+ PRODUCTION SCHEDULING Medical analysis on an automated machine Sophie Debrade sd2829 Alexandre Philippe Ayache apa2117 Pierre Castaing pc2613

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

+ Challenge Framework and notations: Multi-tasks automated machine performs medical 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: Max Throughput s.t. N samples to test M different possible tests time constraint Max Throughput s.t. N samples to test M different possible tests time constraint 3

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

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

+ Case 1: 1 type of test 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 Heuristic: Keep executing all the available tasks on the sample being processed One job at a time 6

+ Case 1: Analysis of the results Analyzing the performance of our algorithm: Analyzing the effectiveness of the machine: 7

+ Case 1: Results of the algorithm (R code) Using our heuristic, we try to maximize the throughput with 1 type of test Performance metrics: throughput & occupancy Test ELISATime constraint: 50 min Throughput: 19 samplesOccupancy: 59.8% 8

+ Case 1: Results of the algorithm (R code) Using our heuristic, we try to maximize the throughput with 1 type of test Performance metrics: throughput & occupancy Test WESTERN BLOTTime constraint: 1h30min Throughput: 11 samplesOccupancy: 28.5% 9

+ Case 1: Results of the algorithm (R code) Using our heuristic, we try to maximize the throughput with 1 type of test Performance metrics: throughput & occupancy Test RT-PCRTime constraint: 2h Throughput: 11 samplesOccupancy: 37.9% 10

+ Case 1: Analysis of the results Analyzing the performance of our algorithm: Finding an Upper Bound for the throughput: Time limit, say 3000 s Job1 takes 2195 s. Lower bound to overlap: UB = ( )/overlap = 23 jobs With our heuristic we obtain 19 jobs 82.6 % approximation of optimal (at least!) 11

+ Case 2: 2 types of test 2 tests – ELISA and Western-Blot. Realistic assumption -> HIV testing. We continue with the first heuristic (once a job is started, it has priority). Scenario 1: we schedule all tests of type 1 and then all tests of type 2. Scenario 2: we alternate some amount of tests of type 1 with some tests of type 2. NB: we use the fact that one WB ≈ 2 ELISA 12

+ Case 2: 2 types of test 2 tests – ELISA and Western-Blot. Scenario 1: we schedule all tests of type 1 and then all tests of type 2. Tried 4 WB - 12Elisa- 4WB – 12Elisa. Makespan =

+ Case 2: 2 types of test 2 tests – ELISA and Western-Blot. Scenario 2: we alternate some amount of tests of type 1 with some tests of type 2. Tried 2 WB - 6Elisa- 2WB – 6Elisa – 2 – 6 – Makespan =

+ Case 2: 2 types of test 2 tests – ELISA and Western-Blot. Conclusion: scenario 2 is better. Hypothesis: since tests Western-Blot are used to confirm false positive from ELISA, there are less WB than ELISA tests. The heuristic we discovered is: Given the ratio of WB vs ELISA (1 vs 3 in our example) schedule using the maximum alternance. 1 – 3 – 1 – 3 – etc. Named it: Smallest Pattern Available (SPA). Heuristic: SPA 15

+ Case 2: Scheduling Tried to schedule a lot of them with our heuristic (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% 16

+ Case 2: Conclusion In the case of two test, ELISA and Western-Blot, we obtained a very good heuristic for a very challenging scheduling problem. Could imagine building an automated robot for HIV testing that would use the SPA heuristic. What we could do next: Repeat this process with the 3 types of tests. Find a Upper Bound for the 2 tests case and improve (lower) the first one. Think a using several robots (and go mad)!!! Change the robot characteristics/choose another robot. 17

+ THANK YOU Any questions?