Public-transit vehicle schedules using a minimum crew-cost approach

Commonly, public transit agencies, with a view toward efficiency, aim at minimizing the number of vehicles in use to meet passenger demand, and therefore at reducing crew cost. This work contributes to achieving these two objectives by proposing the use of two predominant characteristics of public-transit operations planning: (a) different resource requirements between peak and off-peak periods, and (b) working during irregular hours. These characteristics result in split duties (shifts) with unpaid in-between periods. The outcome of this work is an optimal solution for maximizing the unpaid shift periods with the assurance of complying with the minimum number of vehicles attained. The optimization problem utilizes a highly informative graphical technique (deficit function) for finding the least number of vehicles; this enables the construction of vehicle chains (blocks) that take into account maximum unpaid shift periods. The latter consideration is intended to help construct crew schedules at minimum cost. The methodology developed was implemented by two large bus companies and resulted in a significant cost reduction.