An extension of set partitioning with application to scheduling problems

The well known problems of set covering, set partitioning and set packing are defined and their interrelationship is considered. A natural generalisation called the extended set partitioning model is presented and the three standard models are shown to be special cases of this generalisation. In addition, the extended model includes another type of set problem which can be of greater use in certain applications. The model forms the basis of a computer assisted bus crew scheduling system developed by the authors. The system is in regular use by Dublin City Services in the Republic of Ireland. Finally, the equivalence between a special case of the set partitioning problem and the shortest route problem is considered and it is shown that this equivalence also applies to the extended model.