Urban Freight Management with Stochastic Time-Dependent Travel Times and Application to Large-Scale Transportation Networks

Table 1

Notations and variables.

Type	Symbol	Definition
Objective; function; quantities		The number of vehicles out for service
	ST	Total schedule time
	TT	Total travel time
	WT	Total waiting time
	SVT	Total service time
Sets		Set of starting nodes of all vehicles
		Set of end nodes of all vehicles
		Set of all customer nodes
		Set of starting nodes and customer nodes
		Set of customer nodes and end nodes
		Set of all nodes
		Set of all customers
		Subset of set
		Set of links that are present in the networks
Inputs and parameters		The number of time intervals
		Time interval
		An infinite number
		Service time of customer node
		Delivery demand of customer node
		Time window of depot
		Time window constraint of customer node
		Capacity of vehicle
Decision variables		Vehicle’s arrival time at node
		, if any vehicle occupies at time ; otherwise
		Travel times of the optimal path from customer node i to customer node j at departing time interval
		, if vehicle departs from customer node to customer node at time interval ; otherwise
		, if customer node is visited by vehicle ; otherwise,