The Car-Sequencing Problem as n-Ary CSP – Sequential and Parallel Solving

Abstract

The car-sequencing problem arises from the manufacture of cars on an assembly line (based on [1]). A number of cars are to be produced; they are not identical, because different options are available as variants on the basic model. The assembly line has different stations (designed to handle at most a certain percentage of the cars passing along the assembly line) which install the various options. Furthermore, the cars requiring a certain option must not be bunched together, otherwise the station will not be able to cope. Consequently, the cars must be arranged in a sequence so that the capacity of each station is never exceeded. The solving methods for constraint satisfaction problems (CSPs) [2], [3], [4] represent good alternatives for certain instances of the problem. Constraint programming tools [5], [6] use a search algorithm based on Forward Checking (FC) [7] to solve CSPs, with different variable or value ordering heuristics. In this article, we undertake an experimental study for the instances of the car-sequencing problem in CSPLib, encoded as an n-ary CSP using an implementation with constraints of fixed arity 5. By applying value ordering heuristics based on fail-first principle, a great number of these instances can be solved in little time. Moreover, the parallel solving using a shared memory model based on OpenMP makes it possible to increase the number of solved problems.