MATHEMATICAL-MODEL AND METHOD OF SEARCHING FOR A LOCAL EXTREMUM FOR THE NONCONVEX ORIENTED POLYGONS ALLOCATION PROBLEM

This work deals with the problem of optimal allocation of objects of a so-called irregular form. The objects are allocated on a ship of give n width and with defects. This problem is insufficiently studied, but it is typical for many industries and is also interesting for developi ng the theory of solving cutting and packing problems. An analytical m odel of the problem using only continuous variables is written in term s of classical mathematical programming, and it is constructed on the basis of the original theory of Phi-functions and structures of linear inequalities. The presented theory allows one to easily describe the conditions of mutual non-overlapping of objects and their allocation i n the stock region. The exact method for searching a local minimum of the problem from any feasible initial point is based on the applicatio n of the active set strategy ideas. A number of examples of solving pr actical problems are considered.