Optimization of Vehicle Paths considering Carbon Emissions in a Time-Varying Road Network

Table 1

Description of symbols for path optimization problems.

Notation	Definition
N	The set of serial numbers of all demand points, N = {0, 1, ..., n}, where 0 denotes the distribution center and the rest nodes denote demand points
S	The set of originating nodes
E	The set of final arrival nodes
SC	The set of originating nodes and demand nodes
DE	The set of demand nodes and final arrival nodes
B	An infinite number
K	The set of all vehicles, K = {l, 2, ..., n}
F	Denotes the fixed cost of dispatching a vehicle
Cij	The unit transportation rate from point i to point j
qi	The quantity demanded at demand point i
Q	Maximum load capacity of a dispatching vehicle
[ET, LT]	The left and right time windows of the distribution center
[ai, bi]	Left and right time windows for demand point i
Dij	Distance from demand point i to distribution center j
Wik	Time when vehicle k arrives at demand point i
Si	Service time of demand point i
Tijk	Travel time of vehicle k from demand point i to demand point j
ϒ	Price per unit of carbon emissions
Yik	0-1 variable, yik = 1 when the kth vehicle is in service, otherwise yik = 0
P	Overload penalty factor
R	Overtime penalty factor
SD	Any subset of the set of demand points
|SD|	Number of demand points in the set S
Xijk	0-1 variable, xijk = 1 when the kth vehicle passes from point i to point j, otherwise xijk = 0