Combining revenue and equity in capacity allocation of imaging facilities

Because of high procurement and operating costs, imaging facilities (e.g., magnetic resonance imaging (MRI)), are usually critical resources in hospitals. Hospital managers are under high pressure to pursue high utilization of the capacity, which leads to long waiting time for patients. However, different types of patients have different access time targets determined by their priorities according to the urgent levels and payments. The access time target is defined as the maximal amount of time between the appointment date and the examination date. For public hospitals, it is important to manage patient access to critical resources by considering the equity among different types of patients without sacrificing revenue. This paper proposes a nonlinear mixed-integer programming (NMIP) model for allocating the capacity of imaging facilities with the objective of maximizing revenue under the constraints of maintaining equity among different types of patients. The equity constraints are defined as the same access levels for different types of patients and the joint chance constraint for the same service levels in terms of waiting time. To solve this model, each time-slot, rather than the imaging facility, is considered as a server, which leads to an M/D/n queuing model. Based on an analysis of the M/D/n model, an approximation approach is proposed for the NMIP model, and CPLEX is used to solve the approximated model. Extensive numerical experiments based on real data from a large public hospital in Shanghai show the applicability and performance of the proposed model and investigate the impact of different parameters.