Evaluating returns to scale and congestion by production possibility set in intersection form

This research proposes a new method to estimate returns to scale(RTS) of decision making units(DM Us) with multiple inputs and outputs.The state of return to scale includes increasing RTS,constant RTS,decreasing RTS and evidence of congestion.The method is based on the production possibility set in the intersection form given by a set of linear inequalities.We propose and prove the necessary and sufficient conditions for the RTS estimation.With the new procedure,to estimate the RTS of a DM U is simply to ch...     

Dynamic concept of returns to scales and its characteristics on production frontier in intersection form

This paper gives a dynamic concept and a new non-parametric method for evaluating returns to scale(RTS) of economic units with multiple inputs and outputs.It is frequently noticed that when we increase the input of a decision making unit(DMU) with a certain status of RTS,different status of RTS is observed.For example,when we increase the input of a DMU with constant RTS under the traditional method,a decreasing RTS is often observed instead of the expected constant RTS.We thus define the RTS of each DMU in both input expansion and contraction regions respectively.The research starts from transferring the production possibility set into the intersection form,by giving the explicit linear inequality representation of production frontiers.The RTS structural characteristics of DMUs’ on the production frontier are described.Status of RTS of those DMUs on the production frontier include increasing RTS,constant RTS,decreasing RTS,saturated RTS and evidence of congestion.Necessary and suficient conditions for RTS evaluation are provided.The definition and evaluation method given here provide more detailed economic characteristics of DMU for policy makers.     

一类具有双恢复集的局部恢复码的构造

假设C是有限域Fq上的[n,κ]线性码,如果码字的每个坐标是其它至多r个坐标的函数,称C是(n,k,r)局部恢复码,这里r是较小的数.在分布式存储系统中,具有多个恢复集的局部恢复码使得数据在系统中更具实际意义,因为它可以避免热数据的频繁访问.引入代数函数域、特别是Hermite函数域去构造局部恢复码,这类局部恢复码具有...     

Implementation strategies of a contract-based MRI examination reservation process for stroke patients

Timely imaging examinations are critical for stroke patients due to the potential life threat. We have proposed a contract-based Magnetic Resonance Imaging (MRI) reservation process [1] in order to reduce their waiting time for MRI examinations. Contracted time slots (CTS) are especially reserved for Neural Vascular Department (NVD) treating stroke patients. Patients either wait in a CTS queue for such time slots or are directed to Regular Time Slot (RTS) reservation. This strategy creates “unlucky” patients having to wait for lengthy RTS reservation. This paper proposes and analyzes other contract implementation strategies called RTS reservation strategies. These strategies reserve RTS for NVD but do not direct patients to regular reservations. Patients all wait in the same queue and are served by either CTS or RTS on a FIFO (First In First Out) basis. We prove that RTS reservation strategies are able to reduce the unused time slots and patient waiting time. Extensive numerical results are presented to show the benefits of RTS reservation and to compare various RTS reservation strategies.     

Local and global returns to scale in performance measurement

In data envelopment analysis, the type of local returns to scale (RTS) exhibited by a technically efficient unit indicates whether an increase or reduction of the scale of operations could improve the productivity of the unit. One of the approaches to testing RTS is based on the comparison of the efficiency of the unit in specially constructed reference technologies. It has been suggested that this approach is equally suitable for convex and non-convex, including the free disposal hull, technologies. In this paper, we construct examples that show that this suggestion in the case of non-convex technologies is not correct. We show that the type of RTS obtained by this approach is not a local, but global, characteristic of the technology, as it indicates the direction to the most productive scale size of the unit. In non-convex technologies, the local and global classifications of RTS are generally different.     

Measurement of returns to scale using a non-radial DEA model: A range-adjusted measure approach

This research theoretically explores the measurement of returns to scale (RTS), using a non-radial DEA (data envelopment analysis) model. A range-adjusted measure (RAM) is used as a representative of such non-radial models. Historically, a type of RTS has been discussed within an analytical framework of radial models. The radial-based RTS measurement is replaced by the non-radial RAM/RTS measurement in this study. When discussing the non-radial RAM/RTS measurement, this study finds a problem of multiple projections that cannot be found in the radial measurement. In this research, a new linear programming approach is proposed to identify all efficient DMUs (decision making units) on a reference set. The important feature of the proposed approach is that it can deal with a simultaneous occurrence of (a) multiple reference sets, (b) multiple supporting hyperplanes and (c) multiple projections. All of the three difficulties are handled by the proposed RAM/RTS measurement. In particular, we discuss both when the three different types of multiple solutions occur on the RAM/RTS measurement and how to deal with such difficulties. Our research results make it possible to measure not only the type of RTS but also the magnitude of RTS in the RAM measurement.     

Scatter Search and Bionomic Algorithms for the aircraft landing problem

The problem of deciding how to land aircraft approaching an airport involves assigning each aircraft to an appropriate runway, computing a landing sequence for each runway and scheduling the landing time for each aircraft. Runway allocation, sequencing and scheduling for each aircraft must ensure the scheduled landing time lies within a predefined time window and meet separation time requirements with other aircraft. The objective is to achieve effective runway use.In this paper, the multiple runway case of the static Aircraft Landing Problem is considered. Two heuristic techniques are presented: Scatter Search and the Bionomic Algorithm, population heuristic approaches that have not been applied to this problem before.Computational results are presented for publicly available test problems involving up to 500 aircraft and five runways showing that feasible solutions of good quality can be produced relatively quickly.     

A dual simplex-based method for determination of the right and left returns to scale in DEA

This study reviews the concept of the “right” and the “left” returns to scale (RTS) in data envelopment analysis (DEA), and a dual simplex-based method, for determining these two notions in RTS, is proposed, which has computational advantages as compared to the customary method.     

基于直觉犹豫模糊集的TOPSIS法

直觉犹豫模糊集集成了直觉模糊集和犹豫模糊集的优势,能更有效地刻画决策者偏好不一致的情况。距离测度一直是研究的热点问题,但尚没有文献研究直觉犹豫模糊集间的距离测度,因此本文定义了直觉犹豫模糊集间的Hamming距离、Euclidean距离和广义距离,同时考虑每个元素的权重,定义了加权距离。犹豫度是直觉犹豫模糊集的重要特性,因此在考虑犹豫度的基础上,又定义了一些距离测度。这些距离测度不仅考虑了直觉犹豫模糊数间的差异,同时考虑了犹豫度的影响,决策者可以根据对直觉犹豫模糊数和犹豫度之间偏好的不同,设置不同的偏好值得到距离测度。然后基于这些距离测度,又提出了直觉犹豫模糊环境下的TOPSIS法。最后通过实例说明了所提出的TOPSIS法的合理性与实用性。     

A Hybrid Meta-Heuristic for the Batching Problem in Just-In-Time Flow Shops

This paper is concerned with a batching problem encountered in the context of production smoothing in just-in-time manufacturing systems. The manufacturing system of interest is a multi-level system with a flow-shop at the final level. We develop a hybrid meta-heuristic method to solve the batching problem, which is known to be NP-hard. We hybridize strategic oscillation (SO) and path re-linking (PR) methods and compare the hybrid method's performance to two benchmark methods: a bounded dynamic programming method developed for the problem earlier and an implementation of robust tabu search (RTS) meta-heuristic. Through a computational study, we show that the proposed hybrid method is effective in solving the problem within several minutes of computer time and yielding near-optimal results.     

一种新的梯形模糊数间距离及在投资组合模型选择中的应用

给出一种新的模糊数间的距离公式.用新定义的距离公式来度量给定优先资产的条件下投资组合的分散度.用可能性均值度量投资组合的收益,可能性半方差度量投资组合的风险,在收益和风险满足一定的条件下构造分散度模型.通过实例分析,给出的方法不仅分散度更好,而且资产分配多元化程度更高,计算也更简单.     

Rigid versus unique determination of protein structures with geometric buildup

We introduce a geometric buildup approach to the distance geometry problem in protein modeling, and discuss the necessary and sufficient conditions on the distances for rigid or unique determination of a protein structure. We describe a new buildup algorithm for determining protein structures rigidly instead of uniquely. The algorithm requires even fewer distance constraints than the general buildup algorithm. We present the test results from applying the algorithm to determining the protein structures with varying degrees of availability of the distances, and show that the new development increases the modeling ability of the geometric buildup method even more while retaining much of the computational feasibility of the method.     

Controlling chaotic orbits in mechanical systems with impacts

We stabilize desired unstable periodic orbits, embedded in the chaotic invariant sets of mechanical systems with impacts, by applying a small and precise perturbation on an available control parameter. To obtain such perturbation numerically, we introduce a transcendental map (impact map) for the dynamical variables computed just after the impacts. To show how to implement the method, we apply it to an impact oscillator and to an impact-pair system.     

Some effects of aircraft arrival sequence algorithms

Although various airport landing sequencing algorithms have been considered in the literature, little work has been done in comparing their effects on Air Traffic Control, especially against first-come first-served (FCFS) runway sequences, the method most widely used in practice. This paper compares a number of such algorithms using a discrete-event simulation model of an airport with a single landing runway. Statistical methods are used to test for effects of sequencing algorithm, delay-sharing strategy, arrival rate and wake-vortex mix. Little benefit to delay, or stability of sequencing advice, is found from advanced sequencing when small changes are made to inputs calibrated to a specific airspace. Advanced sequencing improves landing rate, compared with FCFS sequencing, only when aircraft arrival rate is greater than maximum runway landing rate, and wake-vortex mix is sufficiently varied. Constrained position shifting constraints limit these improvements and it is shown that deterministic optimal techniques may actually be sub-optimal in a dynamic environment. Our main conclusion is that FCFS is a robust method under many conditions.     

One-sided elasticities and technical efficiency in multi-output production: A theoretical framework

One of the concepts that have sparked considerable interest in the theory of production and efficiency is that of returns to scale (RTS). Economics researchers typically define RTS using the notion of elasticity. Considerable research activity on RTS has also been observed by management science researchers, who utilize the methodology of Data Envelopment Analysis (DEA) to gain insights on RTS. In this paper, we present a theoretical framework that integrates existing economics and management science literature on RTS, and provides a solid foundation for research work in this area. Our framework defines, discusses, and proposes an approach to measure input- and output-oriented elasticities, and one-sided RTS. We demonstrate how the work done in DEA is a special case of our framework, and discuss the conditions under which the resulting two left-hand, and the two right-hand elasticities can be equal. Future research directions are also discussed.     

The measurement of returns to scale under a simultaneous occurrence of multiple solutions in a reference set and a supporting hyperplane

This research theoretically explores the measurement of RTS (Returns to Scale) under a possible occurrence of multiple solutions in DEA (Data Envelopment Analysis). In this study, the occurrence of multiple solutions is classified into Type I and Type II. Type I is an occurrence of multiple solutions in a reference set. Type II is an occurrence of multiple solutions on a supporting hyperplane passing on the reference set. Both Types I and II are very well known among DEA researchers, but previous research has not sufficiently explored a simultaneous occurrence of Type I and Type II in the RTS measurement. The two types of multiple solutions influence a degree of RTS in the DEA measurement. Such a quantitative issue on RTS is examined from the perspective of the Type I and Type II problems. To deal with such difficulties, a new linear programming approach is proposed to identify all efficient DMUs (Decision Making Units) that consist of a reference set, even if multiple solutions occur on the reference set. Based upon the research result, we can identify when multiple solutions of Type I and/or Type II occur on the RTS measurement and how to deal with such difficulties. Our research result makes it possible to measure a degree of scale economies (RTS) under the simultaneous occurrence of Type I and Type II.     

Scale elasticity and returns to scale in the presence of alternative solutions

Scale elasticity (SE) and returns to scale (RTS) are important topics in performance analysis, which help managers to make decisions about the expansion or contraction of the operation of decision making units under assessment. In this paper, some new results about these topics in the presence of alternative solutions, regarding the concept of multifunction, are provided.At first, some properties of some multifunctions (functions), defined with respect to the optimal solutions of DEA models, are established which help us in what follows. In turn, the relationships between the considered multifunctions and the concept of RTS and SE are studied. Finally an approach for the estimation of the RTS classification of units is obtained, which leads to an important corollary as an interesting result which introduces a connection between two concepts, RTS and SE. This is important from an applied point of view. Also, from a technical point of view, the proofs of theorems which give this corollary use a main lemma of convex analysis literature and give a constructive proof about RTS.     

Sufficient Dimension Reduction via Distance Covariance

We introduce a novel approach to sufficient dimension-reduction problems using distance covariance. Our method requires very mild conditions on the predictors. It estimates the central subspace effectively even when many predictors are categorical or discrete. Our method keeps the model-free advantage without estimating link function. Under regularity conditions, root-n consistency and asymptotic normality are established for our estimator. We compare the performance of our method with some existing dimension-reduction methods by simulations and find that our method is very competitive and robust across a number of models. We also analyze the Auto MPG data to demonstrate the efficacy of our method. Supplemental materials for this article are available online.     

Bounded invariant verification for time-delayed nonlinear networked dynamical systems

We present a technique for bounded invariant verification of nonlinear networked dynamical systems with delayed interconnections. The underlying problem in precise bounded-time verification lies with computing bounds on the sensitivity of trajectories (or solutions) to changes in initial states and inputs of the system. For large networks, computing this sensitivity with precision guarantees is challenging. We introduce the notion of input-to-state (IS) discrepancy of each module or subsystem in a larger nonlinear networked dynamical system. The IS discrepancy bounds the distance between two solutions or trajectories of a module in terms of their initial states and their inputs. Given the IS discrepancy functions of the modules, we show that it is possible to effectively construct a reduced (low dimensional) time-delayed dynamical system, such that the trajectory of this reduced model precisely bounds the distance between the trajectories of the complete network with changed initial states. Using the above results we develop a sound and relatively complete algorithm for bounded invariant verification of networked dynamical systems consisting of nonlinear modules interacting through possibly delayed signals. Finally, we introduce a local version of IS discrepancy and show that it is possible to compute them using only the Lipschitz constant and the Jacobian of the dynamic function of the modules.