Multi-product costs and standby capacity derived from queuing theory: the case of Belgian hospitals

Empirical hospital cost function studies can be divided into two categories: studies estimating traditional multi-product cost functions and studies including demand uncertainty (assuming that hospitals provide standby capacity to cope with uncertain demand and stressing that the relationship between the uncertain demand, excess capacity and costs should be investigated). Most studies include (the inverse of) the occupancy rate in a relatively basic cost function. The first contribution of this paper is to incorporate an indicator of reserve capacity into a genuine multi-product cost function. The second contribution is to propose an alternative indicator to proxy the reserve margin. The often used occupancy rate has an important shortcoming: the same occupancy rate can hide different turnaway probabilities and waiting times, obscuring the true degree of reservation quality. Since turnaway probabilities and waiting times are typical queuing theory indicators, an indicator for average waiting time (derived from queuing theory) is incorporated into a proper multi-product cost function to capture the degree of standby capacity into a proper multi-product cost function. The study uses 1997 data on Belgian general care hospitals to estimate a multi-product cost function and calculate cost elasticities, marginal costs and the degree of economies of scale. The results further show that providing standby capacity has a significant impact on total costs.