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Operations Research: revealing the nature of the problem

In «Operations Research», the most prestigious journal in the field of operations research, published the article «Flexible PMP Approach for Large-Size Cell Formation». We talk to one of the authors - Professor of Higher Mathematics Department at the Faculty of Economics HSE Boris Goldengorin.

Борис ГольденгоринIn «Operations Research», the most prestigious journal in the field of operations research, published the article «Flexible PMP Approach for Large-Size Cell Formation». We talk to one of the authors - Professor of Higher Mathematics Department at the Faculty of Economics HSE Boris Goldengorin.

- Boris Isaakovich in «Operations Research» publish your article «Flexible PMP Approach for Large-Size Cell Formation»
- Yes, this article has two more co-authors: my former Ph.D. student at the University of Groningen (the Netherlands) Dmitry Krushinsky and my colleague in the Department of Operations at the University of Groningen professor Jannes Slomp.

- Let us to refine to which branch of science the journal «Operations Research» belongs?
- Operations Research (OR) in North America, South Africa and Australia, and Operational Research in Europe, is an interdisciplinary branch of applied mathematics and formal science that uses methods such as mathematical modeling, statistics, and algorithms to arrive at optimal or near optimal solutions to complex problems. It is typically concerned with optimizing the maxima (profit, assembly line performance, crop yield, bandwidth, etc) or minima (loss, risk, costs, etc.) of some objective function. Operations research helps management achieve its goals using scientific methods.

- What determines the prestige of this journal?
- It is determined, first of all, the composition of the editorial board, reviewers, strict procedures for reviewing an article and the contribution of the published paper to our profession. Many prestigious journals in applied mathematics have relatively small impact factor greater than 0.5, while at the same time, the impact factor of this journal in 2011 is equal to 1.995. This is perhaps the most prestigious scientific journal in the field of operations research.

- What are the requirements of the journal «Operations Research» to the research results submitted for possible publication?
- Journal seeks to publish results that really reveal the nature of a fundamental problem and make a significant contribution - one that will stand the test of time. Scientific papers include works that define new areas of research, in particular innovative concepts, new fruitful mathematical formulations of a problem, and the development of new techniques to attack well-known and new problems.

- You said "the results reveal the nature of a problem." Please explain what kind of problem in your case, is it? And what was its nature after the "opening"?
- This is the p-median problem. It belongs to the class of allocation problems and allows to model and solve applied problems of plants location, quantitative psychology, telecommunication companies, cluster analysis, optimizing product mix, routing, forming production cells, political regionalization, topological design of computer and phone networks,etc. Like many problems in combinatorial optimization, this problem is easy to state but hard to solve. We have discovered an insightful property – the p-median problem become easily solvable when the number of medians tends to their upper bound.

- What are the future research directions of this publication? And if so, in what areas?
- As follows from the title of this article, it is considered an approach to the formation of manufacturing cells. Synonymous with the concept of a cell is a cluster, or notions similar to partition which might be represented on graphs by means of their well-known structures. Among many promising areas we plan to apply the p-median structures to the analysis of market graphs, as well as to construction of high-quality images useful for the tomography technologies.