Contributions to the multiperiod production planning of heterogeneous precast beams

Abstract

In this work, we introduce two novel variants of cutting scheduling problems named Heterogeneous Prestressed Precast Beam Multiperiod Production Planning (HPPBMPP) and Integrated Cutting and Packing Heterogeneous Precast Beam Multiperiod Production Planning (ICP-HPBMPP). Concrete precast beams are those which are cast away from the construction site in a controlled environment and ideal conditions, whilst a prestressed precast beam is a type of concrete precast beams that is stretched with traction elements in order to improve its resistance and behavior in service. Both kinds of beams can be of different lengths, types, and potentially require different curing times. The HPPBMPP consists of planning the usage of the available set of molds within a given time horizon to fulfill a given demand of prestressed precast beams. On the other hand, the ICP-HPBMPP addresses the HPPBMPP applied to precast beams integrated to the cutting phase of bars that are used in the production of such beams. In this scenario, one must take into consideration the generation and the use of leftovers, as well as the possibility of dealing with overlapping bars, i.e., bars that are assembled by connecting two existing bars of smaller sizes. We propose integer linear programming (ILP) models for both problems, in addition to alternative solution methods, such as size-reduction heuristics, priority rules, and genetic algorithms. We argue the NP-hardness of both problems and explore some of their properties, including lower bounds for optimal objective function values and the use of maximal patterns. We discuss the results of computational tests with the exact solution of the ILP models and the alternative solution methods proposed. We conclude with a discussion of the relative merits of the proposed approaches in terms of solution quality. We infer that the proposed size reduction heuristic and genetic algorithms are good alternatives to ILP models producing good solutions with lower computing time for both problems.