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

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

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

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?

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