A Branch-and-Price Algorithm for an Integrated Online and Offline Retailing Distribution System with Product Return

Table 1

The symbols and notations.

	Explanations
Sets
	Set of all nodes (central warehouse, retail stores, and customers)
	Set of retail stores
	Set of customers ordering products online
	Set of customers with product returns
	Set of available vehicles
Parameters
	Vehicle capacity
	Demand of node
	Number of returned products from customer
	Inventory level at retail store
	Delivery cost with traversing arc
	Delivery time with traversing arc
	Service time at the node
Decision variables
	The number of products needed to be picked up at retail store by vehicle
	The product quantity carried by vehicle after leaving node
	The arrive time at node by vehicle
	1 if the arc is traversed by vehicle , and 0 otherwise
	1 if customer is served by store and 0 otherwise