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
Example schedule Project 1 M A / E 1 , E 2 / WB 5 / EQ 4 Job 1 (Tasks 1, 2, 3, 5) M B / E 1 / WB 3 Job 2 (Task 4) M B / E 3 / WB 1 / EQ 8 , EQ 9 Job 3 (Tasks 6, 7) Project 2 M A / E 1 , E 4 / WB 1 Job 4 (Tasks 8, 9, 10, 11) M B / E 2 / WB 1 Job 5 (Task 12) M B / E 2 / WB 2 Job 6 (Tasks 13, 14, 15) M A / E 3 , E 5 / WB 3 Job 7 (Task 16, 17) Danzinger et.al. (TU Wien) Solving TLSP with Flexible Grouping October 2020 2 / 8
Task grouping A job consists of one or several tasks , which define its properties: Job j max r R t � d t Setup time s f Available resources: R j = � R t Time window: α j = max α t , ω j = min ω t ... Danzinger et.al. (TU Wien) Solving TLSP with Flexible Grouping October 2020 3 / 8
Constraint Programming Major challenge: representing grouping Solution: Representative task for each job Task 1 Job a Task 1 Task 2 Task 2 Task 4 Task 3 Job b Task 4 Task 3 Task 5 Task 5 Danzinger et.al. (TU Wien) Solving TLSP with Flexible Grouping October 2020 4 / 8
Constraint Programming: Example Constraints Resource availability: assigned[repr[ t ] , r ] = 1 = ⇒ r ∈ R t ∀ t ∈ Tasks , r ∈ Resources Resource requirements: � max t ′ ∈ Tasks:repr[ t ′ ]= t | Req t ′ | if repr[ t ] = t � assigned[ t , r ] = 0 otherwise r ∈ Resources ∀ t ∈ Tasks Danzinger et.al. (TU Wien) Solving TLSP with Flexible Grouping October 2020 5 / 8
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
Computational results 33 test instances (30 2.4 ● randomly generated, 3 ● 2.2 ● real-world) ● 2.0 (relative to best known) Up to 1500 tasks (90 1.8 projects) Penalty ● 1.6 ● 1.4 Time limit: 2 hours 1.2 30 feasible solutions ● 1.0 TLSP-S: fixed grouping CP VLNS given, results of CP VLNS (TLSP−S) (TLSP−S) Geibinger et al. (CPAIOR 2019) Danzinger et.al. (TU Wien) Solving TLSP with Flexible Grouping October 2020 7 / 8
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
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