Selection of Reinforcement Steel Bars with Markovian Weldability Distribution against their Boron Content

Abstract

Deciding the functional suitability of reinforcement steel bars for welding operations has a dependence on boron content especially if such bars are made from recycled steel. In this study, a mathematical model is developed to optimize the selection decision of recycled steel bars from steel manufacturers considering a Markovian weldability distribution since the boron distribution in steel is predominantly random. In the given model, a building/fabrication contractor intends to select one of two manufacturers of recycled steel bars basing on the weldability of steel as determined by their boron content selected in equal monthly intervals. A Markov decision process approach is adopted where five states of a Markov chain represent possible states of weldability for steel bars. The boron content is minimized in order to achieve maximum weldability capacity 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 boron composition over the planning horizon.