Two-step approach for scheduling jobs to non-related parallel machines with sequence dependent setup times applying job splitting

Abstract

This paper investigates the problem of manufacturing processes by bar-turning machine. The scenario is modeled as a problem of scheduling jobs to non-related parallel machines with sequence dependent setup times applying batch splitting. In order to optimize this problem, we propose a mixed integer linear programming model (MILP). However, as shown in numerical result, it is limited to solve only small instances. Hence, a two-step approach is presented to solve real-size instances. This method uses a relaxed version of the MILP model proposed, however, allowing solutions with sub-tour. Afterwards, a heuristic algorithm is presented to adjust these solutions. The numerical results analyze 20 instances with different sizes, compositions of demand and set of machines. Some general rules to characterize good solutions were presented after investigating the results. These rules associate the quantity of pieces for each demand and the type of machine used, and the complexity of the piece demanded for the type of machine.