A Multi-Period Resource Planning Model for a Rehabilitation System

Abstract

A multi-period mathematical optimization formulation is developed to model flow of patients and resources in a rehabilitation system consisting of several treatment alternatives so that the expected total benefit of the system is maximized. A patient classification scheme based on pretreatment characteristics, treatment attrition rates, expected treatment benefits, and treatment cost per week for each treatment alternative, are utilized. The decision variables at each period (the number of veteran and newly arrived patients to be assigned to each treatment) are constrained by the expected number of patients of each type and treatment capacity. The possibility of a change in a patient’s type, as a result of treatment, is taken into account. The constraints relating one period to its predecessor are considered simultaneously, yielding, together with the objective function of total benefit realized by the decision variables over all periods of the planning horizon, one large linear programming problem.