Review of “Cell formation in industrial engineering: theory, algorithms and experiments” by Boris Goldengorin, Dmitry Krushinsky, Panos M. Pardalos
A review of the book in two perspectives: engineering design and data analysis.
One of the goals of the first edition of this book back in 2005 was to present a coherent theory for K-Means partitioning and Ward hierarchical clustering. This theory leads to effective data pre-processing options, clustering algorithms and interpretation aids, as well as to firm relations to other areas of data analysis. The goal of this second edition is to consolidate, strengthen and extend this island of understanding in the light of recent developments. Moreover, the material on validation and interpretation of clusters is updated with a system better reflecting the current state of the art and with our recent ``lifting in taxonomies'' approach. The structure of the book has been streamlined by adding two Chapters: ``Similarity Clustering'' and ``Validation and Interpretation'', while removing two chapters: ``Different Clustering Approaches'' and ``General Issues.'' The Chapter on Mathematics of the data recovery approach, in a much extended version, almost doubled in size, now concludes the book. Parts of the removed chapters are integrated within the new structure. The change has added a hundred pages and a couple of dozen examples to the text and, in fact, transformed it into a different species of a book. In the first edition, the book had a Russian doll structure, with a core and a couple of nested shells around. Now it is a linear structure presentation of the data recovery clustering.
Lately, the problem of cell formation (CF) has gained a lot of attention in the industrial engineering literature. Since it was formulated (more than 50 years ago), the problem has incorporated additional industrial factors and constraints while its solution methods have been constantly improving in terms of the solution quality and CPU times. However, despite all the efforts made, the available solution methods (including those for a popular model based on the p-median problem, PMP) are prone to two major types of errors. The first error (the modeling one) occurs when the intended objective function of the CF (as a rule, verbally formulated) is substituted by the objective function of the PMP. The second error (the algorithmic one) occurs as a direct result of applying a heuristic for solving the PMP. In this paper we show that for instances that make sense in practice, the modeling error induced by the PMP is negligible. We exclude the algorithmic error completely by solving the adjusted pseudo-Boolean formulation of the PMP exactly, which takes less than one second on a general-purpose PC and software. Our experimental study shows that the PMP-based model produces high-quality cells and in most cases outperforms several contemporary approaches.
In this chapter, we introduce a new heuristic for Cell Formation Problem in its most general formulation with grouping efficiency as an objective function. Suggested approach applies an improvement procedure to obtain solutions with high grouping efficiency. This procedure is repeated until efficiency can be increased for randomly generated configurations of cells. We consider our preliminary results for 10 popular benchmark instances taken from the literature. Also source instances with the solutions we got can be found in the Appendix.
Despite the long history of the cell formation problem (CF) and availability of dozens of approaches, very few of them explicitly optimize the objective of cell formation. These scarce approaches usually lead to intractable formulations that can be solved only heuristically for practical instances. In contrast, we show that CF can be explicitly modelled via the minimum multicut problem and solved to optimality in practice (for moderately sized instances). We consider several real-world constraints that can be included into the proposed formulations and provide experimental results with real manufacturing data.
In this paper we describe the cluster modification for the method of conjugated interactions for resource allocation in real time. In contrast to the original method, this modification allows to guarantee an arbitrarily high stability of the structure of resource allocation regardless of the volatile context of solving the problem.
This article examines the evolution of the significance of cluster territories in resource - driven economies. Authors provides an analysis of factors in turning a territory into a habitat for an industrial cluster. Authors proposes stages in transforming an industrial cluster into an innovation cluster based on saturating the base territory with spatially affined production and scientific units, strong direct and indirect relations, and intensive knowledge flows. The outcome of geographic concentration is expected to be the cluster synergy effects, which "turns into" the cumulative territory effect with reflection in positive social - economic processes. Authors have conducted the testing of particular cluster territories for the intensity of using a cluster territory.
The problem of management of the nonlinear object which is exposed to impact of uncontrollable indignations, is considered in a key of differential game. Synthesis of optimum managements is made with application of transformation of the nonlinear equation of initial object in the differential equation with the parameters depending on a condition. The square-law functional of quality allows to formulate synthesis conditions in the form of need of search of solutions of the equation of Rikkati. The solution of the equation of Rikkati with the parameters depending on a condition, is in a symbolical view with application of algebraic methods that allows to generalize a number of earlier published theoretical results, to receive rather constructive decisions in a number of statements of problems of management.
The article is based upon the fact that the growing demand for master data management systems has not yet produced a commonly accepted metodology for their design and development/ The article offers two mathematical models? that allow a master data management systems designer a way to formally describe their system before development and verify the system quality by measurements? unique to master data management systems.