Models and Algorithms for Solving Large-Scale Scheduling Problems in Production and Hydropower Applications

Scheduling is critical in various industrial applications, ensuring the timely achievement and the efficient utilization of resources. While typically studied in production and manufacturing, scheduling problems have broader relevance. This dissertation presents scalable algorithms for large-scale scheduling problems in production planning and hydropower. The proposed Mathematical programming techniques help solve three problems: hydropower scheduling in single- and multiple-reservoir river systems, and a dual-resource scheduling problem. For hydropower scheduling, models optimize water release at reservoirs and dams to maximize power generation. The model includes socioeconomic dynamic goals for food, energy, and water demand, while also considering realistic potential factors like reservoir characteristics, water routing rules, and power production laws, among others. The approach discretizes water levels, simplifies nonconvex dynamics, and produces user-friendly operational curves for release guidance. Solutions employ large-scale integer linear programs and scalable decomposition algorithms. Real data from the Lower Mekong Basin is used to test these approaches. The dual-resource problem focuses on scheduling jobs requiring both machine and worker resources. Skilled workers handle one job at a time and travel within the facility. Formulated as a mixed-integer linear program with disjunctive constraints, the model prevents simultaneous task execution on the same machine or by the same worker. A decomposition approach treats disjunctive constraints as feasibility cuts added when violated. Acceleration techniques construct upper bounds using partial schedules from the branch-and-bound tree, which are also used to generate optimality cuts. These cuts progressively tighten the formulation, aiming to reduce the solution time. This dissertation presents scalable algorithms for large-scale scheduling problems in production planning and hydropower. Mathematical programming techniques, including decomposition and cutting plane algorithms, solve these problems effectively. The hydropower scheduling models optimize water release for maximum generation, while the dual-resource problem ensures efficient allocation of machine and worker resources. Real data and acceleration techniques enhance the solutions' practicality and efficiency.