A MILP model of scheduling physical therapies with coupled operations in a basic setting rehabilitation center

The physical therapy with coupled operations is a main type of treatments in rehabilitation. Such a therapy is consisted of three consecutive operations: preparing, treating and finishing. Preparing and finishing operations occupies a therapist, which forms coupled-operation. To our best knowledge, there is no work about such a special type of coupled operations which makes scheduling therapies more complicated. The current work deals with scheduling physical therapies with coupled operations in a basic setting rehabilitation center, i.e. one therapist, one equipment for each therapy. The operations are analyzed in detail first. Then, a mixed integer linear programming (MILP) model is formulated based on the operation analysis. Finally, a small instance is tested to evaluate the proposed MILP model solved in Gurobi. The results show that the valid of the proposed model.