Measuring returns to scale in DEA models when the firm is regulated

In the standard framework of data envelopment analysis (DEA) models, the returns to scale are fully characterized using the multiplier on the convexity constraint of inefficient decision making units (DMU) using the projection of the input–output vector on the frontier. In this note, we investigate how the returns to scale measurements in DEA models are affected by the presence of regulatory constraints. These additional constraints change the role played by the convexity constraint. In order to avoid biased estimation of the returns to scale, we show that the interaction between the regulatory and the convexity constraints has to be taken into account.     

Fitting mixed-effects models when data are left truncated

Damage sizes, i.e. all damages occurring to a policy and not only those that are reported to an insurance company, are modelled as a linear mixed model. Only those damages that are larger than their deductibles are reported to the company, and this fact should be taken into account when analyzing such data. In statistical terms, the problem is to make inference in a linear mixed model with left truncated data. Estimation methods based on a Monte Carlo simulation of the likelihood are proposed, and extensive simulations to evaluate the quality of the methods are reported. The proposed methods are then used to analyze claimsizes for some marine insurance data, where shipowners represent random effects and technical data about the ships represent fixed effects.     

Estimating cumulative incidence functions when the life distributions are constrained

In competing risks studies, the Kaplan-Meier estimators of the distribution functions (DFs) of lifetimes and the corresponding estimators of cumulative incidence functions (CIFs) are used widely when no prior information is available for these distributions. In some cases better estimators of the DFs of lifetimes are available when they obey some inequality constraints, e.g., if two lifetimes are stochastically or uniformly stochastically ordered, or some functional of a DF obeys an inequality in an empirical likelihood estimation procedure. If the restricted estimator of a lifetime differs from the unrestricted one, then the usual estimators of the CIFs will not add up to the lifetime estimator. In this paper we show how to estimate the CIFs in this case. These estimators are shown to be strongly uniformly consistent. In all cases we consider, when the inequality constraints are strict the asymptotic properties of the restricted and the unrestricted estimators are the same, thus providing the asymptotic properties of the restricted estimators essentially “free of charge”. We give an example to illustrate our procedure.     

Portfolio optimization when asset returns have the Gaussian mixture distribution

In this paper we consider a portfolio optimization problem where the underlying asset returns are distributed as a mixture of two multivariate Gaussians; these two Gaussians may be associated with “distressed” and “tranquil” market regimes. In this context, the Sharpe ratio needs to be replaced by other non-linear objective functions which, in the case of many underlying assets, lead to optimization problems which cannot be easily solved with standard techniques. We obtain a geometric characterization of efficient portfolios, which reduces the complexity of the portfolio optimization problem.     

Analysis of the impact of price-sensitivity factors on the returns policy in coordinating supply chain

This paper analyzes the impact of price-sensitivity factors on characteristics of returns policy contracts in a single-period product supply chain. The contract considers stochastic and price-dependent demand. We present an analytical model and then use numerical methods with the Stackelberg game to identify the contract properties. We numerically show that a returns policy indeed improves supply chain performance. However, the benefits earned from the returns policy, under price-sensitive and variable demand, are different for different supply chain partners. First, when price-sensitivity is high, profit of the manufacturer decreases with increase in demand variability. Second, when price-sensitivity is sufficiently high and demand variability increases, the manufacturer has to surrender part of the profits to the retailer, in order to continue sales. However, even after surrendering part of the profits to the retailer, the manufacturer still earns profits that are higher than those available in a wholesale price contract. Last, from the perspective of division of channel profits, the retailer is always worse off in case of returns policies than in a wholesale price contract. Therefore, to apply this form of incentive in practice, managements should consider the impact of price-sensitivity on the returns policy and its performance.     

The impacts of the full returns policy on a supply chain with information asymmetry

In contrast to the existing return policies literature assuming that information is symmetrical between the manufacturer and the retailer, we study the full returns policy’s impact on supply chains with information asymmetry. We first study the case that the base level of the demand follows a discrete distribution with two states. We find that the retailer benefits from the full returns policy in all circumstances, while the manufacturer and the supply chain are better off under some conditions. We then consider the situation in which the base level of the demand is a type of AR(1) process.     

A new method based on SOM network to generate coarse meshes for overlapping unstructured multigrid algorithm

A new method to generate coarse meshes for overlapping unstructured multigrid algorithm based on self-organizing map (SOM) neural network is presented in this paper. The application of SOM neural network can overcome some limitations of conventional methods and which is designed to pursuit the best structure relation between fine and coarse unstructured meshes with the object to ensure robust convergence for overlapping unstructured multigrid algorithm. Besides, this method can automate the generation of unstructured meshes and is suitable for both two and three dimensions conditions.     

An investigation on the sensitivity and stability radius of returns to scale and efficiency in data envelopment analysis

An issue which has received widespread attention in rapidly growing field of DEA is the sensitivity of the results of analysis to perturbations in the data.     

Impact of uncertainty in the quality of returns on the profitability of a single-period refurbishing operation

This paper investigates how the profitability of reuse activities is affected by uncertainty regarding the quality of returned products. Specifically, we examine a reverse supply chain consisting of two collection sites and a refurbishing site, which faces stochastic demand for refurbished products in a single-period setting. The quality of returns (refurbishing yield) becomes known only after the transportation of the products to the refurbishing site. We prove that the expected profit function has a unique optimal solution (procurement and production quantities) and we derive the conditions under which it is optimal to use only one of the collection sites. The analysis is supported by numerical results which provide insights regarding the effect of the uncertain yields at the two collection sites and their correlation on optimal decisions and system profitability.     

Optimisation of timetable-based, stochastic transit assignment models based on MSA

Public transport assignment models have increased in complexity in order to describe passengers' route choices as detailed and correctly as possible. Important trends in the development are (1) timetable-based assignment, (2) inclusion of feeder modes, (3) use of stochastic components to describe differences in passengers' preferences within and between purposes and classes (random coefficients), as well as to describe non-explained variation within a utility theory framework, and (4) consideration of capacity problems at coach level, system level and terminal level. In the Copenhagen-Ringsted Model (CRM), such a large-scale transit assignment model was developed and estimated. The Stochastic User Equilibrium problem was solved by the Method of Successive Averages (MSA). However, the model suffered from very large calculation times. The paper focuses on how to optimise transit assignment models based on MSA combined with a generalised utility function. Comparable tests are carried out on a large-scale network. The conclusion is that there is potential of optimising MSA-based methods. Examples of different approaches for this is presented, tested and discussed in the paper.     

The toll effect on price of anarchy when costs are nonlinear and asymmetric

We examine the efficiency of the optimal tolls by establishing the bound for the price of anarchy when the levied tolls are also considered as a part of the cost functions. For linear and nonlinear asymmetric cost functions, we prove that the price of anarchy of the system with tolls is lower than that without tolls. Furthermore, we show that the total disutility caused to the users by the tolls is bounded by a multiple of the original optimal system cost.     

A result on hypothesis testing for a multivariate normal distribution when some observations are missing

Let U_i = (X_i, Y_i), i = 1, 2,…, n, be a random sample from a bivariate normal distribution with mean μ = (μ_x, μ_y) and covariance matrix

. Let X_i, i = n + 1,…, N represent additional independent observations on the X population. Consider the hypothesis testing problem H₀ : μ = 0 vs. H₁ : μ ≠ 0. We prove that Hotelling's T² test, which uses (X_i, Y_i), i = 1, 2,…, n (and discards X_i, i = n + 1,…, N) is an admissible test. In addition, and from a practical point of view, the proof will enable us to identify the region of the parameter space where the T²-test cannot be beaten. A similar result is also proved for the problem of testing μ_x ? μ_y = 0. A Bayes test and other competitors which are similar tests are discussed.     

On a problem of nonstationary two-dimensional motion of micropolar fluid when normal stress and tangential velocity are given on the boundary

The object of this paper is to investigate the solution of nonstationary motion of micropolar fluid in the half-plane when the normal stresses and tangential velocities are given on the boundary. The Laplace-Fourier transform technique is used to point out the solution by quadratures. Numerical results of the physical quantities such as tangential and normal velocities, pressure, microrotation, stresses and momentums are obtained and displayed graphically. The problem could be met in the study of the vibrations of a memberance or a plate contacting with the fluid.     

An economical method of calculating Lagrange multiplier estimates for nonlinear programming problems when many of the constraints are bounds on the variables

Some recent methods for solving nonlinear programming problems make use of estimates of the Lagrange multipliers. These estimates are usually calculated by solving a system oft linear equations, wheret is the number of active constraints. It is shown that, when a large proportion of the active constraints consists of simple upper or lower bounds on the variables, then computational effort can be saved by means of a reorganization of this linear system.     

Estimation of the radius of a circle when the coordinates of a number of points on its circumference are observed: An example of bootstrapping

The bootstrap (Efron, 1979, 1982) is a very simple resampling plan and has shown to be successful in estimating the bias and other measures of statistical error of a number of estimators. It gives freedom from the constraints of traditional parametric theory at the cost of performing the usual statistical calculations a hundred or a thousand times over. In this letter another example of bootstrap estimation of bias is given. It is interesting that Quenouille's (1949) jackknife (see Miller, 1964, for a review) fails completely in this case.