Fleet Allocation and Dynamic Redeployment Yisong Yue CMU amp Lavanya Marla CMU amp Ramayya Krishnan CMU DataDriven Simulation Evaluation most accurate via simulation Given a sample of requests R can simulate how any allocation services R ID: 383180
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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 basesRequirement: best response myopic dispatching
Scenario 1: 2 ambulances
Scenario 2:
3
ambulances
Ambulance Allocation
Ambulance allocation important EMS problem
Where to place ambulance (when)?Contributions:Data-driven simulationAllocation via simulationTheoretical 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 processEach 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 AE.g., # calls not served within 15 minutesWe evaluate system performance via cost reductionGiven an empirical sample of call logs R1,…,RNCompute the expected performance viaStatic Allocation Goal: find an allocation A with good performance
FR(A) = LR(Ø) - LR(A)
F(A) = ( FR1(A) + … + FRN(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 intervalsE.g., every 30 minutesWe consider myopic redeployment algorithmsOptimize for performance of next intervalEquivalent to mini static allocation problemGreedy solutionSample requests for next intervalRun greedy to compute re-allocation
Theoretical Analysis
F is very hard to analyze directly
Interactions between overlapping requestsDefine GR(A) = objective of omniscient dispatchingGR(A) ≥ FR(A)Can be solved via relatively simple IPGR(A) is monotone submodular!Optimality guarantees on G also apply to F!Guarantees via submodularityEven tighter bounds as wellCan also be extended to dynamic redeployment settingOngoing work
Empirical Evaluation
Leveraged historical data of EMS system of Asian city
Built a generative model of requests58 base locations, budget of 58 ambulancesEvaluate over 1 week of requestsThree types of penalty functions consideredL1 : graded penalty based on service timeL2 : higher penalty for un-serviced requestsL3 : 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-
d
ependent bound via
submodularity
Omniscient-Optimal Upper Bound
is
t
ighter bound via extending IP
formu
-
lation
for solving omniscient dispatch