Do market share and efficiency matter for each other? An application of the zero-sum gains data envelopment analysis

Current studies that use traditional data envelopment analysis (DEA) neglect the 100% market share restriction. This study adopts zero-sum gains data envelopment analysis to measure the efficiency scores of securities firms (SFs) and indicates that the traditional DEA model underestimates the efficiency scores of inefficient SFs. This research analyses 266 integrated securities firms in Taiwan from 2001 to 2005 and employs three inputs (fixed assets, financial capital, and general expenses) and a single output (market share). The foreign-affiliated ownership of SFs positively affects the efficiency scores. The two-stage least squares procedure confirms that the market share and efficiency score simultaneously reinforce each other.     

When does a T-junction require a left-turn lane?

A four-state, ergodic Markov chain is used to model a T-junction on a narrow, two-lane, major road. The states are defined more realistically than by previous authors. A formula is obtained for the proportion of traffic configurations in which cars travelling one way are brought to a halt by those turning left onto the minor road. This formula is obtained as a function of four parameters: the mean traffic flows in each direction, the probability that a car on the major road will turn left at the junction and the minimum time gap, in the oncoming flow of traffic, which that manouevre requires. If this proportion is higher than is deemed acceptable, then a left-turn is needed.     

Designing an efficient supply chain network with uncertain data: a robust optimization—data envelopment analysis approach

Designing a supply chain network (SCN) is an important issue for organizations in competitive markets. In this paper, a novel robust SCN that considers the efficiencies and costs simultaneously is proposed. In order to estimate the efficiency of the producers and distributors, data envelopment analysis (DEA) model is incorporated into SCN. Moreover, to handle the uncertainty in data, a scenario-based robust optimization approach is applied. The proposed model finds out the efficient location of producers and distributors and determines the amount of purchases from each supplier in uncertain conditions. To illustrate the application of the proposed model, a numerical example is solved and results are analyzed.     

Does knowledge management matter? Assessing the performance of electricity distribution districts based on slacks-based data envelopment analysis

This study uses slacks-based data envelopment analysis (DEA) to examine the performance of electricity distribution districts (EDDs) in Taiwan in 2004. It also explores the relationship between a knowledge management system (KMS) and variations in the efficiency of EDDs in the Taiwan Power Company from 2000 to 2004. The findings show that the EDDs performed well in terms of managerial efficiency in 2004, and 75% of the districts exhibited an increasing performance variation when using cross-period analysis for that period. We show that there is a positive relationship between a KMS and variations in organizational efficiency. In addition, we present a decision-making matrix and conceptual map to help EDD managers improve their managerial efficiency and skills. This study contributes to the field of knowledge management research by applying the DEA model to link the performance between KMS and an organization. Several significant findings emerge from the study.     

How to generate regularly behaved production data? A Monte Carlo experimentation on DEA scale efficiency measurement

Monte Carlo experimentation is a well-known approach used to test the performance of alternative methodologies under different hypotheses. In the frontier analysis framework, whatever the parametric or non-parametric methods tested, experiments to date have been developed assuming single output multi-input production functions. The data generated have mostly assumed a Cobb–Douglas technology. Among other drawbacks, this simple framework does not allow the evaluation of DEA performance on scale efficiency measurement. The aim of this paper is twofold. On the one hand, we show how reliable two-output two-input production data can be generated using a parametric output distance function approach. A variable returns to scale translog technology satisfying regularity conditions is used for this purpose. On the other hand, we evaluate the accuracy of DEA technical and scale efficiency measurement when sample size and output ratios vary. Our Monte Carlo experiment shows that the correlation between true and estimated scale efficiency is dramatically low when DEA analysis is performed with small samples and wide output ratio variations.     

When does the K4‐free process stop?

The K₄‐free process starts with the empty graph on n vertices and at each step adds a new edge chosen uniformly at random from all remaining edges that do not complete a copy of K₄. Let G be the random maximal K₄‐free graph obtained at the end of the process. We show that for some positive constant C, with high probability as , the maximum degree in G is at most . This resolves a conjecture of Bohman and Keevash for the K₄‐free process and improves on previous bounds obtained by Bollobás and Riordan and by Osthus and Taraz. Combined with results of Bohman and Keevash this shows that with high probability G has edges and is ‘nearly regular’, i.e., every vertex has degree . This answers a question of Erd?s, Suen and Winkler for the K₄‐free process. We furthermore deduce an additional structural property: we show that whp the independence number of G is at least , which matches an upper bound obtained by Bohman up to a factor of . Our analysis of the K₄‐free process also yields a new result in Ramsey theory: for a special case of a well‐studied function introduced by Erd?s and Rogers we slightly improve the best known upper bound.Copyright © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 44, 355‐397, 2014     

When does the top homology of a random simplicial complex vanish?

Several years ago Linial and Meshulam (Combinatorica 26 (2006) 457–487) introduced a model called of random n‐vertex d‐dimensional simplicial complexes. The following question suggests itself very naturally: What is the threshold probability at which the d‐dimensional homology of such a random d‐complex is, almost surely, nonzero? Here we derive an upper bound on this threshold. Computer experiments that we have conducted suggest that this bound may coincide with the actual threshold, but this remains an open question. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 26–35, 2015     

Estimating non-convex production sets – imposing convex input sets and output sets in data envelopment analysis

In this paper, we present Data Envelopment Analysis models for estimating non-convex production sets. In contrast to the Banker et al. (Banker, R.D., Charnes, A. and Cooper, W.W., 1984. Management Science 30 (9), 1078–1092) model, these models give statistically consistent estimators for production sets that are non-convex, but do have convex input sets and/or convex output sets, as is typically assumed in micro-economic theory. In addition, these models suffer less from a finite sample error than the Free Disposable Hull (Deprins, D., Simar, L., Tulkens, H., 1984. In: Marchand, M., Pestieu, P., Tulkens, H. (Eds.), The Performance of Public Enterprises. North-Holland, Amsterdam, pp. 243–267) model.     

When does the zero-one <Emphasis Type="Italic">k</Emphasis>-law fail?

The limit probabilities of the first-order properties of a random graph in the Erd?s–Rényi model G(n, n^?α), α ∈ (0, 1), are studied. A random graph G(n, n^?α) is said to obey the zero-one k-law if, given any property expressed by a formula of quantifier depth at most k, the probability of this property tends to either 0 or 1. As is known, for α = 1? 1/(2^k?1 + a/b), where a > 2^k?1, the zero-one k-law holds. Moreover, this law does not hold for b = 1 and a ≤ 2^k?1 ? 2. It is proved that the k-law also fails for b > 1 and a ≤ 2^k?1 ? (b + 1)².     

When does the k-hyponormality of a 2-variable weighted shift become subnormality?

In this article we construct a sequence of nontrivial classes of 2-variable weighted shifts such that the k-hyponormality of an arbitrary power of a member W(α,β) from Gk is equivalent to its subnormality.     

Luce's Axiom and occupational prestige: Test of a measurement model†

This paper reports research using a psychological theory, R. D. Luce's (1959) individual choice theory, to provide a ratio‐level measurement basis for an important sociological variable, occupational prestige. It is shown that earlier measurement procedures to scale this sociological variable are essentially arbitrary, although heuristically useful. Luce's Axiom of Choice and his Ranking Postulate are then tested on choice sets of occupations where subjects are asked to pair‐compare or rank the occupations on the basis of their prestige. The Axiom receives qualified support, while the Ranking Postulate is not supported. It is concluded that Luce's choice theory can provide a ratio‐level measurement basis for occupational prestige, although a procedure using rankings must be appropriately structured in order to be an adequate instrument of measurement.     

When is the self-intersection of a subvariety a fibration?

We provide a necessary and sufficient condition for the derived self-intersection of a smooth subscheme inside a smooth scheme to be a fibration over the subscheme. As a consequence we deduce a generalized HKR isomorphism. We also investigate the relationship of our result to path spaces in homotopy theory, Buchweitz–Flenner formality in algebraic geometry, and draw parallels with similar results in Lie theory and symplectic geometry.     

When is a Markovian Semigroup Induced by a Semiflow?

t , for t ≥ 0, be a strongly continuous Markovian semigroup acting on C(X), where X is a compact Hausdorf space, and let D denote the domain of its infinitesimal generator Z. Suppose D contains a (perhaps finite) family of functions f separating the points of X and satisfying Zf² = 2fZf. If either (1) there exists δ > 0 such that (T^t f)²∈ D if 0 ≤ t ≤δ for each f in this family; or (1′) for some core D′ of Z, g ∈ D′ implies g²∈ D, then the underlying Markoff process on X is deterministic. That is, there exists a semiflow — a semigroup (under composition) of continuous functions φ_t from X into X — such that T^tf(x) = f(φ_t (x)). If the domain D should be an algebra then conditions (1) and (1′) hold trivially. Conversely, if we have a separating family satisfying Zf² = 2fZf then each of these conditions implies that D is an algebra. It is an open question as to whether these conditions are redundant. If the functions φ_t are homeomorphisms from X onto X, then of course we have a Markovian group induced by a flow. This result is obtained by first providing general results about the null-space N of the (function-valued) positive semidefinite quadratic form defined by < f, g > = Z(fg) - fZg - gZf. The set N can be defined for any generator Z of a strongly continuous Markovian semigroup and is equivalently given by N = {f ∈ D| f²∈ D and Zf² = 2fZf} = {f ∈ D| T^t(f²)-(T^tf)² is o(t²) in C(X)}. In the general case N is an algebra closed under composition with any C¹-function φ from the reals to the reals, and Z(φ[f]) = (Zf)φ′[f] if f ∈ N. This "chain rule" on N (on which Z must act as a derivation) is a special case of a theorem for C²-functions φ which holds more generally for all f in d, viz., Z(φ[f] = (Zf) φ′[f] + ? <f, f> φ″[f], Provided Z is a local operator and D is an algebra. In this case the form < f, g > itself enjoys the relation < φ[f], ψ[g] > = φ′ [f] ψ′[g] < f, g >, for C²functions φ and ψ. Some of the results and their proofs continue to hold when the setting is switched from the commutative C*-algebra C(X) to a general (noncommutative) C*-algebra A. In the norm continuous case we obtain a sharp characterization of Markovian semigroups that are groups: Let T^t = e^tz , defined for t ≥ 0, be a Markovian semigroup acting on a C*-algebra A that is norm continuous, i.e., ||T^t - I|| ⇒ 0 as t ⇒ 0 +. Assume Z(a²) = a(Za) + (Za) a for some (perhaps finite) set of self-adjoint elements a that generate a Jordan algebra dense among the self-adjoint elements of A. The e^tz , -∞ < t < ∞, is a group of Markovian operators.     

When is a stochastic integral a time change of a diffusion?

We give necessary and sufficient conditions that a time change of ann-dimensional Ito stochastic integralX _t of the form