Modeling Selection Criteria for Reinforcement Steel Bars with Stochastic Carbon Equivalent distribution

Abstract

Deciding the functional suitability of recycled steel using carbon equivalent (CE) and strength can be misleading since the formulae used to determine CE do not capture many of the elements that play a decisive role in establishing steel values. In this study, a mathematical model is developed to optimize the selection decision from a steel manufacturer considering a stochastic CE distribution. In the given model, a building/fabrication contractor intends to select one of two manufacturers of recycled steel bars basing on CE as determined by the IIW formula and strength values selected in equal monthly intervals. A Markov decision process approach is adopted where three states of a Markov chain represent possible states of CE of steel bars. The ultimate strength, σ u, of steel is maximized for minimum CE where the decision to select the best steel is made using dynamic programming over a finite period planning horizon. A numerical example demonstrates the existence of an optimal state-dependent selection decision and strength of steel over the planning horizon.