This paper develops a multi-modal transport network model considering various
travel modes including railway, bus, auto, and walking. Travellers are assumed to choose
their multi-modal routes so as to minimise their perceived disutilities of travel following the
Probit Stochastic User Equilibrium (SUE) condition. Factors influencing the disutility of a
multi-modal route include actual travel times, discomfort on transit systems, expected
waiting times, fares, and constants specific to transport modes. The paper then deals with
the multi-modal network design problem (NDP). The paper employs the method of sensitivity
analysis to define linear approximation functions between the Probit SUE link flows
and the design parameters, which are then used as constraints in the sub-problem of the
NDP instead of the original SUE condition. Based on this reformulated NDP, an efficient
algorithm for solving the problem is proposed in the paper. Two instances of this general
NDP formulation are then presented in the paper: the optimal frequency design problem for
public transport services (FDP), and the anti-freezing admixture dispersion problem
(AADP).