Dynamic Capacity Planning and Location of Hierarchical Service Networks Under Service Level Constraints

This paper addresses the problem of joint facility location and capacity planning of hierarchical service networks in order to determine when and where to open/close service units, their capacity and the demand-to-facility allocation. We propose a new hierarchical service network model in which both the facilities and customers have nested hierarchies, i.e., a higher level facility provides all services provided by a lower level facility and a customer requiring a certain level of service will additionally require lower level services. Poisson customer arrivals and random service times are assumed. Each service unit is modeled as an Erlang-loss system and its service level, defined as its customer acceptance probability, is given by the so-called Erlang-loss function. A nonlinear programming model is proposed to minimize the total cost, while keeping the service level of all service units above some given level. Different linearization models of the Erlang-loss function and their properties are proposed. Linearization transforms the nonlinear model into compact mixed integer programs solvable to optimality with standard solvers. Application to a real-life perinatal network is then presented. Note to Practitioners-This paper is motivated by our collaboration with the perinatal network inHauts-de-Seine, Paris, France. It is a network of maternity facilities of different types where at most three levels of services (obstetric, neonatal, and neonatal intensive care) are provided. All facilities provide the lowest level of care: obstetric service. The maternity facilities differ according to the level of service provided. Network shows a nested hierarchical property where a higher level facility provides all services provided by a lower level facility. Each hospital has a limited number of staffed-beds for each service. As the demographic changes, the perinatal network is facing the problem of relocating its perinatal services and adjusting its capacities to match the changing demand. The mathematical models of this paper take into account different options such as opening/closing a service unit, capacity expansion, downsizing, and transfer. The models are used to help decision-makers sorting these decisions to minimize the overall cost of the network without degrading the service level.