Allocating Cost to Shippers in Pickup and Delivery Service

Table 2

Parameter and Variable.

	Parameter
	Total cost is calculated by PDP algorithm (e.g. [5, 6]).
	Cost of shipper allocated by alliance.
	Shipper single stop delivery cost from depot.
	Cost between nodes and , without loss of generality, we set . is Euclidean distance between nodes and .
	Cost contribution factors, including and .
	Marginal cost contribution rate of node .
	Dispersion degree of node with other nodes.
	Marginal cost, which is the decreased value of the total route length after removing node while keeping others with the original visiting sequence.
	Let be the index of the th shipper in the sequence of ordered cost contribution factors.
	Set of node delivered by same vehicle.
	The set of nodes.
	The set of pickup nodes.
	Variable
	Cost of node allocated by alliance.
	A minimum penalized slack in the constraints defining the core to keep the grand coalition “stable”.
	Minimum difference between the cost of shipper and its cost based on geographical location.