Computation of efficient targets in DEA models with production trade-offs and weight restrictions

Recently new models of data envelopment analysis (DEA) were introduced that incorporate production trade-offs between inputs and outputs or based on them weight restrictions. In this paper, we develop a computational procedure suitable for the practical application of such models. We show that the standard two-stage optimisation procedure used in DEA to test the full efficiency of units and identify their efficient targets may work incorrectly in the new models. The modified procedure consists of three stages: the first evaluates the radial efficiency of the unit, the second identifies its efficient target, and the third its reference set of efficient peers. Each stage requires solving one linear program for each unit.     

Tabu Search Heuristics for the Arc Routing Problem with Intermediate Facilities under Capacity and Length Restrictions

This paper deals with the Arc Routing Problem with Intermediate Facilities under Capacity and Length Restrictions(CLARPIF), a variant of the classical Capacitated Arc Routing Problem(CARP), in which vehicles may unload or replenish at intermediate facilities and the length of any route may not exceed a specified upper bound. Three heuristics are developed for the CLARPIF: the first is a constructive procedure based on a partitioning approach while the second and the third are tailored Tabu Search procedures. Computational results on a set of benchmark instances with up to 50 vertices and 92 required edges are presented and analyzed.     

On universal deformations in analysis of Signorini’s nonlinear theory of hyperelastic media

It is shown that uniform compression/tension and simple shear as universal deformations are quite useful in studying Signorini’s nonlinear theory of hyperelastic materials. They make it possible to formulate restrictions for the elastic constants of the theory and to explain the Poynting effect __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 54–60, December 2007.     

A sample path analysis of M/GI/1 queues with workload restrictions

A simple random time change is used to analyze M/GI/1 queues with workload restrictions. The types of restrictions considered include workload bounds and rejection of jobs whose waiting times exceed a (possibly random) threshold. Load dependent service rates and vacations are also allowed and in each case the steady state distribution of the workload process for the system with workload restrictions is obtained in terms of that of the corresponding M/ GI/1 queue without restrictions. The novel sample path arguments used simplify and generalize previous results.     

Theoretical study of the6Σ+,6Π, and4Σ+ van der Waals states of NO

Summary Potential energy curves for the weakly bound⁶⁺,⁶, and⁴⁺ states of NO are presented at various levels of correlation treatment. The binding energies for the van der Waals minima vary from about 30 cm^–1 for the⁶⁺ state to about 20 cm^–1 for the⁴⁺ and⁶ states. We investigate the importance of constraining the wave function to dissociate to a spherically symmetric O atom where the oxygen 2p orbitals are equivalent. For high levels of correlation treatment, we find that these restrictions have little effect on the potential, while greatly increasing the length of the CI expansion.     

Constructive methods in convexC 2 interpolation using quartic splines

Using quartic splines on refined grids, we present a method for convexity preservingC ² interpolation which is successful for all strictly convex data sets. In the first stage, one suitable additional knot in each subinterval of the original data grid is fixed dependent on the given data values. In the second stage, a visually pleasant interpolant is selected by minimizing an appropriate choice functional.     

Feasible algorithms for approximate reasoning using fuzzy logic

Deductive reasoning with classical logic is hampered when imprecision is present in the variables, although human reasoning can cope quite adequately with vague concepts. A new approach to reasoning which allows imprecise conclusions to be drawn consistently from imprecise premises was introduced by Baldwin [2]. This method is economical in calculation as it avoids the high dimensionality that fuzzy set representations often involve.This paper briefly reviews the method from an operational viewpoint, isolating the individual processes that are used in the method. A feasible algorithm for computing each process is then presented.It is assumed that the reader is familiar with the concept of, and operations on, fuzzy sets introduced by Zadeh [14].     

Free energy models for nonuniform classical fluids

A number of techniques are presented for extrapolating from knowledge of the direct correlation function for a uniform fluid at various densities to that of the free energy and associated density profile of a nonuniform fluid. A primitive mathematical model is followed by models based upon physical characteristics of exactly solved systems, from the nonnegativity of linear response functions to the explicit form of a nonuniform hard rod fluid. Attention is paid to physical requirements which are not satisfied and suggestions are made for future progress.     

Review of Methods for Increasing Discrimination in Data Envelopment Analysis

We present a review of methods for increasing discrimination between efficient DMUs in Data Envelopment Analysis. These methods were classified into two groups: those that incorporate a priori information and those that do not use or minimize the use of such a priori information. We also compare these methodologies regarding their specific characteristics.     

Pearson's correlation between three variables; using students’ basic knowledge of geometry for an exercise in mathematical statistics

The well known recurrence formulae for means and standard deviations have been extended to encompass bivariate data. The effectiveness of this technique is enhanced with the aid of a microcomputer.