Solving the Dynamic Ambulance Dispatching & Relocation Problem using Approximate Dynamic Programming. Dr. Verena Schmid

Transcription

1 Solving the Dynamic Ambulance Dispatching & Relocation Problem using Approximate Dynamic Programming Dr. Verena Schmid

2 literature overview solution approach conclusio problem description & motivation data & results mathematical problem formulation 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

3 problem description & motivation faced by Emergency Service Providers (ESPs) manage fleet of ambulances reach patients in case of emengency asap fundamental decisions ambulance location dispatching reinsertion relocate where which where next where else 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

4 Q1: where to locate ambulances optimize coverage areas/patients reachable within given time limit 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

5 Q1: where to locate ambulances using real street network 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

6 Q1: where to locate ambulances using time dependent travelling times 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

7 Q2: which ambulance shall be sent dispatching immediate response time! future response times 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

8 Q3: where to send ambulance next reinsertion determine next waiting location future response times! 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

9 Q4: send ambulances somewhere else relocation determine new waiting location future response times! 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

10 dispatching & reinsertion process arrival of request assign vehicle start of service (at patient) end of service (at patient) start of service (at hospital) end of service (at hospital) start of service (at patient) arrival (at waiting location) dispatch time travel time time (to patient) service time (at patient) travel time time (to hospital) service time (at hospital) travel time time (to waiting location) response time travel time time (to patient) 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

11 literature overview solution approach conclusio problem description & motivation data & results mathematical problem formulation 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

12 basic notation states capture current situation (ambulances + requests) S t (R t,d t ) decisions made dynamically over time immediate contribution C(S t,x t ) decisions have a downstream impact on future need estimate for value of being in a state V t (S t ) sources of randomness requests, durations dynamic evolution x t W t 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

13 optimization myopic policy optimize wrt immediate contribution optimize underlying stochastic problem immediate contribution expected future contribution value of next state current state decision random input 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

14 state (in more detail) resources (ambulances) attribute vector resource state vector demand (requests) attribute vector demand state vector state decision elementary decisions decision variable 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

15 states (example) t = 10:30am resource state idle ambulances current location available since busy ambulances next location available next demand state location arrival time priority 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

16 model (constraints) flow conservation on request at most one idle ambulance can be dispatched to any request for ambulances only idle ambulances can be dispatched ambulances just becoming idle have to be dispatched or relocated status of busy ambulances cannot be changed 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

17 literature overview solution approach conclusio problem description & motivation data & results mathematical problem formulation 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

18 dynamic programming stochastic optimization problem basic idea recursive step backward in time curses of dimensionality state vector S t grows very quickly size of outcome space of random variable W t size of decision vector x t 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

19 approximate dynamic programming (ADP) stochastic optimization problem basic idea make decisions based on approximation of value function step forward in time (sample what might happen) iteratively. using a fresh set of sample realizations update value function approximation 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

20 literature overview solution approach conclusio problem description & motivation data & results mathematical problem formulation 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

21 data real data street network: city of Vienna (1.7 mio inhabitants, 41.5 hectare) fleet of 14 ambulance vehicles, 16 locations requests average # of emergencies per day volume itself highly dependent on time of day exponentially distributed interarrival times spatial poisson process based on distribution of origins 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

22 road network & waiting locations 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

23 interarrival times 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

24 origin & destination of requests 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

25 experiment setup experiment setup training phase (10 5 iterations) fixed step size = 0.2 temporal (spatial) aggregation parameter t = s = 4 sampled data from estimated distributions 5 independent test runs 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

26 first training: 10 5 iterations 2 decisions which vehicle to dispatch where to relocate benchmark policies relocate to home location relocate to closest location relocate to random location adp (closest! regulatory rules) 4.51 min(current strategy) 4.61 min(naïve strategy) 5.12 min 4.05 min 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

27 relax this assumption 2 decisions which vehicle to dispatch where to relocate benchmark policy relocate to home location adp send closest send any (closest! regulatory rules) 4.60 min(current strategy) 4.05 min 4.01 min 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

28 response times over course of day 5.5 average response time (over day) current naive random adp (+R) st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

29 literature overview solution approach conclusio problem description & motivation data & results mathematical problem formulation 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

30 conclusion contribution formulated a dynamic model for the ambulance dispatching and relocation model solved using ADP outperformed benchmark policies (random/naïve/current) pays off to deviate from current dispatching rules (13%) consider other vehicles (not just closest one) for dispatching relocate vehicles adequately after finishing service relocate vehicles empty to cope with current situation 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

31 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32

32 Thank you for your attention! Questions Dr. Verena Schmid Europa Universität Viadrina Frankfurt (Oder) Information & Operations Management (IOM) Lehrstuhl für Betriebswirtschaftslehre, insbesondere Supply Chain Management h:// 1st International Workshop on Planning of Emergency Services :: Amsterdam :: Dr. Verena Schmid :: June 25-27, of 32