Three-Step Mathematical Model for Optimizing Rebar Cutting-Stock with Practical Application

Abstract

Theory of operations research is applied in this paper. The minimum total cost of steel reinforcement work was used as the objective function, and a three-step mathematical model to optimize the rebar cutting-stock was developed for building the finished rebars. Model I was applied to determine the whole raw material rebars that build the finished rebar. Models II and III were then applied to obtain the cut rebars needed to form the remaining rebar length of the finished rebar. The optimization results of the three-step model were combined to obtain a rebar cutting-stock list and method. Note the following results: (1) Considering comprehensively the effects of labor and material costs in the models led to the least rebar waste and number of welding spots, and thus the minimum total cost was reached. (2) In Model I, the minimum of cost sum of the rebar waste and welding spot count was taken as the objective to use the longer whole rebars first to minimize cutting and welding operations, and reducing the remaining rebar count reduced the subsequent calculation workload of Models II and III. (3) In model II, a constraint that every rebar section length be restricted to three nonoverlapping cases was imposed, which ensured that welding spots were not located in the midspan of a finished rebar. (4) In the practical case study considered, the rebar waste rate was 0.44%, and the finished rebars including 1 or 2 welding spots accounted for 90% of all finished rebars, which shows that the overall number of welding spots was small. The optimization not only clearly saved the rebar material cost but also decreased the labor cost of cutting and welding.