Optimization of the retail steel distribution industry

The present work proposes new heuristics and algorithms for the 3D Cutting and Packing class of problems. Specifically the cutting stock problem and a real-world application from the retail steel distribution industry are addressed. The problem being addressed for the retail steel distribution industry is the retail steel cutting problem, which is how to cut steel in order to satisfy the customized orders. Both of the problems have to meet the guillotine cut constraint, i.e. each cut has to be complete or edge-to-edge. Different types of Cutting and Packing problems were studied in order to cope with all the constraints and specificities of the retail steel cutting problem. This real-world problem is a mix of several theoretical Cutting and Packing class of problems becoming thus too hard to define the problem as only one. However, the cutting stock problem is the one that better describes the retail steel cutting problem and it was used in order to validate the developed algorithms. A study of the available algorithms in the literature for this class of problems was done in order to find the most suitable one for the addressed problems. Nevertheless, the best algorithms found, had to be extended to the three dimensional problem. Two algorithms are proposed in this study: a deterministic 3D packing heuristic algorithm based on Extreme Points heuristic and an Ant Colony Optimization algorithm based on the packing heuristic. The guillotine cut is assessed using two new proposed methods. One is concerned with the optimality of the used space using virtual cuts (open guillotine cut). The other depends entirely on the first set of decisions as the cuts cannot be changed. Heuristics for the packing orientation and direction or for the cutting decision are also proposed. For the cutting stock problem it was possible to improve the results in three benchmarks used in the literature. Two found the optimal value with the deterministic packing algorithm and one found a better solution than the one found in the literature, using the Ant Colony Optimization. For the retail steel cutting problem it was possible to reduce the scrap metal to an insignificant value (0.5%) with any of the proposed algorithms compared to the solution provided by F.Ramada (18%) . Index Terms — Cutting and Packing, Cutting Stock Problem, Heuristics, Metaheuristics, Guillotine cut, Retail steel distribution