A Lexicographic Bi-objective Scheduling Problem from Steel Production Systems

Wire rod and bar rolling is an essential process in a steel production system (SPS). This work considers a lexicographic bi-objective scheduling problem originated from it. As a medium process in SPS, both the impacts of its upstream process, i.e., release time constraints, and the requirements of its downstream process, i.e., due time constraints, on SPS performance, must be considered. The concerned problem aims to minimize the number of tardy tasks as a main objective and total setup time as a secondary one. It is solved via a two-stage method. The first-stage problem is handled with an off-the-shelf optimization software, and the second one with iterated greedy algorithms (IGAs). We compare the performance of IGAs under different strategies and select the best one to solve it. By comparing the experimental results an exact single-objective method's, this paper shows that the proposed method can solve the problem fast with excellent results in terms of the number of tardy tasks and setup time, i.e., the secondary objective, on average. Its usage can result in significant performance improvement in steel production over the existing practice.