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.

[1]  Benar Fux Svaiter,et al.  A Practical Optimality Condition Without Constraint Qualifications for Nonlinear Programming , 2003 .

[2]  George L. Nemhauser,et al.  Handbooks in operations research and management science , 1989 .

[3]  Huifu Xu,et al.  An Implicit Programming Approach for a Class of Stochastic Mathematical Programs with Complementarity Constraints , 2006, SIAM J. Optim..

[4]  Hong Kam Lo,et al.  Global Optimum of the Linearized Network Design Problem with Equilibrium Flows , 2010 .

[5]  Hong Kam Lo,et al.  Multi-fleet ferry service network design with passenger preferences for differential services , 2008 .

[6]  Hong Kam Lo,et al.  ROUTING THROUGH DYNAMIC OCEAN CURRENTS: GENERAL HEURISTICS AND EMPIRICAL RESULTS IN THE GULF STREAM REGION , 1995 .

[7]  Hong Kam Lo,et al.  FERRY SERVICE NETWORK DESIGN: OPTIMAL FLEET SIZE, ROUTING AND SCHEDULING , 2004 .

[8]  Michael Patriksson,et al.  Stochastic mathematical programs with equilibrium constraints , 1999, Oper. Res. Lett..

[9]  T. Iryo.  Properties of dynamic user equilibrium solution: existence, uniqueness, stability, and robust solution methodology , 2013 .

[10]  Shuaian Wang,et al.  Essential elements in tactical planning models for container liner shipping , 2013 .

[11]  Hong Kam Lo,et al.  Transit Network Design under Demand Uncertainty , 2012 .

[12]  M. Fukushima,et al.  Solving stochastic mathematical programs with equilibrium constraints via approximation and smoothing implicit programming with penalization , 2008, Math. Program..

[13]  Giulio Erberto Cantarella,et al.  Modelling sources of variation in transportation systems: theoretical foundations of day-to-day dynamic models , 2013 .

[14]  Hong Kam Lo,et al.  Ferry service network design under demand uncertainty , 2013 .

[15]  M. Patriksson.  On the applicability and solution of bilevel optimization models in transportation science: A study on the existence, stability and computation of optimal solutions to stochastic mathematical programs with equilibrium constraints , 2008 .

[16]  Hai Yang,et al.  Modeling the capacity and level of service of urban transportation networks , 2000 .

[17]  Stella Dafermos,et al.  Traffic Equilibrium and Variational Inequalities , 1980 .

[18]  Xiaojun Chen,et al.  Robust Wardrop’s user equilibrium assignment under stochastic demand and supply: Expected residual minimization approach , 2011 .

[19]  M. Bell.  STOCHASTIC USER EQUILIBRIUM ASSIGNMENT IN NETWORKS WITH QUEUES , 1995 .

[20]  Hong Kam Lo,et al.  ADAPTIVE SHIP ROUTING THROUGH STOCHASTIC OCEAN CURRENTS: GENERAL FORMULATIONS AND EMPIRICAL RESULTS , 1998 .

[21]  Qiang Meng,et al.  Liner ship route schedule design with sea contingency time and port time uncertainty , 2012 .

[22]  Jane J. Ye,et al.  Necessary and sufficient optimality conditions for mathematical programs with equilibrium constraints , 2005 .

[23]  W. Y. Szeto,et al.  A cell-based variational inequality formulation of the dynamic user optimal assignment problem , 2002 .

[24]  Qiang Meng,et al.  General stochastic user equilibrium traffic assignment problem with link capacity constraints , 2008 .

[25]  J. F. Benders.  Partitioning procedures for solving mixed-variables programming problems , 1962 .

[26]  R. Wets,et al.  L-SHAPED LINEAR PROGRAMS WITH APPLICATIONS TO OPTIMAL CONTROL AND STOCHASTIC PROGRAMMING. , 1969 .

[27]  Hai Yang,et al.  A stochastic user equilibrium assignment model for congested transit networks , 1999 .

[28]  Alaa Mustapha Elyamak.  Fleet Sizing and Scheduling Model of Container Carriers between Two Ports , 2008 .

[29]  Hai Yang,et al.  Global optimization methods for the discrete network design problem , 2013 .

[30]  Hai Yang,et al.  TRAFFIC RESTRAINT, ROAD PRICING AND NETWORK EQUILIBRIUM , 1997 .

[31]  W. Y. Szeto,et al.  A CELL-BASED SIMULTANEOUS ROUTE AND DEPARTURE TIME CHOICE MODEL WITH ELASTIC DEMAND , 2004 .

[32]  A. Ruszczynski.  Stochastic Programming Models , 2003 .