Purchasing Organization and Design: A Literature Review

This paper presents the results of a comprehensive literature review of the organization of purchasing covering the period from 1967 to 2009. The review provides a structured overview of prior research topics and findings and identifies gaps in the existing literature that may be addressed in future research. The intention of the review is to a) synthesize prior research, b) provide researchers with a structural framework on which future research on the organization of purchasing may be oriented, and c) suggest promising areas for future research.purchasing, supply, procurement, organization, institutional structure, structure, institution, design, performance, literature review

Designing as Interpretation

The paper suggests an interpretative approach to the empirical study of design processes. Design processes are conceived as social processes of interpretation and construction of meaning, and potentially of context generation. In contrast to models which conceive designing as a goal-directed process, an interpretative approach suggests a methodological reorientation. It assumes that design goals are more or less incomplete and vague at the beginning of a design process and are interpreted in contexts and in part are created by designers in the design process on the basis of their experience, embodied skills, and practices. The interpretative paradigm in design research seeks to observe, investigate, and describe practices that designers use in the process. Rather than attempting to determine and prescribe how practitioners ought to do their work, the research question is on how work is actually done - how interpretation is achieved by designers in particular design processes. An extract is analysed in some detail in the paper. These data are taken from the transcript of a case study of a design process in practice. Sociological and socio-linguistic (‘sensitizing’) concepts such as frames and contexts are adopted to describe and analyze some practices observed in the episodes. The paper focuses on an aspect of designing – various forms of involvement and stances designers’ take on in the meaning making process of interpretative design work. Interpretative analysis takes into account designers’ alignments which constitute “participation frameworks” and ground designers’ multimodal practices in different media (language, drawing, gesture). Goffman’s (1981) concept of “footing” is used to reveal more subtle shifts in stances that designers take in designing. Investigation of referential practices designers use in some utterances in the observed design conversation suggests that designers step into, displace, and position themselves in transformed, “keyed” situations to experience the solicitations of design situations more directly and to take the role of others as well as the role of objects. These practices appear to be part of designers’ ability to construct meaning by establishing perspectives and getting “maximal grip” on design situations so as to exert their skills. Analysis of types of stances designers take in an observed design process, some of which addressed in the paper, may provide a way to describe an aspect of designers’ artistry and to characterize the particularities of unique design processes. The suggested approach is intended to contribute to a better theoretical understanding of designing and to the methodology of design research as an ‘epistemology of practice’. Interpretative analysis also aims to provide description of designers’ practices which may, as its practical benefits, contribute to ‘the reflective turn’ in design research. Keywords: Design Research Methodology; Design Practices; Framing; Case Study</p

On the ff-matching polytope and the fractional ff-chromatic index

Our motivation is the question of how similar the $f$-colouring problem is to the classic edge-colouring problem, particularly with regard to graph parameters. In 2010, Zhang, Yu, and Liu gave a new description of the $f$-matching polytope and derived a formula for the fractional $f$-chromatic index, stating that the fractional $f$-chromatic index equals the maximum of the fractional maximum $f$-degree and the fractional $f$-density. Unfortunately, this formula is incorrect. We present counterexamples for both the description of the $f$-matching polytope and the formula for the fractional $f$-chromatic index. Finally, we prove a short lemma concerning the generalization of Goldberg's conjecture

Euler tours in hypergraphs

We show that a quasirandom $k$-uniform hypergraph $G$ has a tight Euler tour subject to the necessary condition that $k$ divides all vertex degrees. The case when $G$ is complete confirms a conjecture of Chung, Diaconis and Graham from 1989 on the existence of universal cycles for the $k$-subsets of an $n$-set.Comment: version accepted for publication in Combinatoric

On the decomposition threshold of a given graph

We study the $F$-decomposition threshold $\delta_F$ for a given graph $F$. Here an $F$-decomposition of a graph $G$ is a collection of edge-disjoint copies of $F$ in $G$ which together cover every edge of $G$. (Such an $F$-decomposition can only exist if $G$ is $F$-divisible, i.e. if $e(F)\mid e(G)$ and each vertex degree of $G$ can be expressed as a linear combination of the vertex degrees of $F$.) The $F$-decomposition threshold $\delta_F$ is the smallest value ensuring that an $F$-divisible graph $G$ on $n$ vertices with $\delta(G)\ge(\delta_F+o(1))n$ has an $F$-decomposition. Our main results imply the following for a given graph $F$, where $\delta_F^\ast$ is the fractional version of $\delta_F$ and $\chi:=\chi(F)$: (i) $\delta_F\le \max\{\delta_F^\ast,1-1/(\chi+1)\}$; (ii) if $\chi\ge 5$, then $\delta_F\in\{\delta_F^{\ast},1-1/\chi,1-1/(\chi+1)\}$; (iii) we determine $\delta_F$ if $F$ is bipartite. In particular, (i) implies that $\delta_{K_r}=\delta^\ast_{K_r}$. Our proof involves further developments of the recent `iterative' absorbing approach.Comment: Final version, to appear in the Journal of Combinatorial Theory, Series

Resolution of the Oberwolfach problem

The Oberwolfach problem, posed by Ringel in 1967, asks for a decomposition of $K_{2n+1}$ into edge-disjoint copies of a given $2$-factor. We show that this can be achieved for all large $n$. We actually prove a significantly more general result, which allows for decompositions into more general types of factors. In particular, this also resolves the Hamilton-Waterloo problem for large $n$.Comment: 28 page

Optimal path and cycle decompositions of dense quasirandom graphs

Motivated by longstanding conjectures regarding decompositions of graphs into paths and cycles, we prove the following optimal decomposition results for random graphs. Let $0<p<1$ be constant and let $G\sim G_{n,p}$. Let $odd(G)$ be the number of odd degree vertices in $G$. Then a.a.s. the following hold: (i) $G$ can be decomposed into $\lfloor\Delta(G)/2\rfloor$ cycles and a matching of size $odd(G)/2$. (ii) $G$ can be decomposed into $\max\{odd(G)/2,\lceil\Delta(G)/2\rceil\}$ paths. (iii) $G$ can be decomposed into $\lceil\Delta(G)/2\rceil$ linear forests. Each of these bounds is best possible. We actually derive (i)--(iii) from `quasirandom' versions of our results. In that context, we also determine the edge chromatic number of a given dense quasirandom graph of even order. For all these results, our main tool is a result on Hamilton decompositions of robust expanders by K\"uhn and Osthus.Comment: Some typos from the first version have been correcte