Decomposition Method for New Single-Machine Scheduling Problems from Steel Production Systems

Production scheduling is a crucial task in modern steel plants. The scheduling of a wire rod and bar rolling process is challenging in many steel plants, which has a direct impact on their production efficiency and profit. This article studies a new single-machine scheduling problem with sequence-dependent setup time, release time, and due time constraints originated from a wire rod and bar rolling process in steel plants. In this problem, jobs have been assigned to batches in advance. The objective is to schedule the batches and jobs on continuous time to minimize the number of late jobs. A mixed-integer program is created as a baseline model. A baseline method is used to solve this NP-hard problem by solving the baseline model. We further design a two-stage decomposition method after analyzing the characteristics of this problem. Both actual and simulated instances with varying sizes are solved by using the proposed methods. The results demonstrate that the baseline method can only solve some small-scale cases, while the decomposition method can solve all small-scale cases and some medium-scale cases. Finally, we reveal the impacts of different instances on the performance of the proposed decomposition method. Note to Practitioners-This article deals with a new single-machine scheduling problem arising from an industrial wire rod and bar rolling process. A baseline method is given to tackle this problem by solving an established mixed-integer program. Afterward, a two-stage decomposition method is proposed such that an industrial size problem can be solved. Computational results of both actual and simulated cases show that it is more efficient than the baseline method in solving the scheduling problem. It can get an optimal solution of the concerned problem with one-week-scale batches and jobs in short time, thereby proving the readiness to put it in industrial use.