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The purpose of this paper is to investigate the extension of Delaunay refinement algorithms to work directly with a curved geometry in arbitrary dimensional spaces, which is also able to refine geometry pieces of different dimensions altogether.

The extension of Delaunay refinement is based on ideas of the Bowyer‐Watson algorithm and Ruppert algorithm.

The attempt to extend the fundamental ideas of Delaunay refinement to cope with curved geometries led to an algorithm whose performance in practice, regarding speed and mesh quality, is comparable to classical Delaunay refinement for flat geometries. Unfortunately, there are only theoretical guarantees that the refinement itself works under some conditions. No theoretical mesh quality bounds are provided.

A mesh refinement algorithm that deals with curved geometries is a key feature for adaptive mesh generators, so that points are inserted properly in the curved pieces instead of in linear approximations of them. For instance, it is well known that sharp edges are singular points of finite element formulations. This singularity fulfills in practice as mesh is refined around them. Those corners can be rounded up to avoid singularities. Furthermore, with this kind of tool, for instance, a user could start to mesh a disc from a single triangle representing it. Points would be efficiently inserted in the circle as needed during refinement.

This paper introduces the concept of manifold complex and also an extension of Delaunay refinement algorithm to deal with curved geometries.

Theory is needed for a discipline to mature. This research aims to provide a summary analysis of the theories being used in contemporary logistics and supply chain management (SCM) studies.

A comprehensive literature review of articles appearing in five top tier logistics and SCM journals is conducted in order to identify how often theory is used and to classify the specific theories used. An analysis of the theoretical categories is presented to explain the type and frequency of theory usage.

Over 180 specific theories were found within the sampled articles. Theories grouped under the competitive and microeconomics categories made up over 40 per cent of the theoretical incidences. This does not imply all articles utilize theory. The research found that theory was explicitly used in approximately 53 per cent of the sampled articles.

Two implications are central. First, in the minds of editors, reviewers and authors is approximately 53 per cent theory use enough? Literature suggests there continues to be a need for theory‐based research in the discipline. A first step may be to increase our theory use, and to clearly describe the theory being used. Second, the vast majority of theories used in recent logistics and SCM research originated in other disciplines. Growth in the discipline dictates the need for greater internal theory development.

Despite multiple calls for the use of theory in logistics and SCM, little formal research has been produced examining the actual theories being used. This research provides an in‐depth review and analysis of the use of theory in logistics and SCM research during the period 2004‐2009.