Solving the patient admission scheduling problem using constraint aggregation
本文提出一种两阶段优化方法，通过约束聚合缩小整数规划模型规模，在13个基准实例上为6个实例找到更优解，并缩短了已知最优解的计算时间。
Patient admission scheduling (PAS) consists of assigning patients to beds over a planning horizon to maximize treatment efficiency, patient satisfaction, and hospital utilization while meeting all necessary medical constraints and considering patient preferences as much as possible. There are several different variants of the PAS problem in the literature, which differ mainly in the constraints that must be satisfied (hard) or can be violated (soft). Due to the intrinsic difficulty of the PAS problem, solving large integer programming (IP) models to optimality is challenging. In this paper, we consider the widely studied variant of the PAS problem that has the maximum number of soft constraints, and focus on how to reduce the size of IP formulations of the PAS problem to improve the solving efficiency. We employ a two-stage optimization method where the first stage builds reduced models by constraint aggregation to improve the typical formulation of the PAS problem. Experimental results on the 13 benchmark instances in the literature indicate that our method can obtain new improved solutions (new upper bounds) for 6 instances, including one proven optimal solution. For the 5 other instances whose optimal solutions are known, our approach can reach these known optimal solutions in a shorter computation time compared to the existing methods. In addition, we apply our method to the original PAS problem, which has the maximum number of hard constraints, and perform computational experiments on the same 13 benchmark instances. Our method yields 5 new best solutions and proves optimality for 6 instances.