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PRODUCTION SCHEDULING Medical a nalysis on an automated machine

PRODUCTION SCHEDULING Medical a nalysis on an automated machine. Sophie Debrade sd2829 Alexandre Philippe Ayache apa2117 Pierre Castaing pc2613. Need to test samples for HIV, Hepatits C, B, etc. Robot automating the process . Problem Definition. Framework and notations:

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PRODUCTION SCHEDULING Medical a nalysis on an automated machine

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  1. PRODUCTION SCHEDULINGMedicalanalysis on an automated machine Sophie Debrade sd2829 Alexandre Philippe Ayache apa2117 Pierre Castaing pc2613

  2. Need to test samples for HIV, Hepatits C, B, etc. Robot automating the process. ProblemDefinition

  3. Framework and notations: • Multi-tasksautomated machine performsmedical tests • Tasks : Rince, Inject, Mix,… • Different test: 1..i..n • Duration of the task: Pij • Waiting time after the task has lower (Lij) and upper (Uij) bounds • Problem formulation: Challenge Max Throughput s.t. N samples to test M different possible tests time constraint

  4. Protocoles of the Tests TEST ELISA TEST WESTERN BLOT REVERSE TRANCRIPTION POLYMERASE CHAIN REACTION

  5. Data of the Tests TEST ELISA TEST WESTERN BLOT REVERSE TRANCRIPTION POLYMERASE CHAIN REACTION

  6. 2 samples – Test ELISA • Scenario 1: If do task j for Sample 1, then do task j for Sample 2 • Scenario 2: Keep executing all the available tasks on the sample that is being processed Case 1: 1 type of test Heuristic: Keepexecuting all the availabletasks on the samplebeingprocessed One job at a time

  7. Analyzing the performance of ouralgorithm: Analyzing the effectiveness of the machine: Case 1: Analysis of the results

  8. Test ELISA Time constraint: 50 min Case 1: Results of the algorithm (R code) Usingourheuristic, wetry to maximize the throughputwith 1 type of test Performance metrics: throughput & occupancy Throughput: 19 samplesOccupancy: 59.8%

  9. Test WESTERN BLOT Time constraint: 1h30min Case 1: Results of the algorithm (R code) Usingourheuristic, wetry to maximize the throughputwith 1 type of test Performance metrics: throughput & occupancy Throughput: 11 samplesOccupancy: 28.5%

  10. Test RT-PCR Time constraint: 2h Case 1: Results of the algorithm (R code) Usingourheuristic, wetry to maximize the throughputwith 1 type of test Performance metrics: throughput & occupancy Throughput: 11 samplesOccupancy: 37.9%

  11. Analyzing the performance of ouralgorithm: • Finding an UpperBound for the throughput: • Time limit, say 3000 s • Job1 takes 2195 s. Lowerbound to overlap: 20+15. • UB = (3000-2195)/overlap = 23 jobs • Withourheuristicweobtain 19 jobs • 82.6 % approximation of optimal (at least!) Case 1: Analysis of the results

  12. 2 tests – ELISA and Western-Blot. • Realisticassumption -> HIV testing. • We continue with the first heuristic (once a job isstarted, it has priority). • Scenario 1: weschedule all tests of type 1 and then all tests of type 2. • Scenario 2: wealternatesomeamount of tests of type 1 withsome tests of type 2. • NB: we use the factthat one WB ≈ 2 ELISA Case 2: 2 types of test

  13. 2 tests – ELISA and Western-Blot . • Scenario 1: weschedule all tests of type 1 and then all tests of type 2. • Tried 4 WB - 12Elisa- 4WB – 12Elisa. Makespan = 5765. Case 2: 2 types of test

  14. 2 tests – ELISA and Western-Blot. • Scenario 2: wealternatesomeamount of tests of type 1 withsome tests of type 2. • Tried 2 WB - 6Elisa- 2WB – 6Elisa – 2 – 6 – 2 - 6. Makespan = 5680. Case 2: 2 types of test

  15. 2 tests – ELISA and Western-Blot. • Conclusion: scenario 2 isbetter. • Hypothesis: since tests Western-Blot are used to confirm false positive from ELISA, thereare less WB than ELISA tests. • The heuristicwediscoveredis: • Given the ratio of WB vs ELISA (1 vs 3 in ourexample) scheduleusing the maximum alternance. • 1 – 3 – 1 – 3 – etc. • Namedit: Smallest Pattern Available (SPA). Case 2: 2 types of test Heuristic: SPA

  16. Tried to schedule a lot of themwithourheuristic (and our R code). • Using SPA and assuming a ratio of 1 WB-10 ELISA, with a time limit of 6 hours. • Throughput: 17 WB and 166 ELISA • Occupancy of 84% Case 2: Scheduling

  17. In the case of two test, ELISA and Western-Blot, weobtained a very good heuristic for a verychallengingschedulingproblem. • Could imagine building an automated robot for HIV testingthatwould use the SPA heuristic. • Whatwecould do next: • Repeatthisprocesswith the 3 types of tests. • Find a UpperBound for the 2 tests case and improve (lower) the first one. • Think a usingseveral robots (and go mad)!!! • Change the robot characteristics/chooseanother robot. Case 2: Conclusion

  18. THANK YOUAny questions?

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