Integrated Cutting and Packing Heterogeneous Precast Beams Multiperiod Production Planning Problem
This addresses a domain-specific optimization problem in construction manufacturing, with incremental improvements in solution methods.
The paper tackles the integrated cutting and packing problem for heterogeneous precast beams in multiperiod production planning by proposing an integer linear programming model and a genetic algorithm, with the genetic algorithm finding good-quality solutions for large instances quickly, though exact methods struggle with medium and large problems.
We introduce a novel variant of cutting production planning problems named Integrated Cutting and Packing Heterogeneous Precast Beams Multiperiod Production Planning (ICP-HPBMPP). We propose an integer linear programming model for the ICP-HPBMPP, as well as a lower bound for its optimal objective function value, which is empirically shown to be closer to the optimal solution value than the bound obtained from the linear relaxation of the model. We also propose a genetic algorithm approach for the ICP-HPBMPP as an alternative solution method. We discuss computational experiments and propose a parameterization for the genetic algorithm using D-optimal experimental design. We observe good performance of the exact approach when solving small-sized instances, although there are difficulties in finding optimal solutions for medium and large-sized problems, or even in finding feasible solutions for large instances. On the other hand, the genetic algorithm could find good-quality solutions for large-sized instances within short computing times.