Book review “Cell formation in industrial engineering: theory, algorithms and experiments” by Boris Goldengorin, Dmitry Krushinsky, Panos M. Pardalos

Abstract

When I saw the title of the book, I thought of that as another sortie at bioinformatics by the operations research community. Indeed by googling “Cell formation” one gets within a lot of stuff on the biological cell processes. What a group of combinatorial optimization experts can do to advance a murky business of life developments? Yet by looking at the intro, I see the book is on “industrial cell formation”, which is a quite different business. It appears the cell formation problem (CFP) here belongs in a growing field of research related to the issues of partitioning a set of technology units in clusters that concentrate as many operations as possible within themselves so that those remaining in-between are minimized. I cannot help but bring inmymemories related to this “discovery”. That was exactly the problem posed before me by Arkady Gelman who unexpectedly entered my office in the Summer 1967 at which I, a fresh PhD in ComputationalMathematics, was trying to penetrate the mathematics of competitive equilibrium and fixed point theorems. This was the starting point of my lifelong addiction to cluster analysis research. Back then I formalized the Gelman’s problem as of finding a partition with the maximum within cluster summary similarities or, equivalently, the minimum between-cluster summary similarities. Jointly with my only collaborator of that time, late Volodia Kupershtokh (1945–2001), we came to the conclusion that the problem as is, at nonnegative similarities, has trivial solutions only. One way to go was to restrict ourselves with pre-specified cluster cardinalities at which we came up with what later was called Kernighan-Lin algorithm, and estimates that hold “almost always” ([1], Our first results: [2]). Another way tomove onwas foundwhenwe noticed that the problem