Integrated Cutting and Packing Heterogeneous Precast Beams Multiperiod Production Planning Problem

TL;DR

This paper introduces a new integrated planning problem for precast beams, proposing an ILP model and a genetic algorithm, with the latter effectively solving large instances quickly despite challenges in optimality for bigger problems.

Contribution

It presents a novel problem formulation, an ILP model with a tighter lower bound, and a genetic algorithm tailored for large-scale precast beam production planning.

Findings

Exact method works well for small instances.

Genetic algorithm finds good solutions quickly for large instances.

Challenges remain in solving medium and large instances optimally.

Abstract

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.