The Fourth-Party Logistics Routing Problem Using Ant Colony System-Improved Grey Wolf Optimization

Table 1

Parameter definition of the model.

Parameter	Parameter description
	The number of city nodes in the transportation network; it also indicates the label of endpoint.
	The number of edges (3PLs) between node and node .
	The k^th edge between node and node , where , and k is the index number of edges.
	The time of node , including the time of processing, inventory, loading, and unloading.
	The cost of node , including the cost of processing, inventory, loading, and unloading.
	The time of the 3PL provider in edge .
	The cost of the 3PL provider in edge .
	The transport time of the route.
	The transport cost of the route.
	The minimum time of the 3PL provider in edge .
	The maximum time of the 3PL provider in edge .
	The shortest transport time between node and node .
	The longest transport time between node and node .
	The minimum transport time of the route.
	The maximum transport time of the route.
	The minimum cost of the 3PL provider in edge .
	The maximum cost of the 3PL provider in edge .
	The maximum transport cost between node and node .
	The maximum transport cost between node and node .
	The minimum transport cost of the route.
	The maximum transport cost of the route.
	The due date required by the customer.
	The total cost required by the customer.
	Weight of the time.
	Weight of the cost.
	Transport capacity of the 3PL provider in edge .
	Reputation of the 3PL provider in edge .
	The required transport capacity from the task.
	The amount of task that transits at the node.
	The delay probability of transportation tasks.
	The probability of the overspending of transportation tasks.
	The required reputation required by the customer.
	The route from node to node .
	The proportion of transport tasks undertaken by edge .
	Whether the 3PL provider is selected between node and node to undertake the transportation task, which is a 0-1 variable.
	Whether the edge is selected to undertake the transportation task, which is a 0-1 variable.
	Whether to select node as a transit node, which is a 0-1 variable.