Non-guillotine placement of rectangles into a strip of given width

In this paper an exact method to solve the combinatorial problem of non-guillotine placement of rectangles into a strip is proposed. A mathematical model of the problem is constructed on the basis of the original theory of Φ-functions and structures of linear inequalities. The method for searching for the global extremum which can be reached at a vertex of the feasible region is a combination of combinatorial and continuous optimisation techniques. The means of transition from one connected component of the feasible region to another one is considered.