1. Role and Potential of TAs for Industrial Scheduling Problems
AMETIST Meeting December 1-2, 2003
Role and Potential of TAs for Industrial Scheduling Problems
Some Thoughts and Conjectures
Sebastian Engell

2. Approaches to Scheduling Problems
Exact Branch and Bound (MI(N)LP-Solvers, e.g. CPLEX)
Equation-based models
Exact lower bounds, optimality certificates
High modelling effort, unintuitive
Equivalent formulations lead to different behaviours of the solver
High computing times for large problems
Genetic Algorithms
Can efficiently provide solutions to large and nonlinear problems
Model can be algorithmic
Highly constrained problems require tailored algorithms with heuristics
Relative quality of the solution cannot be assessed
Constraint Programming
Efficient for highly constrained problems
Intuitive models
Not well suited for cost optimisation

3. Approaches to Scheduling Problems (2)
Heuristic Branch and Bound
can be much more effective than classical MILP
problem class specific, tailored algorithms
no optimality certificates
Timed Automata
universal modelling paradigm for many scheduling problems
modular, graphical and intuitive
uncertainty can be modelled easily (intervals for durations)
powerful tools
models become large for large problems
classes of constraints
optimality certificates
performance

4. The Users’ View
Realistic scheduling problems are too large to be solved to optimality by any single available general purpose method
Combination of methods, e.g. TA with MILP-solvers
Integration of heuristics in a transparent fashion
Models need to be formulated and maintained – modelling effort is a critical parameter for success in applications
Timed automata are very promising in this respect
Real problems contain uncertainties – must be modelled
Timed automata provide models with uncertain parameters
More general uncertainties?
Real problems are highly constrained
Advantageous for TA-based solvers
Classes of constraints that can be handled?

5. Conclusions and Further Work
TA-based analysis is a relatively new technology compared e.g. to constraint programming and MILP solvers
The assessment of its potential will require some time as well as the further improvement of the performance of the tools – Thanks to the Case Study providers!
Open issues:
Quick feasible solutions and risk assessment are more important than strict optimality!
Solutions should be uncertainty-conscious: best case, worst case, average performance, risk conscious
Combinations of solution algorithms for improved range and performance