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.