An extended slacks-based measure model for data envelopment analysis with negative data

Data envelopment analysis (DEA) is a non-parametric approach based on linear programming that has been widely applied for evaluating the relative efficiency of a set of homogeneous decision-making units (DMUs) with multiple inputs and outputs. The original DEA models use positive input and output variables that are measured on a ratio scale, but these models do not apply to the variables in which negative data can appear. However, with the widespread use of interval scale data and undesirable data, the emphasis has been directed towards the simultaneous consideration of the positive and negative data in DEA models. In this paper, using the slacks-based measure, we propose an extended model to evaluate the efficiency of DMUs, even if some variables are measured on an interval scale and some on a ratio scale. Moreover, the extended model allows for the presence of all interval-scale variables, which are capable of taking both negative and positive values.     

An axiomatic characterization of the potential decisiveness index

Let us consider that somebody is extremely interested in increasing the probability of a proposal to be approved by a certain committee and that to achieve this goal he/she is prepared to pay off one member of the committee. In a situation like this one, and assuming that vote-buying is allowed and free of stigma, which voter should be offered a bribe? The potential decisiveness index for simple games, which measures the effect that ensuring one positive vote produces for the probability of passing the issue at hand, is a good tool with which to acquire the answer. An axiomatic characterization of this index is given in this paper, and its relation to other classical power indices is shown.     

No-wait scheduling of position dependent jobs and adjustable processing intervals

In this paper, we consider a single machine no-wait scheduling model whereby job processing times are general functions of their position in the job sequence. We assume that the single machine must operate at a certain cycle, which can be determined by the scheduler. Furthermore, exactly one job has to be completed by the end of each cycle. Using different variations of the Linear Assignment Problem formulation, we develop polynomial time algorithms for minimizing the following objectives: makespan, total completion time, maximum earliness and total earliness.     

Time-dependent discrete road network design with both tactical and strategic decisions

This paper aims to model and investigate the discrete urban road network design problem, using a multi-objective time-dependent decision-making approach. Given a base network made up with two-way links, candidate link expansion projects, and candidate link construction projects, the problem determines the optimal combination of one-way and two-way links, the optimal selection of capacity expansion projects, and the optimal lane allocations on two-way links over a dual time scale. The problem considers both the total travel time and the total CO emissions as the two objective function measures. The problem is modelled using a time-dependent approach that considers a planning horizon of multiple years and both morning and evening peaks. Under this approach, the model allows determining the sequence of link construction, the expansion projects over a predetermined planning horizon, the configuration of street orientations, and the lane allocations for morning and evening peaks in each year of the planning horizon. This model is formulated as a mixed-integer programming problem with mathematical equilibrium constraints. In this regard, two multi-objective metaheuristics, including a modified non-dominated sorting genetic algorithm (NSGA-II) and a multi-objective B-cell algorithm, are proposed to solve the above-mentioned problem. Computational results for various test networks are also presented in this paper.     

Conceptual modelling and the project process in real simulation projects: a survey of simulation modellers

A survey was used to obtain information on the processes and methods used by simulation experts in real projects. The 102 survey respondents answered questions about their most recent simulation project. This paper presents some of the survey results, focussing mainly on conceptual modelling and the pattern of time allocation to different topics. There are a wide range of findings that include the modellers making changes to the initial conceptual model during subsequent tasks in most of the projects usually by adding complexity, model coding taking on average about twice the time of other topics, and the topics generally occurring in single blocks of time (at the resolution of the survey data collection) but with considerable overlaps. The results give an insight into the way experts approach simulation projects and their problem solving strategies. A potential application is in training novice modellers, particularly in developing ‘craft skills’. The results also provide an empirical basis for further research, especially in conceptual modelling.     

A Quantitative Regularity Estimate for Nonnegative Supersolutions of Uniformly Parabolic Equations

This note establishes an interior quantitative lower bound for nonnegative supersolutions of fully nonlinear uniformly parabolic equations. The result may be interpreted as a quantitative version of a growth lemma established by Krylov and Safonov for nonnegative supersolutions of linear uniformly parabolic equations in nondivergence form. Our approach is different, and follows from an application of a reverse Holder inequality. The result is the parabolic analogue of an elliptic regularity estimate established by Caffarelli, Souganidis, and Wang in the stochastic homogenization of fully nonlinear uniformly elliptic equations.     

Existence of solutions for semilinear elliptic boundary value problems on arbitrary open sets

We show the existence of a weak solution of a semilinear elliptic Dirichlet problem on an arbitrary open set Ω. We make no assumptions about the open set Ω and very mild regularity assumptions on the semilinearity f, plus a coerciveness assumption which depends on the optimal Poincaré–Steklov constant λ₁. The proof is based on Schaefer’s fixed point theorem applied to a sequence of truncated problems. We state a simple uniqueness result. We also generalize the results to Robin boundary conditions [17].     

Partial Data for the Neumann-to-Dirichlet Map

We show that measurements of a Neumann-to-Dirichlet map, with either inputs or outputs restricted to part of the boundary, can determine an electric potential on that domain. Given a convexity condition on the domain, either the set on which measurements are taken, or the set on which input functions are supported, can be made to be arbitrarily small. The result is analogous to the result by Kenig, Sjöstrand, and Uhlmann for the Dirichlet-to-Neumann map. The main new ingredient in the proof is an improved Carleman estimate for the Schrödinger operator with appropriate boundary conditions. This is proved by Fourier analysis of a conjugated operator along the boundary of the domain.     

Orientations of ZnO grown on GaN

On semipolar epitaxial ZnO grown by chemical vapor deposition consists of two distinct orientations as evidenced by transmission electron microscopy and X‐ray diffraction. The initially grown ZnO on GaN follows the GaN lattice with the epitaxial relationship of // and The other oriented ZnO domains then grow on faceted with and with good coherency with the ‐oriented grains. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)