Succeed--rst or Fail--rst: a Case Study in Variable and Value Ordering 1 a Revised Version of a Paper Presented at the Ilog Solver and Ilog Schedule 2nd International Users'

It is well known that appropriate variable and value ordering heuristics are often crucial when solving constraint satisfaction problems. A variable ordering heuristic which is often recommended, and is often successful, is based on the `failrst' principle: choose next the variable with the smallest remaining domain. General-purpose value ordering heuristics are less common, but it has been argued that a value which has least e ect on future choices should be chosen, a kind of `succeedrst' strategy. This paper considers variable and value ordering heuristics for the car sequencing problem. A number of cars are to be made on a production line: each of them may require one or more options which are installed at di erent stations on the line. The option stations have lower capacity than the rest of the production line, e.g. a station may be able to cope with at most one car out of every two. The cars are to be arranged in sequence so that these capacities are not exceeded. The choice of variable and value ordering heuristics has a dramatic e ect on solution time for this problem. However, the failrst variable ordering heuristic does not give good results: and in fact it is shown that dynamic variable ordering is unsuitable for this problem. Similarly, succeedrst value ordering does not work, and an ordering based on failrst is a better choice. Reasons why conventional wisdom fails in this case, and could be expected to fail in similar cases, are identi ed.