Bi-objective scheduling of physical therapy treatments with coupled operations for inpatients in rehabilitation departments

In recent years, the field of physical therapy has experienced significant growth, particularly due to the impact of the Covid-19 pandemic. However, the capacity of rehabilitation services remains inadequate. This current study deals with scheduling physical therapies with coupled operations and multiple resources in rehabilitation departments, considering bi-objective optimization by minimizing both makespan and waiting time. Based on detailed analysis of practical operations, a mixed integer linear programming model is formulated. For smallsize instances, optimal solutions can be obtained using software such as Gurobi. To handle large instances, a compound NSGA-II algorithm (CNSGA-II) is proposed. CNSGA-II consists of First-NSGA-II and Second-NSGA-II, which are associated with patient sequences and their respective treatments. Furthermore, practical heuristics are used to improve the initial solutions for CNSGA-II. The results of a real -work instance show that makespan is reduced by approximately 8.0%-10.8% and the maximum waiting time is reduced by about 26.4%-30.0%, comparing to the Queue Length Priority Algorithm commonly used in practice. The proposed CNSGA-II is further assessed using randomly generated instances and compared to MOEA/D and NSGA-II based on HV and IGD metrics. The results indicate the superior performance and effectiveness of the proposed CNSGA-II algorithm.