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PRODUCTION SCHEDULINGMedical analysis on an automated machine
Sophie Debrade sd2829 Alexandre Philippe Ayache apa2117
Pierre Castaing pc2613
2+Problem Definition
Need to test samples for HIV, Hepatits C, B, etc.
Robot automating the process.
3+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
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+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
7+Case 1: Analysis of the results
Analyzing the performance of our algorithm:
Analyzing the effectiveness of the machine:
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 ELISA Time constraint: 50 min
Throughput: 19 samples Occupancy: 59.8%
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 WESTERN BLOT Time constraint: 1h30min
Throughput: 11 samples Occupancy: 28.5%
10+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-PCR Time constraint: 2h
Throughput: 11 samples Occupancy: 37.9%
11+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: 20+15. UB = (3000-2195)/overlap = 23 jobs With our heuristic we obtain 19 jobs 82.6 % approximation of optimal (at least!)
12+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
13+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 = 5765.
14+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 – 2 - 6. Makespan
= 5680.
15+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
16+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%
17+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.
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THANK YOUAny questions?