A bi-layer optimization approach for a hybrid flow shop scheduling problem involving controllable processing times in the steelmaking industry

• A SCC scheduling problem with controllable processing times is formulated.
• A SCC scheduling problem is decomposed into two tractable subproblems.
• A HDE algorithm is proposed for the parallel machine scheduling subproblem.
• An IBLS heuristic method is proposed to solve the HFS scheduling subproblem.

A steelmaking-continuous casting (SCC) scheduling problem is an example of complex hybrid flow shop scheduling problem (HFSSP) with a strong industrial background. This paper investigates the SCC scheduling problem that involves controllable processing times (CPT) with multiple objectives concerning the total waiting time, earliness/tardiness and adjusting cost. The SCC scheduling problem with CPT is seldom discussed in the existing literature. This study is motivated by the practical situation of a large integrated steel company in which the just-in-time (JIT) and cost-cutting production strategy have become a significant concern. To address this complex HFSSP, the scheduling problem is decomposed into two subproblems: a parallel machine scheduling problem (PMSP) in the last stage and an HFSSP in the upstream stages. First, a hybrid differential evolution (HDE) algorithm combined with a variable neighborhood decomposition search (VNDS) is proposed for the former subproblem. Second, an iterative backward list scheduling (IBLS) algorithm is presented to solve the latter subproblem. The effectiveness of this bi-layer optimization approach is verified by computational experiments on well-designed and real-world scheduling instances. This study provides a new perspective on modeling and solving practical SCC scheduling problems.