1. Car Sequencing Problem An update

3. How to certify output Standard output The Certificate class

4. Easy Problems We have a directory of easy problems How were these made? Why do we need easy problems?

6. Heuristics Variable ordering Choose time slot that can accept least classes (sdf) Value ordering What class should we put in that slot? - class with least options? - class where product of (nonzero) options is low? - class of least demand?

12. And so on

14. BMS paper is well worth a look

15. IF S[i] = c THEN for 0 j m O[i][j] = o[c][j] The Link Constraint m is # options

16. IF S[i] = c THEN for 0 j m O[i][j] = o[c][j] The Link Constraint Using ifOnlyIf ifOnlyIf(S[i] = c, and(O[i][0] =o[c][0], …, O[i][m]=o[c][m]))

17. IF S[i] = c THEN for 0 j m O[i][j] = o[c][j] The Link Constraint Using implies implies(S[i] = c, O[i][0]=o[c][0]). implies(S[i] = c, O[i][m]=o[c][m])

18. IF S[i] = c THEN for 0 j m O[i][j] = o[c][j] The Link Constraint Using implies implies(S[i] = c, O[i][0]=o[c][0]). implies(S[i] = c, O[i][m]=o[c][m]) What happens if due to propagation some O[i][j] is set? P Q and Q is false?

19. IF S[i] = c THEN for 0 j m O[i][j] = o[c][j] How big is the model? Using implies implies(S[i] = c, O[i][0]=o[c][0]). implies(S[i] = c, O[i][m]=o[c][m]) How many of these constraints are there? How big is the model?

20. Have a look at the p/q constraint How big is the model?

21. Two models linked? One has S, a sequence of classes The other has an array of cars allocated positions This might allow better heuristics

22. Channeling

23. Questions?