Analyzing economies of scale and scope in hospitals by use of case mix planning

This study analyzes the effect of economies of scale and scope on the optimal case mix of a hospital or hospital system. With respect to the ideal volume and patient composition, the goal is to evaluate (i) the impact of changes in the efficiency of resource use with increasing scale, and (ii) to determine the potential effects of spreading fixed costs over a greater number of patients. The problem is formulated as a non-linear mixed integer program. It turns out that this non-linear program is too difficult to be solved with standard software. As an alternative, an iterative procedure using piecewise linear approximations to derive lower and upper bounds is proposed and shown to converge to the optimum. The procedure is applied using a public database on German hospital costs and performance statistics. Results indicate that changes in the efficiency of resource use with increasing scale have a considerable impact if similar services can be consolidated, e.g., among different departments. However, if the scope for decision-making regarding the case mix of a hospital is limited, such changes may be negligible.