Robust optimization for integrated scrap steel charge considering uncertain metal elements concentrations and production scheduling under time-of-use electricity tariff

Under the background of time-of-use electricity tariff, the problems of scrap steel charge optimization considering metal elements concentrations uncertainty and scrap steel melt shop production scheduling optimization are integrally studied in this paper using robust optimization approaches. First, taking the parallel electric arc furnaces melt shop as the research object, this paper constructs a robust optimization model about integrated scrap steel charge considering uncertain metal elements concentrations and production scheduling under time-of-use electricity tariff applying a block modeling method. Then, based on the assumptions that the random parameter values of scrap steel metal elements concentrations are distributed in the "bounded uncertainty" set and "bounded symmetric uncertainty" set respectively, the robust optimization model is transformed into two deterministic counterpart models. Finally, Cplex software is used to solve the nominal model and two deterministic counterpart models, the results of which are also compared with two-stage optimization strategy results, indicating the feasibility and effectiveness of the models. Meanwhile, the impacts of uncertainty of metal elements concentrations on production costs, the impacts of time-of-use electricity tariff on production scheduling, and the impacts of electricity tariff fluctuations on the consumption of scrap steels and ferroalloys and the number of setups are analyzed.