 1–25] and on a probabilistic approach [Daraio, C., Simar, L., 2005. Introducing environmental variables in nonparametric frontier models: A probabilistic approach. Journal of Productivity Analysis 24 (1), 93–121] to find out the factors explaining mutual funds’ performance. Within this framework, a decomposition of conditional efficiency is proposed, and its usefulness for economic interpretation analysed. Our approach is illustrated by using US mutual funds data, grouped for category by objective. Economies of scale, slacks and market risks are investigated. A comparison of traditional, nonparametric and robust performance measures is also offered.     

Incentive schemes for resolving Parkinson’s Law in project management

Project management is a business process that supports about 30% of the world’s economic activity. Yet projects routinely suffer from the influence of Parkinson’s Law. This behavioural phenomenon routinely results in failure to deliver work that is completed early before its assigned deadline. As a consequence, the late completion of other work is not offset, and overall project performance suffers. Hence, project success rates below 40% are widely reported.Our work uses mechanism design within non-cooperative game theory. A particular issue in the design process is to eliminate the possibility that a project worker with multiple dependent tasks can improve their incentive payment by falsely reporting some of their task completion times. From our review of the academic and business literature of project management, no incentive scheme used in practice accomplishes this.Our results include the design of incentive schemes that eliminate or mitigate Parkinson’s Law. These schemes apply to projects designed under either traditional Critical Path Method (CPM) planning or modern Critical Chain Project Management (CCPM) planning, and are also invulnerable to group strategy. A large-scale computational study validates the resulting benefit to project performance as substantial and also robust across different project characteristics. We also provide what is apparently the first analytical comparison between traditional CPM and modern CCPM planning systems.The incentive schemes we propose are simple and easily implementable. We recognize that performance incentives are structured differently by each organization, but our work provides a flexible basis from which various practical schemes can be designed.     

Nonconforming Mixed Finite Element Method for Time-Dependent Maxwell's Equations with ABC

In this paper, a nonconforming mixed finite element method (FEM) is presented to approximate time-dependent Maxwell's equations in a three-dimensional bounded domain with absorbing boundary conditions (ABC). By employing traditional variational formula, instead of adding penalty terms, we show that the discrete scheme is robust. Meanwhile, with the help of the element's typical properties and derivative transfer skills, the convergence analysis and error estimates for semi-discrete and backward Euler fully-discrete schemes are given, respectively. Numerical tests show the validity of the proposed method.     

Optimal bandwidth selection for conditional efficiency measures: A data-driven approach

In productivity analysis an important issue is to detect how external (environmental) factors, exogenous to the production process and not under the control of the producer, might influence the production process and the resulting efficiency of the firms. Most of the traditional approaches proposed in the literature have serious drawbacks. An alternative approach is to describe the production process as being conditioned by a given value of the environmental variables (Cazals, C., Florens, J.P., Simar, L., 2002. Nonparametric Frontier estimation: A robust approach. Journal of Econometrics 106, 1–25; Daraio, C., Simar, L., 2005. Introducing environmental variables in nonparametric Frontier models: A probabilistic approach. Journal of Productivity Analysis 24(1), 93–121). This defines conditional efficiency measures where the production set in the input ×$\times$ output space may depend on the value of the external variables. The statistical properties of nonparametric estimators of these conditional measures are now established (Jeong, S.O., Park, B.U., Simar, L., 2008. Nonparametric conditional efficiency measures: Asymptotic properties. Annals of Operations Research doi: 10.1007/s10479-008-0359-5). These involve the estimation of a nonstandard conditional distribution function which requires the specification of a smoothing parameter (a bandwidth). So far, only the asymptotic optimal order of this bandwidth has been established. This is of little interest for the practitioner. In this paper we fill this gap and we propose a data-driven technique for selecting this parameter in practice. The approach, based on a Least Squares Cross Validation procedure (LSCV), provides an optimal bandwidth that minimizes an appropriate (weighted) integrated Squared Error (ISE). The method is carefully described and exemplified with some simulated data with univariate and multivariate environmental factors. An application on real data (performances of Mutual Funds) illustrates how this new optimal method of bandwidth selection works in practice.     

The unconditional stability and mass‐preserving S‐DDM scheme for solving parabolic equations in three dimensions

In this paper, the unconditional stability and mass‐preserving splitting domain decomposition method (S‐DDM) for solving three‐dimensional parabolic equations is analyzed. At each time step level, three steps (x‐direction, y‐direction, and z‐direction) are proposed to compute the solutions on each sub‐domains. The interface fluxes are first predicted by the semi‐implicit flux schemes. Second, the interior solutions and fluxes are computed by the splitting implicit solution and flux coupled schemes. Last, we recompute the interface fluxes by the explicit schemes. Due to the introduced z‐directional splitting and domain decomposition, the analysis of stability and convergence is scarcely evident and quite difficult. By some mathematical technique and auxiliary lemmas, we prove strictly our scheme meet unconditional stability and give the error estimates in L²‐norm. Numerical experiments are presented to illustrate the theoretical analysis.     

Analysis of supply chains with quantity based fixed incentives

This paper examines the use of quantity based fixed incentives to coordinate inventory decisions in a decentralized supply chain. We consider a two stage supply chain of autonomous supplier and distributor and prove that the optimal ordering policy for the newsvendor distributor under fixed incentives is an (s,S)$(s\text{,}S)$ type policy. We further show that external and internal quantity based incentives can restore channel coordination in single period and channel members can benefit through arbitrary splitting of the resulting additional chain profit. The single period results are extended to multiple periods and the impact of fixed incentives on the distributor’s optimal stocking policy and channel efficiency are examined under three different multi-period supplier strategies. Numerical examples are used to compare the multi-period strategies and to provide additional managerial insights. The results show that contrary to common belief, incentive plans developed and maintained based only on current inventory data perform poorly in long term and that such incentive plans must be periodically updated to enhance their efficiency. Furthermore, we show that high level of incentives designed to push too much inventory downstream of the supply chain can actually reduce the chain’s efficiency.     

考虑互惠公平的创新顾客激励契约研究

基于公平偏好理论的互惠公平,从创新顾客的互惠偏好程度、激励契约类型与激励效果的关系入手,构建创新顾客参与企业创新活动的激励模型。通过模型求解和分析,探讨激励契约的外部性和互惠关系对于激励效果的影响;此外,进一步分析如何联合经济激励和心理激励,降低企业获得创新顾客高努力投入的成本;最后,通过仿真实验,验证模型分析结果。研究发现:当创新顾客之间出现互惠关系时,最优激励契约取决于创新顾客心理偏好与风险态度之间的相互作用:当创新顾客的风险规避程度较低时,最优激励契约为相对绩效契约;当创新顾客的风险规避程度较高时,最优激励契约为团队报酬契约。     

Bayesian detection of clusters in efficiency score maps: An application to Brazilian energy regulation

An original application of an approach first used in epidemiology investigation was developed and implemented in energy regulation benchmarking. Using Brazilian electricity energy distribution utilities, the proposed methodology applies spatial Bayesian analysis to estimate the number of clusters and the utilities in each cluster. By dividing the utilities into smaller, but geographically closer groups, it can be argued that local determinants of production or environmental components are accounted in the benchmarking model. Thus, the proposed method requires the spatial location of the utilities and their cost efficiencies, estimated previously by the regulator. Results show two detected clusters with high and low efficiencies located in the east and west of Brazil. After applying the regulator model to the detected groups, significant changes in cost efficiencies were estimated for a few utilities. This is important information that can be used by the regulator to estimate future cost incentives.     

VARIATIONAL DISCRETIZATION OF A CONTROL-CONSTRAINED PARABOLIC BANG-BANG OPTIMAL CONTROL PROBLEM

We consider a control-constrained parabolic optimal control problem without Tikhonov term in the tracking functional.For the numerical treatment,we use variational discretization of its Tikhonov regularization:For the state and the adjoint equation,we apply Petrov-Galerkin schemes in time and usual conforming finite elements in space.We prove a-priori estimates for the error between the discretized regularized problem and the limit problem.Since these estimates are not robust if the regularization parameter tends to zero,we establish robust estimates,which--depending on the problem's regularity——enhance the previous ones.In the special case of bang-bang solutions,these estimates are further improved.A numerical example confirms our analytical findings.     

Superconvergent estimates of conforming finite element method for nonlinear time‐dependent Joule heating equations

In this article, we study the superconvergence analysis of conforming bilinear finite element method (FEM) for nonlinear Joule heating equations. Based on the rigorous estimates together with high accuracy analysis of this element, mean value technique and interpolation postprocessing approach, the superclose and superconvergent estimates about the related variables in H¹‐norm are derived for semidiscrete and a linearized backward Euler fully discrete schemes, which extends the results of optimal estimates obtained for conforming FEMs in the previous literature. At last, a numerical experiment is performed to verify the theoretical analysis.     

A Posteriori Error Estimates for Distributed Convex Optimal Control Problems

In this paper, we present an a posteriori error analysis for finite element approximation of distributed convex optimal control problems. We derive a posteriori error estimates for the coupled state and control approximations under some assumptions which hold in many applications. Such estimates, which are apparently not available in the literature, can be used to construct reliable adaptive finite element approximation schemes for control problems. Explicit estimates are obtained for some model problems which frequently appear in real-life applications.     

Statistical inference for DEA estimators of directional distances

In productivity and efficiency analysis, the technical efficiency of a production unit is measured through its distance to the efficient frontier of the production set. The most familiar non-parametric methods use Farrell–Debreu, Shephard, or hyperbolic radial measures. These approaches require that inputs and outputs be non-negative, which can be problematic when using financial data. Recently, Chambers et al. (1998) have introduced directional distance functions which can be viewed as additive (rather than multiplicative) measures efficiency. Directional distance functions are not restricted to non-negative input and output quantities; in addition, the traditional input and output-oriented measures are nested as special cases of directional distance functions. Consequently, directional distances provide greater flexibility. However, until now, only free disposal hull (FDH) estimators of directional distances (and their conditional and robust extensions) have known statistical properties (Simar and Vanhems, 2012). This paper develops the statistical properties of directional d estimators, which are especially useful when the production set is assumed convex. We first establish that the directional Data Envelopment Analysis (DEA) estimators share the known properties of the traditional radial DEA estimators. We then use these properties to develop consistent bootstrap procedures for statistical inference about directional distance, estimation of confidence intervals, and bias correction. The methods are illustrated in some empirical examples.     

Worst case vs. average performance estimates for unconstrained NMPC schemes

We consider performance estimates for unconstrained NMPC schemes under a controllability assumption. By means of worst case and average estimates, we investigate the effect of varying control horizons on the performance and compare the results with numerical simulations. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Efficiency in the Greek insurance industry

This paper employs the two-stage procedure of Simar and Wilson (2007) to analyse the effects of deregulation on the efficiency of the Greek insurance industry. The efficiency is estimated by means of data envelopment analysis (DEA). The companies are ranked according to their CRS efficiency score for the period 1994–2003. The first stage results indicate a decline in efficiency over the sample period, while the second stage results confirm that the competition for market shares is a major driver of efficiency in the Greek insurance industry.     

Multigrid second-order accurate solution of parabolic control-constrained problems

A mesh-independent and second-order accurate multigrid strategy to solve control-constrained parabolic optimal control problems is presented. The resulting algorithms appear to be robust with respect to change of values of the control parameters and have the ability to accommodate constraints on the control also in the limit case of bang-bang control. Central to the development of these multigrid schemes is the design of iterative smoothers which can be formulated as local semismooth Newton methods. The design of distributed controls is considered to drive nonlinear parabolic models to follow optimally a given trajectory or attain a final configuration. In both cases, results of numerical experiments and theoretical twogrid local Fourier analysis estimates demonstrate that the proposed schemes are able to solve parabolic optimality systems with textbook multigrid efficiency. Further results are presented to validate second-order accuracy and the possibility to track a trajectory over long time intervals by means of a receding-horizon approach.     

Utility-based two-stage models with fairness concern

This paper studies the impact of social comparison and fairness concerns on the efficiency of a two-stage process. The decision maker of each stage cares about not only the absolute score of his efficiency, but also the relative status when comparing with the other. By incorporating the utility theory and the concept of fairness, an efficiency-based Neumann–Morgenstern cardinal utility is defined to compose of basic utility from his self-efficiency and additional utility from the fairness concern of the other’s efficiency. Utility-based two-stage models are proposed to optimize the utilities of the stages rather than only the efficiencies instead. We characterize the concern of fairness as advantageous and disadvantageous inequity based on equitable outcome comparison. By investigating the non-cooperating relationship between two stages, we show that the stage dominating the process has the incentive to optimize his efficiency without ignoring that of the other, which is contrary to the conventional situation. In addition, the coefficients of equitable outcome and inequity significantly affect the efficiencies of both stages. We further investigate the cooperation between two stages and find that the efficiencies of the stages vary with the coefficients of unfairness perceptions. Numerical analysis verifies the validity of the proposed models and identifies the impacts of the coefficients of equitable outcome and inequity on the stages’ and overall efficiencies.     

Two energy-conserving and compact finite difference schemes for two-dimensional Schrödinger-Boussinesq equations

In this paper, we study two compact finite difference schemes for the Schrödinger-Boussinesq (SBq) equations in two dimensions. The proposed schemes are proved to preserve the total mass and energy in the discrete sense. In our numerical analysis, besides the standard energy method, a “cut-off” function technique and a “lifting” technique are introduced to establish the optimal H¹ error estimates without any restriction on the grid ratios. The convergence rate is proved to be of O(τ² + h⁴) with the time step τ and mesh size h. In addition, a fast finite difference solver is designed to speed up the numerical computation of the proposed schemes. The numerical results are reported to verify the error estimates and conservation laws.