# Heterogeneous Prestressed Precast Beams Multiperiod Production Planning Problem: Modeling and Solution Methods

## TL;DR

This paper introduces a formal model and solution methods for the complex scheduling problem of producing heterogeneous prestressed precast beams, including integer programming models, heuristics, and computational analysis based on real-world data.

## Contribution

It formally defines the HPPBMPP, proves its NP-hardness, and develops four novel integer programming models along with a heuristic and priority rules for effective solutions.

## Key findings

- Models solve small instances optimally
- Heuristic produces high-quality solutions for most cases
- Computational tests validate the models and heuristic

## Abstract

A prestressed precast beam is a type of beam that is stretched with traction elements. A common task in a factory of prestressed precast beams involves fulfilling, within a time horizon, the demand ordered by clients. A typical order includes beams of different lengths and types, with distinct beams potentially requiring different curing periods. We refer to the problem of planning such production as Heterogeneous Prestressed Precast Beams Multiperiod Production Planning (HPPBMPP). We formally define the HPPBMPP, argue its NP-hardness, and introduce four novel integer programming models for its solution and a size reduction heuristic (SRH). We propose six priority rules to produce feasible solutions. We perform computational tests on a set of synthetic instances that are based on data from a real-world scenario and discuss a case study. Our experiments suggest that the models can optimally solve small instances, while the SRH can produce high-quality solutions for most instances.