Air-Ambulance Routing at Ornge

1. Air-Ambulance Routing at Ornge Gurur Urlu Kerem Aydın Mustafa Ayberk Yamak

2. Introduction • General Information About Ornge • The Problem Definition • Constraints • Structures of Problem • Impact & Next Step • Other Research & Question • Model

3. General Information About Ornge-1 • Provides ambulance services for Ontario, • Serves for 13 million residents over 1 million square km, • Each year transports 19,000 patients.

4. General Information About Ornge-2 • Two kinds of transportation • Scene Calls • Interfacility Transports

5. General Information About Ornge-3 • Scene Calls; • Responding to calls from accident locations by helicopter(land if needed) • Occurs abruptly

6. General Information About Ornge-4 • Interfacility Transfers; Transfers patients between medical facilities There are 3 types of interfacility transfers • Emergent(42%) • Urgent(21%) • Non-Urgent(37%)*

7. Non-Urgent Interfacility Transports • Staffed and equipped for non-urgent requests, • Seconded for emergent transports if needed(time-sensitive conditions, overwhelming demands), • Has sharing of aircraft with emergent/urgent calls(ignored), • Has 10-20 requests per day(sometimes 30), • Uses fixed-wing aircrafts.

8. Problem Definition • How to schedule and route avaliable aircraft to handle the requests at minimal cost.

9. Constraints • An aircraft can handle up to 4 requests within a duty shift • The requests can be handled in any order, subject to time restrictions • Some aircrafts can carry up to 2 patients(some can carry only one) • Some patients cannot be transported with another patient.

10. Previous System • Previously, Ornge flight planners manullay determined the aircraft assignments and routes based on experience.

11. Current System-1 • Develped in 2009 • An optimization-based tool determining optimal assignment of requests to aircraft and the optimal routes to fly • Uses intuitive Excell interface and C++ impelementation and invokes an IP solver which returns the optimization results to the Excell tool.

12. Current System-2 • Flight planners set up the problem in Excell tool, • Obtain the solution, • Study the practicality of the solution, • Adherence the policies, • Solve it again.

13. Tests on the Tool • Tested using retrospective Ornge data from randomly selected dates between July 2010 and February 2011. • Estimated decreases of 12% in flying hours, 12% in distance flown, 16% in cost • In May 2011, they implemented the application to real time on a test basis. During the first 8 months it resulted in only 3% decrease in average daily cost. • However,

14. Current System-3 • The mathematical problem of Ornge in OR literature is known to be a static dial-a-ride problem with non-homogeneous vehicles and multiple depots. • It is static because, Two approaches based on IP formulations • One differ in vehicle-specific arcs, • Other applies to homogenous vehicle fleets.

15. The Differences of Ornge’s Problem Their problem is first to address such a problem in the air-medical industry • Non-homogenous vehicles • Application differs since the schedule differs each day.(origins and destinations)

16. Ornge on Duty...

17. Structure of Problem • Structure of Requests • Structure of Aircraft • Definition of Leg • Structure of Routes&Costs • Requirements for Routes

18. Structure of Requests • Origin • Destination • Pickup after • Drop off before • Level of care • Stretchers • Escorts • Solitary • Maximum time

19. Structure of Aircrafts • Base • Level of care • Stretchers • Escort capacity • Airspeed • Fuel cost • Charter cost • Advanced charter cost

20. Definition of Leg Takeoff and a landing with no intermediate stops. Each plane that is used flies a route that consist of multiple leg.

21. Structure of Routes & Costs • Fuel cost • Charter cost • Detention cost

22. Requirements for Routes • Aroute can not last longer than a specific government-mandated length of time. • A route can not be so long that a patient is kept on board for too long relative to the time the patient would have been on board if he or she had flown directly directly from origin to destination.

23. Impact & Next Steps-1 According to retrospective study between July 2010 – February 2011, they choose randomly 50 days and for each step they completed following steps; • Retrieved actual schedule • Established optimized plan • Calculate total flying time, distance travelled and number of legs • Calculate cost • Used expert opinions

24. Impact & Next Steps-2 Before discussing, acknowledge 3 limitations; • Weather conditions • Effect of unscheduled urgent/emergent calls • Difference between realized cost & cost modelled in the optimization tool

25. Impact & Next Steps-3 During the study period; • 838 request • 16.8 ± 5.4 daily mean • Optimized plan’s cost saving: 16.5%

26. Impact & Next Steps-4 Table: Summary statistics show the differences in characteristics in plans that the flight planners developed with and without the optimization tool.

27. Impact & Next Steps-5 When we give the limitations discussed previously; • Actual saving cost is smaller than 16.5% However;

28. Impact & Next Steps-6 Orgne finds this tool succesfull and uses it!!!!

29. Other Research Question • Where should aircraft be based around the province to minimize expected daily cost? (ambulance-location problems) • Can one answer this question with a single model that treats both non-urgent and urgent/emergent calls, as opposed to treating these classes of calls and their associated aircraft seperately?(two-stage stochastic programming or dynamic dial-a-ride problem)

30. Set Partitioning Integer Problem • Set X is a set of nonempty subsets of X which is disjoint union of the subsets

31. A Family of Sets P • Does not contain the empty set • The union of the sets in P is equal to X • Intersection of two distinct sets is empty

32. How Many Variables? • r: # of requests • p: # of planes • For example; r=30 and p=40, the result is 1,277,200 • However some of them are infeasible and the real is 750,000 • Let variables are

33. Parameters if request i is included in j. column and 0 otherwise if plane i is included in j. column and 0 otherwise m-dimensional column vector and is 1 for all i cost of completing the set of request in the j. column with the associated plane

34. The Model

35. How We Compute c? • Ignore many of the side constraints of the problem such as need to transport some patients alone but assume that all planes can carry two patients

36. What About Routes? • Fix a particular column j • represents the minimal cost of handling the set of requests • If consists of a single request cost is flying from plane’s base to the request’s origin • Suppose that it consists of k>1 requests • Consider all k! orderings • routes are possible • Suppose that first patient already picked up

37. Following Actions • Drop off the current patient and pick up the next patient • Pick up next patient and drop off the current patient • Pick up the next patient and drop off the next patient

38. Test for Feasibility • Consider the plane’s characteristics • Enforce a minimum turnaround time and also add time

39. Total Computation • where the upper bound

40. Thank You Thank You