Ferry service network design with stochastic demand under user equilibrium flows

This paper develops a service reliability-based formulation for ferry service network design with stochastic demand under user equilibrium flows while considering two types of services, regular and ad hoc. Regular services operate with a fixed schedule; whereas ad hoc services are those subcontracted or outsourced to a third party and have a higher unit cost. Two ad hoc provision schemes are studied. Scheme A considers that the demand information is known in advance by passenger reservation, and the company makes use of this information to plan for ad hoc services. In Scheme B, the demand realization is only known as passengers arrive at the piers and the company calls upon ad hoc services in case of demand overflow. In Scheme A, we utilize the notion of service reliability (SR) to address the issue of demand uncertainty and formulate the problem as a two-phase stochastic program in which the schedule of regular services and ad hoc services are derived sequentially. The user equilibrium (UE) assignment with capacity constraint is formulated via a linear programming (LP) approach considering overflow delays. A SR-based gradient solution approach is developed to solve the model. Scheme B, as expected, requires more resources to operate, for which a SR-based non-linear model is developed. The value of reservation to the company is defined as the operating cost difference between these two schemes. We apply the methods to ferry service network design in Hong Kong, and then compare the UE (Scheme A) and system optimal (SO) solutions, in terms of service deployment and computation time, to contrast the solution quality arising from the inclusion of equilibrium flows. The value of advance reservation information between Scheme A and Scheme B is presented as well.