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 is shown to typically find good-quality solutions for large-sized instances within short computing times.
Highlights
Nowadays, concrete precast production is increasingly trending in constructions sites
We refer to this problem as the Integrated Cutting and Packing Heterogeneous Precast Beams Multiperiod Production Planning Problem (ICP-HPBMPP)
The mathematical model we propose is based on the model by [2], which deals with the cutting stock/leftover problem, and on the model by [1] for the HPBMPP
Summary
Concrete precast production is increasingly trending in constructions sites. We consider the integration into a single production planning problem of the cutting process of bars, or of overlapping bars, which must be packed in the molds for the production of a given demand of beams. We refer to this problem as the Integrated Cutting and Packing Heterogeneous Precast Beams Multiperiod Production Planning Problem (ICP-HPBMPP). The production cost with an optimized process will be lower, which may lead to a reduction of the final product’s price, increasing competitiveness It is argued in [1] that the HPBMPP is NP-hard since it includes, as a particular case, the classical onedimensional cutting stock problem.
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