We present an approximate dynamic programming approach for making ambulance redeployment decisions in an emergency medical service system. The primary decision is where we should redeploy idle ambulances so as to maximize the number of calls reached within a given delay threshold. We begin by formulating this problem as a dynamic program. To deal with the high-dimensional and uncountable state space in the dynamic program, we construct approximations to the value functions that are parameterized by a small number of parameters. We tune the parameters of the value function approximations using simulated cost trajectories of the system. Computational experiments demonstrate the performance of the approach on emergency medical service systems in two metropolitan areas. We report practically significant improvements in performance relative to benchmark static policies.

In this paper we consider approximate dynamic programming methods for ambulance redeployment. We first demonstrate through simple examples how typical value function fitting techniques, such as approximate policy iteration and linear programming, may not be able to locate a high-quality policy even when the value function approximation architecture is rich enough to provide the optimal policy. To make up for this potential shortcoming, we show how to use direct search methods to tune the parameters in a value function approximation architecture so as to obtain high-quality policies. Direct search is computationally intensive. We therefore use a post-decision state dynamic programming formulation of ambulance redeployment that, together with direct search, requires far less computation with no noticeable performance loss. We provide further theoretical support for the post-decision state formulation of the ambulance-deployment problem by showing that this formulation can be obtained through a limiting argument on the original dynamic programming formulation.

Ambulance redeployment is the practice of repositioning ambulance fleets in real time in an attempt to reduce response times to future calls. When redeployment decisions are based on real-time information on the status and location of ambulances, the process is called system-status management. An important performance measure is the long-run fraction of calls with response times over some time threshold. We construct a lower bound on this performance measure that holds for nearly any ambulance redeployment policy through comparison methods for queues. The computation of the bound involves solving a number of integer programs and then simulating a multiserver queue. This work originated when one of the authors was asked to analyze a response to a request-for-proposals (RFP) for ambulance services in a county in North America.

In this paper we consider approximate dynamic programming methods for ambulance redeployment. We first demonstrate through simple examples how typical value function fitting techniques, such as approximate policy iteration and linear programming, may not be able to locate a high-quality policy even when the value function approximation architecture is rich enough to provide the optimal policy. To make up for this potential shortcoming, we show how to use direct search methods to tune the parameters in a value function approximation architecture so as to obtain high-quality policies. Direct search is computationally intensive. We therefore use a post-decision state dynamic programming formulation of ambulance redeployment that, together with direct search, requires far less computation with no noticeable performance loss. We provide further theoretical support for the post-decision state formulation of the ambulance-deployment problem by showing that this formulation can be obtained through a limiting argument on the original dynamic programming formulation.1. Introduction. Emergency medical service (EMS) providers are tasked with staffing and positioning emergency vehicles to supply a region with emergency medical care and ensure short emergency response times. Large operating costs and increasing numbers of emergency calls (henceforth "calls") make this a demanding task. One method commonly used to reduce response times to calls is known as ambulance redeployment. Ambulance redeployment, also known as move-up or system-status management, is the strategy of relocating idle ambulances in real time to minimize response times for future calls. When making ambulance redeployment decisions it is necessary to take into account the current state of the system, which may include the position and operating status of ambulances in the fleet, the number and nature of calls that are queued for service and external factors such as traffic jams and weather conditions. Furthermore, the system evolves under uncertainty and the probability distributions for where and when future calls are likely to arrive influence how the ambulances should be