SYSTÉMOVÁ INTEGRACE 4/2007 76 Computer Aided Solution for Driver Scheduling in Public Transportation Penka Martincová, Katarína Zábovská, Michal Zábovský University of Zilina, Faculty of Management Science and Informatics, penka.martincova@fri.uniza.sk, katarina.zabovska@fri.uniza.sk, michal.zabovsky@fri.uniza.sk Abstract: The operating cost of public transport depends mostly on drivers than on vehicles. Finding the optimal work package is NP-hard and hence special algorithms and enhanced computing must be used. Because of legal differences, it is not possible to apply rules and experiences for working shifts creation form other countries in general and hence this paper is focused to specific solution for public companies if the legal scope of Slovak Republic. Keywords: public transportation, operating costs, shifts scheduling, driver scheduling, operational research Introduction The problem of scheduling public transport and its drivers is in the centre of research interest over many years. Presented solutions techniques are in particular of two kinds. The first approach is based on simultaneous creation of vehicle schedules and is, almost entirely, used in Czech and Slovak Republic. The main disadvantage of such approach is that idle vehicle time is quite significant because of a legal restriction of driving and working time. Different technique is based on vehicle schedules created first, without any driver constraints, and consequently the created set of shifts is covered by driver schedules created again without any connections to vehicles. As a result is produced set of working shifts where drivers are changing particular vehicle couple of times. Because of legal differences, it is not possible to apply rules and experiences for working shifts creation from other countries and hence this paper is focused to process of valid shifts creation for public transportation companies in the legal scope of Slovak Republic. The most successful commercial driver scheduling packages TRACK II (Fores, Troll and Wren, 2002) and HASTUS (Hamer and Seguin, 1992) model the problem using mathematical programming. Mathematical programming approaches are basically of two types. First one, “generate and select”, is included in TRACK II and based on pre-generated set of working shifts. As, for computational complexity, resulted set is only a small subset of all possible shifts and thus this technique cannot guarantee to find optimal solution of the model. Column generation and branch-and-bounds technique (Wolsey, 1998, Barnhart et al., 1998) dealing with this problem by generating “useful” shifts from the implicitly defined full set of potential shifts. In practice, despite of current technologies, computational complexity is significant and problem of finding optimal solution cannot, in general, be found. Fortunately, intelligent use of heuristics together with computational power allows achieving acceptable schedules in reasonable time [1].