Mathematical programming models for scheduling multiple cascaded waterway locks

•A cascaded-lock scheduling problem (CLSP) with generic settings is developed.•Two mixed integer programming models are proposed to optimally solve the CLSP.•Numerical experiments confirm the general applicability and effectiveness of the proposed models.•Performances of the proposed two models are compared, with their features analyzed. Two mixed integer programming (MIP) models are proposed to optimally solve the cascaded-lock scheduling problem (CLSP) with generic settings on inland waterways, innovatively from job shop scheduling (JSS) and multi-commodity flow (MCF) perspectives. Real-data-based instances with various traffic properties and lock configurations are employed to test the two proposed models on the branch-and-bound framework, which demonstrate that on average the JSS formulation outperforms MCF. Furthermore, a comparison study conducted between the JSS-based model and an existing MIP model which was proposed for the CLSP with a specific setting proves the superiority of the proposed JSS-based CLSP formulation.