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This paper presents a robust approach to solve Hoist Scheduling Problems (HSPs) based on an integration of Constraint Logic Programming (CLP) and Mixed Integer Programming (MIP). By contrast with previous dedicated models and algorithms for solving classes of HSPs, we define only one model and run different solvers. The robust approach is achieved by using a CLP formalism. We show that our models for different classes of industrial HSPs are all based on the same generic model. In our hybrid algorithm search is separated from the handling of constraints. Constraint handling is performed by constraint propagation and linear constraint solving. Search is applied by labelling of boolean and integer variables. Computational experience shows that the hybrid algorithm, combining CLP and MIP solvers, solves classes of HSPs which cannot be handled by previous dedicated algorithms. For example, the hybrid algorithm derives an optimal solution, and proves its optimality, for multiple-hoists scheduling problems.