1. May 31, 2009 Industrial Engineering Research Conference - 2009 Slide 1 Scheduling Radar Warning Receivers (RWRs) Scott R. Schultz Mercer University / Mercer Engineering Research Center F.M. Barron Paul MacNeil Eric Mullenax

2. May 31, 2009 Industrial Engineering Research Conference - 2009 Slide 2 About the Speaker Dr. Scott Schultz – associate professor Mercer University, and consultant at Mercer Engineering Research Center. Industry Experience: 13 years automotive experience – Ford Motor Company. 2 years furniture experience – Furniture Manufacturing Management center. Consulting – manufacturing and military Teaching Experience: 6 years as Industrial Engineer – Mercer Univ. Simulation Production, scheduling, inventory control Operations Research others…

3. May 31, 2009 Industrial Engineering Research Conference - 2009 Slide 3 Problem Statement  Develop an RWR scheduler that minimizes the time to detect multiple threats across multiple frequency bands.

4. May 31, 2009 Industrial Engineering Research Conference - 2009 Slide 4 RWR Scheduling Definitions Pulse Width (PW) Revisit Time (RT) Illumination Time (IT) Pulse Repetition Interval (PRI) Beam Width (BW) Definitions: Revisit Time (RT) – time to rotate 360 degrees (rotating radar) Illumination Time (IT) – function of RT and BW Pulse Width (PW) – length of time while target is energized Pulse Repetition Interval (PRI) – time between pulses Time

5. May 31, 2009 Industrial Engineering Research Conference - 2009 Slide 5 Example RWR Schedule RWR Schedule – a series of dwells on different frequency bands: sequence and length

6. May 31, 2009 Industrial Engineering Research Conference - 2009 Slide 6 RWR Scheduling Problem Objective – detect all threats as fast as possible (protect the pilot) How to sequence dwells? How to determine dwell length? How to evaluate / score schedules? Meta-Heuristics Simulation

7. May 31, 2009 Industrial Engineering Research Conference - 2009 Slide 7 RWR Scheduling Approach Meta-Heuristics: Simulated Annealing (SA) SA Components: Solution representation Neighborhood generation scheme Solution evaluation/score

8. May 31, 2009 Industrial Engineering Research Conference - 2009 Slide 8 RWR Scheduling Approach RWR SA Solution Representation: Assumptions: Unit Time Idle Time fills space from end of last dwell to total cycle time.

9. May 31, 2009 Industrial Engineering Research Conference - 2009 Slide 9 RWR Scheduling Approach RWR SA Neighborhood generation scheme: Two Examples: Add or Subtract a Unit of TimeSplit a Dwell

10. May 31, 2009 Industrial Engineering Research Conference - 2009 Slide 10 Solution Evaluation: Simulation Approach: Given that the offset for each threat pulse train is unknown. Determine:MTDAT - expected time to detect all threats, MaxDAT - maximum time to detect all threats Note different offsets Threat detected in cycle 1 Threat detected in cycle 2 RWR Scheduling Approach

11. May 31, 2009 Industrial Engineering Research Conference - 2009 Slide 11 n = 1 i = 1 Generate offset for threat i ~ U(0,RT i ) Determine time when RWR schedule coincides with threat i i = i + 1 i < I Objective: Evaluate / Score a single RWR schedule. N – number of iterations I – number of threats n = n + 1 Update MTDAT, MaxDAT n < N Done Yes No RWR Scheduling Approach

12. May 31, 2009 Industrial Engineering Research Conference - 2009 Slide 12 When does the MTDAT running average begin to converge? MTDAT running average: 3 threats MTDAT running average: 5 threats MTDAT running average: 10 threats RWR Scheduling Approach

13. May 31, 2009 Industrial Engineering Research Conference - 2009 Slide 13 Compare SA to Simple Heuristic: Experimental Design Pre-determined Cycle Time Heuristic: Set the number of dwells equal to the number of frequency bands, Set the dwell time as calculated below: dwell time = int((RWR cycle time – retune time * number of bands )/ number of bands) Any time left over is assumed idle time and placed at the end of the schedule

14. May 31, 2009 Industrial Engineering Research Conference - 2009 Slide 14 Problem Parameters: Retune Time: 1 Time Unit (  sec) RWR Cycle Times: Evaluate from 40 to 90 (  sec) Threat List: 5 Enemy Radars Experimental Design

15. May 31, 2009 Industrial Engineering Research Conference - 2009 Slide 15 Problem Parameters: Retune Time: 1 Time Unit (  sec) RWR Cycle Times: Evaluate from 40 to 90 (  sec) Threat List: 5 Enemy Radars Experimental Design

16. May 31, 2009 Industrial Engineering Research Conference - 2009 Slide 16 Results: Note: MTDAT approaching infinity for pre-determined cycle time heuristic at some cycle times due to synchronization. Results

17. May 31, 2009 Industrial Engineering Research Conference - 2009 Slide 17 Results

18. May 31, 2009 Industrial Engineering Research Conference - 2009 Slide 18 Conclusions SA outperforms simple heuristic SA approach presented for developing RWR schedules using the performance measure “mean time to detect all threats”, MTDAT. SA will converge on an RWR schedule having a particular cycle time, however this is dependent on the initial cycle time and bounded by cycle times which are synchronized with a threat’s revisit time. Synchronization poses an interesting challenge compared to many SA applications of discrete optimization problems which converge to a global optimal solution independent of the starting solution.

19. May 31, 2009 Industrial Engineering Research Conference - 2009 Slide 19 RWR Research - Status Future: Investigate alternative means of generating scores to avoid costly simulation Research literature identified Compare to enhanced evaluator (simulator) Assess impact of multiple radars in RWR platform Replace single radar with one monitoring high frequencies and one monitoring lower frequencies Math Model?

20. May 31, 2009 Industrial Engineering Research Conference - 2009 Slide 20 Research Sponsor Sponsors: RAPCEval - collaborative Air Force and university education and research program to support advances in electronic combat technology. The RAPCEval program is overseen by a steering committee of scientists and engineers from the Air Force Research Laboratory at Wright Patterson AFB, the Warner Robins Air Logistics Center at Robins AFB, Mercer University, Mercer Engineering Research Center (MERC), Wright State University, and Rose-Hulman Institute of Technology who are charged with ensuring that student research is of sufficient interest to the USAF and also of high academic quality. Mercer Engineering Research Center – located in Warner Robins, Georgia, a non profit operating unit of Mercer University. MERC employs over 150 engineers, scientists, and support staff. Engineering, Logistics, management, and educational services are provided to a wide range of government and commercial customers