Deficit function related to public transport: 50 year retrospective, new developments, and prospects

- Making, for the first time, a systematic, comprehensive, and thorough retrospective examination of the major developments of the Deficit Function (DF) and its modelling and applications in public transport (PT) planning and operations over the past 50 years.
- Showing and proving that the graphical DF concept helps in creating efficient PT vehicle schedules, timetables, crew duties, networks of routes, bus rapid transit systems, and operational parking spaces.
- Showing how the DF concept allows for methods and tools to be employed to improve PT patronage and livability from the perspective of PT users, and reduce operation costs, from the perspective of PT operators.
- Lately, as an example, a highly informative DF graphical optimization technique was developed for one of the largest bus transit companies in the world, where the total number of vehicles and crew duties were reduced by 6% to 12% and 8% to 15%, respectively.
- Encouraging and stimulating further interest for research in the use of the DF modelling as a bridge between the world of researchers and the world of practitioners.

The Deficit Function (DF), with its graphical concept and modelling, was introduced 50 years ago by Linis and Maksim (1967) under the title of “On the problem of constructing routes.” Since then, there have been many developments in the understanding of the theoretical, methodological and application aspects of the DF concept. This work, for the first time, makes a comprehensive and thorough retrospective examination of the major developments of DF modelling and applications in public transport (PT) planning and operations over the past 50 years, introduces some new developments, and offers future research directions. It is shown and proven that the graphical DF concept helps in creating efficient PT vehicle schedules, timetables, crew duties, networks of routes, bus rapid transit systems, and operational parking spaces. For instance, in one large bus company the total number of vehicles and crew duties were reduced by 6% to 12% and 8% to 15%, respectively. This work intends to stimulate further use of the DF concept as a bridge between the world of researchers and the world of practitioners.