An Efficient Simulation-based Approach to Ambulance Fleet Allocation and Dynamic Redeployment Yisong Yue (CMU) & Lavanya Marla (CMU) & Ramayya Krishnan (CMU) Data-Driven Simulation • Evaluation most accurate via simulation • Given a sample of requests R, can simulate how any allocation services R • Example: 4 requests, 2 bases Scenario 1: 2 ambulances Scenario 2: 3 ambulances Ambulance Allocation • Ambulance allocation important EMS problem • Where to place ambulance (when)? • Contributions: • Data-driven simulation • Allocation via simulation • Theoretical guarantees Generative Model for Requests • Generative model of requests from historical data Assumption: distribution of emergency requests is independent of EMS (ambulance) behavior • Requests sampled as Poisson process • Each sampled request is fully deterministic • Simulating with any allocation is fully deterministic Evaluating System Performance • For a given request log R, and allocation A • Let L R (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 R 1 ,…,R N • Compute the expected performance via F R (A) = L R (Ø) - L R (A) F(A) = ( F R1 (A) + … + F RN (A) ) / N Greedy Algorithm • δ F (a|A) = F(A + a) – F(A) • Lazy variant runs in seconds [Leskovec et al., 2007] 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 Theoretical Analysis • F is very hard to analyze directly • Interactions between overlapping requests • Define G R (A) = objective of omniscient dispatching • G R (A) ≥ F R (A) • Can be solved via relatively simple IP • G R (A) is monotone submodular! • Optimality guarantees on G also apply to F! • Guarantees via submodularity Empirical Evaluation • 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 • L 1 : graded penalty based on service time • L 2 : higher penalty for un-serviced requests • L 3 : threshold penalty for 15-min service time % serviced in 15 min % not serviced Static Allocation Dynamic Allocation % serviced in 15 min % not serviced Theoretical Bounds Submodular Upper Bound is data- dependent bound via submodularity Omniscient-Optimal Upper Bound is tighter bound via extending IP formu lation for solving omniscient dispat

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

Download PPTX Report

Upload
fynn
View
69
Download
1

Tags:

Embed Size (px)

DESCRIPTION

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 - PowerPoint PPT Presentation

Citation preview

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

Yisong Yue (CMU) & Lavanya Marla (CMU) & Ramayya Krishnan (CMU)

Data-Driven Simulation• 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 dispatchingScenario 1: 2 ambulances Scenario 2: 3 ambulances

Ambulance Allocation• Ambulance allocation important EMS problem

• Where to place ambulance (when)?• Contributions:

• Data-driven simulation• Allocation via simulation• Theoretical guarantees

Generative Model for Requests• Generative model of requests from historical data

Assumption: distribution of emergency requestsis independent of EMS (ambulance) behavior

• Requests sampled as Poisson process• Each sampled request is fully deterministic • Simulating with any allocation is fully deterministic

Evaluating System Performance• 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

FR(A) = LR(Ø) - LR(A)

F(A) = ( FR1(A) + … + FRN(A) ) / N

Greedy Algorithm

• δF(a|A) = F(A + a) – F(A)• Lazy variant runs in seconds [Leskovec et al., 2007]

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

Theoretical Analysis• 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

Empirical Evaluation• 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

% se

rvic

ed in

min

% n

ot se

rvic

Stati

cAl

loca

tion