University of Leeds SCHOOL OF COMPUTER STUDIES

In this paper, the problem of bus driver scheduling is introduced, and some of the constraints and conditions existing in different user environments are presented. The way in which such conditions may affect solution methods is discussed. The development of driver scheduling by computer through the five prevous Workshops is presented, and the range of solution methods as evidenced by published papers is summarised. Particular attention is paid to the work presented at the later workshops, but papers published elsewhere are also introduced, and the authors draw on their own knowledge to augment the published material. Introduction In this paper we present a survey of computer approaches to transit driver scheduling, with particular emphasis on the state of the art as it existed at the time of the Montreal Workshop on Computer-Aided Scheduling of Public Transport in 1990 [5]. We start by outlining the driver scheduling problem and its variants. We then classify solution methods, and outline a wide range of reported work in the field. We conclude by speculating on future developments. The paper relies heavily on presentations made at the five international Workshops [1,2,3,4,5] held from 1975, and draws also on other published material and on the authors' own knowledge. Most papers which relate to driver scheduling and were presented at the Workshops are listed in the References under the main heading for the relevant Workshop, even if they are not explicitly mentioned here. The papers for the first Workshop exist in preprint form only, but are listed, while some of the presentations at the fourth and fifth Workshops were not included in the proceedings and are not listed here. Scheduling terminology differs widely between countries, between organisations within a single country, and even between parts of a single organisation. Hartley [2-16] has produced a glossary which includes alternative terms for the same concept, and alternative concepts for the same term. We attempt here while following Hartley to use terms which do not have alternative meanings and are easily understood. Thus, we use block to mean a sequence of trips assigned successively to one bus, beginning with a pull-out and ending with a pull-in. A bus which leaves the depot more than once in a day consists of several blocks. A shift is the work scheduled to be performed by a driver in one day. The driver scheduling problem The process of driver scheduling is the construction of a set of legal shifts (including overtime portions where allowed) which together cover all the blocks in a particular vehicle schedule, that is, in a schedule for several vehicles which may reflect the whole operation of an organisation, or a self-contained part of that operation. The problem is generally known as run-cutting in North America, and is often referred to as crew scheduling elsewhere. Blocks may be considered as being divided into units of work which start and finish at relief