Capacity Management in Networks: A Structural Estimation Approach for Hospital Inpatient Wards

Problem definition: Addressing capacity management within a multifaceted network of resources is a critical challenge in service operations management. As resources are often shared to serve multiple classes of customers in such systems, customer routing often depends on the congestion levels of these resources, which in turn are affected by customer routing, creating a feedback loop. Consequently, when evaluating the impact of substantial capacity changes in the network, one must account for the complexity resulting from resource sharing, endogenous routing policies, and the feedback loop between routing policies and congestion levels that has the potential to alter the equilibrium of the system. This complexity renders conventional approaches insufficient for an accurate assessment. Methodology/results: To tackle these challenges, we develop a structural estimation approach that relies on two key components. First, we estimate the routing policy via a choice model that allows the routing policy to depend on not only the focal resource’s utilization but all connected resources’ utilization. We adopt a control function approach with instrumental variables to estimate the loads’ effect in routing without bias. Second, we incorporate the estimated routing policy into a queueing network model that captures the detailed system dynamics and evaluates the equilibrium performance of the entire network. We apply our approach to the specific empirical setting of the hospital inpatient ward network. We show that our proposed approach outperforms two alternative models and highlight the importance of accounting for network equilibrium effects when evaluating substantial capacity changes. Managerial implications: We provide prescriptive capacity allocation recommendations to hospital managers. More generally, our findings underscore the importance of a comprehensive understanding of the interdependencies between customer routing decisions and the levels of congestion present at various resources, shedding light on broader strategies for improving the operational performance of service networks. Funding: This work was supported by the Division of Civil, Mechanical and Manufacturing Innovation [Grant 1944209].