A Hybrid Learning–Optimization Framework for the Booking Stays Problem at Summer Resorts via Supervised Variable Fixing

This paper studies the Booking Stays Assignment Problem (BSAP), a large-scale problem in which the Mohammedia Foundation for Social Works of Judges allocates a limited pool of vacation residences among thousands of competing members under priority, quota, preference, and consecutiveness constraints. Our aim is to make the exact solution of this problem both tractable and transparent: we analyze its computational difficulty, accelerate its exact solution, and turn its outcome into an interpretable forecast of each applicant’s chances. Methodologically, we first show that, without its consecutiveness constraints, the BSAP reduces to an efficiently solvable assignment core, so that its difficulty originates in those constraints, and we bound—under an explicit enumeration scheme—the super-exponential overhead they induce. We then recast variable fixing as a supervised binary classification problem over the decision variables: four candidate models (logistic regression, random forest, gradient boosting, and a neural network) are trained on eight seasons of real institutional records (2018–2025), and a confidence threshold pre-fixes the most certain variables while an exact MILP solver resolves the rest. Models are compared on a chronological, out-of-season test (training on 2018–2022, testing on the unseen 2025 season) using dedicated selection measures and proper calibration scores. The main findings confirm a decoupling between the two roles: logistic regression fixes the most variables at zero optimality gap and thus best accelerates the solver, whereas the random forest is the best-calibrated estimator (lowest Brier score and log-loss) and is adopted for the applicant-facing probability. Notably, the neural network, despite its high capacity, is the least well calibrated at the individual level. The resulting framework is transparent, preserves the institution’s priority rules, and provides real-time decision support to both applicants and administrators.