Optimal spares allocation to an exchangeable-item repair system with tolerable wait

In a multi-location, exchangeable-item repair system with spares, the expected waiting time and the fill rate measures are oftentimes used as the optimization criteria for the spares allocation problem. These measures, however, do not take into account that customers will tolerate a reasonable delay and therefore, the firm does not incur reputation costs if customers wait less than their tolerable wait. Accordingly, we generalize the expected waiting time and fill rate measures to reflect customer patience. These generalized measures are termed the truncated waiting time and the window fill rate, respectively. We develop efficient algorithms to solve the problem for each of the criteria and demonstrate how incorporating customer patience provides considerable savings and profoundly affects the optimal spares allocation.