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A polynomial-time ambulance redeployment policy

A polynomial-time ambulance redeployment policy. 1 st International Workshop on Planning of Emergency Services Caroline Jagtenberg R. van der Mei S. Bhulai. Overview. EMS: Static vs Dynamic S olutions Performance Estimation Our proposed method

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A polynomial-time ambulance redeployment policy

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  1. A polynomial-time ambulance redeployment policy 1st International Workshop on Planning of Emergency Services Caroline Jagtenberg R. van der Mei S. Bhulai A polynomial time ambulance redeployment policy

  2. Overview EMS: Static vs Dynamic Solutions Performance Estimation Our proposed method A tractable case study A realistic case study A polynomial time ambulance redeployment policy

  3. Emergency Medical Services Accident occurs Closest idle ambulance is sent Ambulance arrives at accident scene Patient may need transportation to hospital Ambulance becomes available How to position ambulances in order to minimize response times? A polynomial time ambulance redeployment policy

  4. Problemformulation Given: Locations of bases Number of available ambulances Expecteddemandat everylocation Drivingtimesbetweenlocations Optimize: Distribution of idle ambulances over the bases in order to minimize fraction arrivals later than a certain threshold time(patientfriendly) We may relocate an ambulance only when it becomes idle (crew friendly) A polynomial time ambulance redeployment policy

  5. Static vs dynamic solutions Static solution: each ambulance is sent back to its ‘home base’ whenever it becomes idle. Note: the ambulance does not need to arrive there, it can be dispatched while on the road A solution is a base for each ambulance Dynamic solution: make decisions based on current realizations (e.g., locations of accidents, which ambulances are idle, etc.) A solution describes how to redistribute ambulances A polynomial time ambulance redeployment policy

  6. Estimating performance Simulation model: Specify locations (x,y,p) Calls arrive according to a Poisson distribution Closest idle ambulance is sent Patient needs hospital treatment w.p. 0.8 When an ambulance becomes idle, make a decision (relocation) Performance (cost) is measured by the fraction of ambulances arriving later than a certain threshold A polynomial time ambulance redeployment policy

  7. A Dutch region modeled A polynomial time ambulance redeployment policy

  8. A Dutch region modeled A polynomial time ambulance redeployment policy

  9. The best staticsolution? A polynomial time ambulance redeployment policy

  10. The best static solution: A polynomial time ambulance redeployment policy

  11. Dynamic solution: Ambulance redeployment policy Previous work: R. Alanis, A. Ingolfsson, B. Kolfal (2013) ‘A Markov Chain Model for an EMS System with Repositioning’ M. S. Maxwell, S. G. Henderson, H. Topaloglu (2009) ‘Ambulance redeployment: An Approximate Dynamic Programming Approach’ A polynomial time ambulance redeployment policy

  12. A heuristicbased on MEXCLP: Maximum Expected Covering LocationProblem (MEXCLP) Daskin, 1983 Uses a pre-determined ‘busy fraction’ q: If a demand node has k ambulances nearby, the node is covered w.p. 1 – qk Let di be the demand at location i. Then the coverage of location i is given by: A polynomial time ambulance redeployment policy

  13. Dynamic MEXCLP Only consider currently idle ambulances Pretend moving ambulances are already at their destination At a decision moment, calculate marginal contribution in coverage for each possible base:  Choose the base that yields the largest marginal contribution (greedy) A polynomial time ambulance redeployment policy

  14. Computation Time O( |W| * |A| * |J| ) Where: W are the base stations A are the ambulances J are the demand nodes A polynomial time ambulance redeployment policy

  15. Performance Benchmark: the best static policy has a performance of ~ 7.4% The Dynamic MEXCLP heuristic has a performance of ~ 6.2% A polynomial time ambulance redeployment policy

  16. Performance A polynomial time ambulance redeployment policy

  17. A larger, more realistic region A polynomial time ambulance redeployment policy

  18. A larger, more realistic region A polynomial time ambulance redeployment policy

  19. Static and dynamic MEXCLP policy A polynomial time ambulance redeployment policy

  20. Sensitivity to the busy fraction A polynomial time ambulance redeployment policy

  21. Response times A polynomial time ambulance redeployment policy

  22. Possible improvements Also taking into account ambulances that will become available soon Calculate the trade-off between distance and coverage improvement A polynomial time ambulance redeployment policy

  23. Thank you for your attention Questions? A polynomial time ambulance redeployment policy

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