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Solving the Test Laboratory Scheduling Problem with Flexible Grouping Philipp Danzinger Tobias Geibinger Florian Mischek Nysret Musliu Christian Doppler Laboratory for Artificial Intelligence and Optimization for Planning and Scheduling,

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Solving the Test Laboratory Scheduling Problem with Flexible Grouping

Philipp Danzinger Tobias Geibinger Florian Mischek Nysret Musliu

Christian Doppler Laboratory for Artificial Intelligence and Optimization for Planning and Scheduling, DBAI, TU Wien

October 2020

Danzinger et.al. (TU Wien) Solving TLSP with Flexible Grouping October 2020 1 / 8

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Example schedule

Project 1

Job 1 (Tasks 1, 2, 3, 5) MA / E1, E2 / WB5 / EQ4 Job 2 (Task 4) MB / E1 / WB3 Job 3 (Tasks 6, 7) MB / E3 / WB1 / EQ8, EQ9

Project 2

Job 4 (Tasks 8, 9, 10, 11) MA / E1, E4 / WB1 Job 5 (Task 12) MB / E2 / WB1 Job 6 (Tasks 13, 14, 15) MB / E2 / WB2 Job 7 (Task 16, 17) MA / E3, E5 / WB3 Danzinger et.al. (TU Wien) Solving TLSP with Flexible Grouping October 2020 2 / 8

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Task grouping

A job consists of one or several tasks, which define its properties: Job j

Setup time

sf dt max rR

t

Available resources: Rj = Rt Time window: αj = max αt, ωj = min ωt ...

Danzinger et.al. (TU Wien) Solving TLSP with Flexible Grouping October 2020 3 / 8

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Constraint Programming

Major challenge: representing grouping Solution: Representative task for each job

Task 1 Task 2 Task 3 Task 4 Task 5 Job a

Task 1 Task 2 Task 4

Job b

Task 3 Task 5 Danzinger et.al. (TU Wien) Solving TLSP with Flexible Grouping October 2020 4 / 8

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Constraint Programming: Example Constraints

Resource availability: assigned[repr[t], r] = 1 = ⇒ r ∈ Rt ∀t ∈ Tasks, r ∈ Resources Resource requirements:

r∈Resources

assigned[t, r] =

maxt′∈Tasks:repr[t′]=t |Reqt′|

if repr[t] = t

therwise

∀t ∈ Tasks

Danzinger et.al. (TU Wien) Solving TLSP with Flexible Grouping October 2020 5 / 8

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Very Large Neighborhood Search

Repeatedly generate and solve simplified CP instances: Only 1 project can be scheduled, the rest of the schedule is fixed Number increases when stuck Tabu list Some scheduling-only steps, with fixed grouping

Danzinger et.al. (TU Wien) Solving TLSP with Flexible Grouping October 2020 6 / 8

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Computational results

33 test instances (30 randomly generated, 3 real-world) Up to 1500 tasks (90 projects) Time limit: 2 hours 30 feasible solutions TLSP-S: fixed grouping given, results of Geibinger et al. (CPAIOR 2019)

VLNS CP (TLSP−S) VLNS (TLSP−S) 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 Penalty (relative to best known)

Danzinger et.al. (TU Wien) Solving TLSP with Flexible Grouping October 2020 7 / 8

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Conclusions

First constraint programming model for TLSP Mapping of tasks to each other allows handling of variable number of jobs Extension of VLNS for TLSP-S to work with TLSP Improved results despite unknown initial grouping New best known solutions for several large benchmark instances (including real-world data sets) Solution successfully deployed in test laboratory of a large company

Danzinger et.al. (TU Wien) Solving TLSP with Flexible Grouping October 2020 8 / 8