+ PRODUCTION SCHEDULING Medical analysis on an automated machine Sophie Debrade sd2829 Alexandre...

+

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%



Test WESTERN BLOT Time constraint: 1h30min




Test RT-PCR Time constraint: 2h


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


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.


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.


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?

+ PRODUCTION SCHEDULING Medical analysis on an automated machine Sophie Debrade sd2829 Alexandre...

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