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Table 1 Notations used in formulations

From: A bi-objective model for uncertain multi-modal shortest path problems

Notations Definition
V = set of nodes in the multi-modal network.
E = set of arcs in the multi-modal network.
M = set of the transport modes, M={p,b,m,t}.
p = the private mode.
b = the bus mode.
m = the metro mode.
t = the transfer mode.
i,j = index of nodes, i,jN.
(i,j,k) = connections between the adjacent nodes of mode k.
ξ ijk = travel time/transfer time on arc (i,j,k).
c ijk = travel cost on arc (i,j,k), kM{t}.
d k = fixed cost when entering mode k.
x ijk = 1, if arc (i,j,k) is on the path, 0 otherwise, (i,j,k)E.
y k = 1, if x ijk =1 for a certain (i,j,k)E, 0 otherwise, kM{t}.