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

Document Type

Journal Article

Publication Date


Subject Area

mode - bus rapid transit, operations - scheduling, planning - methods


Deficit function, Public transport, Operations planning, Human-machine interactive, Graphical optimization method, History of work done


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.


Permission to publish the abstract has been given by Elsevier, copyright remains with them.


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