An Efficient Simulation-based Approach to Ambulance Fleet Allocation and Dynamic Redeployment

1. An Efficient Simulation-based Approach to Ambulance Fleet Allocation and Dynamic Redeployment Yisong Yue (CMU) & Lavanya Marla (CMU) & Ramayya Krishnan (CMU) Ambulance Allocation Evaluating System Performance Theoretical Analysis • Ambulance allocation important EMS problem • Where to place ambulance (when)? • Contributions: • Data-driven simulation • Allocation via simulation • Theoretical guarantees • For a given request log R, and allocation A • Let LR(A) denote the penalty of simulating R using A • E.g., # calls not served within 15 minutes • We evaluate system performance via cost reduction • Given an empirical sample of call logs R1,…,RN • Compute the expected performance via • Static Allocation Goal: find an allocation A with good performance • F is very hard to analyze directly • Interactions between overlapping requests • Define GR(A) = objective of omniscient dispatching • GR(A) ≥ FR(A) • Can be solved via relatively simple IP • GR(A) is monotone submodular! • Optimality guarantees on G also apply to F! • Guarantees via submodularity • Even tighter bounds as well • Can also be extended to dynamic redeployment setting • Ongoing work FR(A) = LR(Ø) - LR(A) Data-Driven Simulation F(A) = ( FR1(A) + … + FRN(A) ) / N • Evaluation most accurate via simulation • Given a sample of requests R, can simulate how any allocation services R • Example: 4 requests, 2 bases • Requirement: best response myopic dispatching Empirical Evaluation Greedy Algorithm • Leveraged historical data of EMS system of Asian city • Built a generative model of requests • 58 base locations, budget of 58 ambulances • Evaluate over 1 week of requests • Three types of penalty functions considered • L1 : graded penalty based on service time • L2 : higher penalty for un-serviced requests • L3 : threshold penalty for 15-min service time Scenario 1: 2 ambulances Scenario 2: 3 ambulances Generative Model for Requests • δF(a|A) = F(A + a) – F(A) • Lazy variant runs in seconds [Leskovec et al., 2007] • Generative model of requests from historical data Static Allocation % serviced in 15 min % not serviced Assumption: distribution of emergency requests is independent of EMS (ambulance) behavior Dynamic Redeployment • Dynamic redeployment requires an allocation policy. • We consider policies that redeploy at regular intervals • E.g., every 30 minutes • We consider myopic redeployment algorithms • Optimize for performance of next interval • Equivalent to mini static allocation problem • Greedy solution • Sample requests for next interval • Run greedy to compute re-allocation Dynamic Allocation % not serviced % serviced in 15 min Submodular Upper Bound is data- dependent bound via submodularity Omniscient-Optimal Upper Bound is tighter bound via extending IP formu- lation for solving omniscient dispatch Theoretical Bounds • Requests sampled as Poisson process • Each sampled request is fully deterministic • Simulating with any allocation is fully deterministic