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.
We consider a market graph model of the Russian stock market. To study the peculiarity of the Russian market we construct the market graphs for different time periods from 2007 to 2011. As characteristics of constructed market graphs we use the distribution of correlations, size and structure of maximum cliques, and relationship between return and volume of stocks. Our main finding is that for the Russian market there is a strong connection between the volume of stocks and the structure of maximum cliques for all periods of observations. Namely, the most attractive Russian stocks have a strongest correlation between their returns. At the same time as far as we are aware this phenomenon is not related to the well developed USA stock market.