An integer linear programming model of staff retention and termination based on multiattribute utility theory

An integer linear programming formulation was used to model several staffing alternatives available to the director of a recreation therapy department. The utility function of the decision maker was assessed using two attributes of effectiveness: performance and experience. Two utility approximations were obtained for each staff member based upon the average performance rating and number of years of experience both as a recreation therapist and at the facility. The utility obtained was viewed as a proxy for, and a comparative measure of, effectiveness, which considers the criteria of training and experience. The individuals who comprise the most effective combination of therapists, given staff reductions, were obtained by maximizing the sum of staff values. The first constraint set involved a budgetary constraint, coverage constraints, and an EEOC policy restriction. The coverage restriction and the budget were varied to reflect changes in the department resources. The model was validated with the department supervisor for the case of a one-position, 10% budget decrease.