A constraint programming pre-processor for a bus driver scheduling system

A heuristic method for analyzing driver scheduling problem

“…Furthermore, since there are usually far more relief opportunities than needed in a driver schedule, the driver scheduling problem is the problem of selecting a good subset of relief opportunities, which collectively contribute to the least number of driver duties and the lowest costs of the duties, hence, a good driver schedule. Research in the past decades has demonstrated that this is very difficult to achieve (see some ongoing research efforts in this area: [9], [10], [13]- [15], [26], and [38]). Suffice it to say, the common goal of the driver scheduling systems is to identify such a subset, irrespective of the methods they are using.…”

“…The complexity of an ILP, as explained in [26], depends primarily on the number of constraints and the number of variables in a problem. In a set covering formulation of driver scheduling, the number of constraints corresponds to the number of pieces of work to be covered and the number of variables is the number of potential duties generated from the pieces of work.…”

“…The success of a set covering approach therefore depends on the success in reducing the number of relief opportunities. A preprocessor based on constraint programming was proposed to select relief opportunities in TRACS II [15], [26]. The idea is to represent a scheduling problem as a constraint satisfaction problem and then to use a search algorithm to select relief opportunities.…”

“…The search algorithm focuses on the formation of meal break chains and also allows some random choice of relief opportunities. Results showed that using constraint programming as a preprocessor for TRCAS II can greatly reduce the time to produce a schedule [26]. As an example, by tackling a problem with 69 duties in the driver schedule, TRACS II alone took 98.42 min, whereas by including the preprocessor, it took 60.27 min.…”

“…Practical mathematical programming approaches have used heuristics to reduce the size of the problem [21], [30], and the combination has led to successful driver scheduling systems that solve large and complex problems [5], [8], [9], [11], [16], [25]. Most recently, constraint programming has been found useful in assisting mathematical programming to reduce the complexity of the scheduling problems [2], [15], [26]. A new type of heuristics, called meta-heuristics, has begun to show some promise to driver scheduling problems.…”