CCR or BCC: what if we are in the wrong model?

The CCR model by Charnes et al. (Eur J Oper Res 2:429–444, 1978) together with the BCC model by Banker et al. (Manag Sci 30:1078–1091, 1984) are the most popular approaches of measuring efficiency among a group of decision making units, DMUs, in data envelopment analysis, DEA. The right choice of a DEA model—CCR or BCC—often, if not always, is a difficult decision. To evaluate a DMU’s efficiency for both models might be helpful, but it does not always capture the essential issues at stake. In this paper we propose a comparative analysis of both concepts: How does activity scaling under constant BCC-efficiency influence CCR-efficiency. And inversely, how does BCC-efficiency behave when activity scaling under constant CCR-efficiency is applied. Such findings of mutual effects improve a DMU’s ability to reassess upsizing and downsizing of activities. Moreover, it allows for exact calculations of the resulting economic effects, and these effects give new insights beyond classical DEA. Finally, scale efficiency turns out to be the ideal concept to control these activity changes, rather than just CCR- or BCC-efficiency. We use a little numerical example to emphasize advantages of the new concept and sketch the new findings for a theater scenery.     

An Evaluation of Staff Preference for Graphic Characteristics

The purpose of the current study was to assess staff preference for how data were displayed on graphs. Specifically, preference for line versus bar graphs was assessed, as well as preference for data displayed as one date in time versus multiple dates showing performance trends. A secondary purpose of the study was to assess staff comprehension of the data presented across different graphic displays. Participants included 60 entry-level direct care staff and 25 seasoned therapists. Therapists had more advanced training in applied behavior analysis than the direct care staff. The vast majority of direct care staff preferred data depicted as a bar graph versus data depicted as a line graph, even preferring a single bar graph over a time-series line graph. The therapists preferred time-series line graphs to bar graphs. Most staff demonstrated understanding of the data, regardless of how it was depicted.     

Total and forcing total edge-to-vertex monophonic number of a graph

For a connected graph \(G = \left( V,E\right) \), a set \(S\subseteq E(G)\) is called a total edge-to-vertex monophonic set of a connected graph G if the subgraph induced by S has no isolated edges. The total edge-to-vertex monophonic number \(m_{tev}(G)\) of G is the minimum cardinality of its total edge-to-vertex monophonic set of G. The total edge-to-vertex monophonic number of certain classes of graphs is determined and some of its general properties are studied. Connected graphs of size \(q \ge 3 \) with total edge-to-vertex monophonic number q is characterized. It is shown that for positive integers \(r_{m},d_{m}\) and \(l\ge 4\) with \(r_{m}< d_{m} \le 2 r_{m}\), there exists a connected graph G with \(\textit{rad}_ {m} G = r_{m}\), \(\textit{diam}_ {m} G = d_{m}\) and \(m_{tev}(G) = l\) and also shown that for every integers a and b with \(2 \le a \le b\), there exists a connected graph G such that \( m_{ev}\left( G\right) = b\) and \(m_{tev}(G) = a + b\). A forcing subset for S of minimum cardinality is a minimum forcing subset of S. The forcing total edge-to-vertex monophonic number of S, denoted by \(f_{tev}(S)\) is the cardinality of a minimum forcing subset of S. The forcing total edge-to-vertex monophonic number of G, denoted by \(f_{tev}(G) = \textit{min}\{f_{tev}(S)\}\), where the minimum is taken over all total edge-to-vertex monophonic set S in G. The forcing total edge-to-vertex monophonic number of certain classes of graphs are determined and some of its general properties are studied. It is shown that for every integers a and b with \(0 \le a \le b\) and \(b \ge 2\), there exists a connected graph G such that \(f_{tev}(G) = a\) and \( m _{tev}(G) = b\), where \( f _{tev}(G)\) is the forcing total edge-to-vertex monophonic number of G.     

Uniqueness of equilibria in atomic splittable polymatroid congestion games

We study uniqueness of Nash equilibria in atomic splittable congestion games and derive a uniqueness result based on polymatroid theory: when the strategy space of every player is a bidirectional flow polymatroid, then equilibria are unique. Bidirectional flow polymatroids are introduced as a subclass of polymatroids possessing certain exchange properties. We show that important cases such as base orderable matroids can be recovered as a special case of bidirectional flow polymatroids. On the other hand we show that matroidal set systems are in some sense necessary to guarantee uniqueness of equilibria: for every atomic splittable congestion game with at least three players and non-matroidal set systems per player, there is an isomorphic game having multiple equilibria. Our results leave a gap between base orderable matroids and general matroids for which we do not know whether equilibria are unique.     

Optimization problems with color-induced budget constraints

In 1984, Gabow and Tarjan provided a very elegant and fast algorithm for the following problem: given a matroid defined on a red and blue colored ground set, determine a basis of minimum cost among those with k red elements, or decide that no such basis exists. In this paper, we investigate extensions of this problem from ordinary matroids to the more general notion of poset matroids which take precedence constraints on the ground set into account. We show that the problem on general poset matroids becomes -hard, already if the underlying partially ordered set (poset) consists of binary trees of height two. On the positive side, we present two algorithms: a pseudopolynomial one for integer polymatroids, i.e., the case where the poset consists of disjoint chains, and a polynomial algorithm for the problem to determine a minimum cost ideal of size l with k red elements, i.e., the uniform rank-l poset matroid, on series-parallel posets.     

Leader individual differences,situational parameters,and leadership outcomes: A comprehensive review and integration

In this article, we provide a wide-ranging review of recent research on leader individual differences. The review focuses specifically on the explosion of such research in the last decade. The first purpose of this review is to summarize and integrate various conceptual frameworks describing how leader attributes influence leader emergence and leader effectiveness. The second purpose is to provide a comprehensive review of empirical research on this relationship. Also, most prior reviews primarily examined leader personality traits; this review includes a broader array of leader attributes, including cognitive capacities, personality, motives and values, social skills, and knowledge and expertise. The final broad purpose of this paper is to review and integrate situational and contextual parameters into our conceptual framing of leader individual differences. Few, if any, prior reviews have systematically accounted for the critical role of such parameters in cuing, activating, or delimiting the effects of particular leader attributes. We do so in this article.     

Approximation strategy-proof mechanisms for obnoxious facility location on a line

In the facility location game on a line, there are some agents who have fixed locations on the line where an obnoxious facility will be placed. The objective is to maximize the social welfare, e.g., the sum of distances from the facility to all agents. On collecting location information, agents may misreport the locations so as to stay far away from the obnoxious facility. In this paper, strategy-proof mechanisms are designed and the approximation ratio is used to measure the performances of the strategy-proof mechanisms. Two objective functions, maximizing the sum of squares of distances (maxSOS) and maximizing the sum of distances (maxSum), have been considered. For maxSOS, a randomized 5/3-approximated strategy-proof mechanism is proposed, and the lower bound of the approximation ratio is proved to be at least 1.042. For maxSum, the lower bound of the approximation ratio of the randomized strategy-proof mechanism is proved to be 1.077. Moreover, a general model is considered that each agent may have multiple locations on the line. For the objective functions maxSum and maxSOS, both deterministic and randomized strategy-proof mechanisms are investigated, and the deterministic mechanisms are shown to be best possible.     

On tree representations of relations and graphs: symbolic ultrametrics and cograph edge decompositions

Tree representations of (sets of) symmetric binary relations, or equivalently edge-colored undirected graphs, are of central interest, e.g. in phylogenomics. In this context symbolic ultrametrics play a crucial role. Symbolic ultrametrics define an edge-colored complete graph that allows to represent the topology of this graph as a vertex-colored tree. Here, we are interested in the structure and the complexity of certain combinatorial problems resulting from considerations based on symbolic ultrametrics, and on algorithms to solve them.This includes, the characterization of symbolic ultrametrics that additionally distinguishes between edges and non-edges of arbitrary edge-colored graphs G and thus, yielding a tree representation of G, by means of so-called cographs. Moreover, we address the problem of finding “closest” symbolic ultrametrics and show the NP-completeness of the three problems: symbolic ultrametric editing, completion and deletion. Finally, as not all graphs are cographs, and hence, do not have a tree representation, we ask, furthermore, what is the minimum number of cotrees needed to represent the topology of an arbitrary non-cograph G. This is equivalent to find an optimal cograph edge k-decomposition \(\{E_1,\dots ,E_k\}\) of E so that each subgraph \((V,E_i)\) of G is a cograph. We investigate this problem in full detail, resulting in several new open problems, and NP-hardness results.For all optimization problems proven to be NP-hard we will provide integer linear program formulations to solve them.     

Bounds on the domination number of a digraph

A vertex subset S of a digraph D is called a dominating set of D if every vertex not in S is adjacent from at least one vertex in S. The domination number of D, denoted by \(\gamma (D)\), is the minimum cardinality of a dominating set of D. The Slater number \(s\ell (D)\) is the smallest integer t such that t added to the sum of the first t terms of the non-increasing out-degree sequence of D is at least as large as the order of D. For any digraph D of order n with maximum out-degree \(\Delta ^+\), it is known that \(\gamma (D)\ge \lceil n/(\Delta ^++1)\rceil \). We show that \(\gamma (D)\ge s\ell (D)\ge \lceil n/(\Delta ^++1)\rceil \) and the difference between \(s\ell (D)\) and \(\lceil n/(\Delta ^++1)\rceil \) can be arbitrarily large. In particular, for an oriented tree T of order n with \(n_0\) vertices of out-degree 0, we show that \((n-n_0+1)/2\le s\ell (T)\le \gamma (T)\le 2s\ell (T)-1\) and moreover, each value between the lower bound \(s\ell (T)\) and the upper bound \(2s\ell (T)-1\) is attainable by \(\gamma (T)\) for some oriented trees. Further, we characterize the oriented trees T for which \(s\ell (T)=(n-n_0+1)/2\) hold and show that the difference between \(s\ell (T)\) and \((n-n_0+1)/2\) can be arbitrarily large. Some other elementary properties involving the Slater number are also presented.     

Perceived managerial and leadership effectiveness within a Moroccan Higher Education Institution

The purpose of this research was to determine what behaviourally distinguishes effective and ineffective managers within a Moroccan Higher Education Institution (HEI). The critical incident technique (CIT) was the methodology deployed to collect data from participants in terms of how they perceive managers as either effective or ineffective. The collected data (CIs) were subjected to content and thematic analysis that resulted in derived positive and negative behavioural statements (BSs). A total of 42 participants/informants were interviewed and revealed a total of 418 CIs, of which 189 were positive CIs and 229 were negative. The analysis revealed a total of 49 BSs, of which 19 were positive and 30 were negative behavioural indicators. The findings of this investigation bring empirical evidence to understand what and how managers are perceived as effective or ineffective in the Moroccan academic context and, therefore, adds to the literature. The information obtained can also provide rich information/knowledge that can be used as a basis to address the behavioural developmental needs of managers in HEIs. This research adds value by following by following two previous replication studies in a French and a Hungarian HEI; moreover, this study is the first to be conducted in the Moroccan/North African region.