Selecting an Insurance Carrier Based on Geographic Coverage Using the Spherical Law of Cosines

1. Selecting an Insurance Carrier Based on Geographic Coverage Using the Spherical Law of Cosines John ToczekDecision SupportAramark

2. Background 180,000 Employees in the U.S.Thousands of injuries each yearState requirements for emergency care

3. A B C Aetna Cigna Quiz BlueCross Which insurance company should I choose for best coverage?

4. A B C Quiz Cigna Aetna BlueCross Which insurance company should I choose for best coverage?

5. ARAMARK and 'Provider A' Emergency Care Locations

7. Pairing Aramark locations to Emergency Care locations Aramark locations 'Provider A' emergency locations 453 rows 4859 rows

8. Pairing Aramark locations to Emergency Care locations DATA COMBOS; set ARAMARK; if _N_ <=453;*Aramark locations (453max); do i=1 to 4859; *Emergency locations (4859max); set EMERGENCY point=i nobs=n; output; end; run;

9. DATA COMBOS; 2.5 million rows

10. Calculating the distance between two points on a sphere in SAS Spherical Law of Cosines Distance between two points on a sphere = arcos ( sin(A-lat*0.0174)*sin(B-lat*0.0174) + cos(A-lat*0.0174)*cos(B-lat*0.0174)*cos(B-lon*0.0174-A-lon*0.0174) )*3959;

11. Calculating the distance between two points on a sphere in SAS Spherical Law of Cosines DATA DISTANCE; SET COMBOS; DIST = arcos(sin(A_Lat*0.017453) *sin(E_Lat*0.017453)+cos(A_Lat*0.017453) *cos(E_Lat*0.017453)*cos(E_lon*0.017453-A_Lon*0.017453)) *3959; RUN;

12. DATA DISTANCE; (mi.) ~2 million rows

13. DATA DISTANCE; (mi.) ~2 million rows

14. DATA DISTANCE; (mi.) PROC REPORT DATA=DISTANCE out=FINAL; COLUMN DIST ARAMARK; DEFINE ARAMARK / GROUP; DEFINE DIST / MIN; RUN; ~2 million rows

15. DATA FINAL; (mi.) 453 rows PROC REPORT DATA=DISTANCE out=FINAL; COLUMN DIST ARAMARK; DEFINE ARAMARK / GROUP; DEFINE DIST / MIN; RUN;

16. Questions?

17. Why not use Pythagorean? • 3% error between SLOC and Pythagorean • For 100 miles actual distance, Pythagorean would show 97 miles. Small but significant for this application

18. AbstractSelecting an Occupational Medicine Network Provider Based on Geographic Coverage Using the Spherical Law of CosinesARAMARK corporation employs 200,000 people domestically and is a leading provider of food and facilities management services to Business, Education, Healthcare, and Sports and Entertainment clients in the US, generating $11.6 billion of sales in 2006. In order to provide timely and efficient medical treatment to its employees in the event of an injury, in certain states where permitted by law, ARAMARK selects an occupational medicine network provider who has Urgent Care Facilities (UCF) near ARAMARK locations of business.  In choosing an occupational medicine provider, ARAMARKmust select one that provides the most comprehensive  geographic network of these UCFs so that response time and injury severity are minimized.SAS, in conjunction with the Spherical Law of Cosines, is used to calculate the distance between each ARAMARKlocation and each UCF. This amounts to over 2 million separate distance calculations for California alone. To find the nearest UCF, the data is collapsed using a DEFINE DISTANCE / MIN within a PROC REPORT.  The resulting table is a list of ARAMARK locations, the nearest UCF, and the distance to that UCF.  Runtime for the code is under 5 minutes.John Toczek is an Operations Research Analyst for ARAMARKCorporation in the Global Risk Management Division.  He earned his Bachelor of Science degree in Chemical Engineering at Drexel University (1996) and his Master of Science in Operations Research from Virginia Commonwealth University (2005).  He can be reached at toczek-john@aramark.com.