Car Sequencing Problem

An update

How to certify output

Standard output

The Certificate class

Easy Problems

We have a directory of easy problems

How were these made?

Why do we need easy problems?

Heuristics

Variable orderingChoose time slot that can accept least classes (sdf)

Value orderingWhat class should we put in that slot? - class with least options? - class where product of (nonzero) options is low? - class of least demand?

And so on

And so on

BMS paper is well worth a look

IF S[i] = cTHEN for 0 ≤ j ≤ m O[i][j] = o[c][j]

The Link Constraint

m is # options

IF S[i] = cTHEN 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]))

IF S[i] = cTHEN 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])

IF S[i] = cTHEN 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 topropagation some O[i][j] is set?

P Qand Q is false?

IF S[i] = cTHEN 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 theseconstraints are there?

How big is the model?

Have a look at the p/q constraint

How big is the model?

Two models linked?

One has S, a sequence of classes

The other has an array of cars allocated positions

This might allow better heuristics

Channeling

Questions?