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

Algorithm 2

Label-setting algorithm.

	Require: updated based on due cost and
	Ensure: The solution S1;
(1)	Generate an initial label ;
(2)	Set and ;
(3)	for alldo;
(4)	Set and ;
(5)	end for
(6)	whiledo
(7)	Choose a label ;
(8)	for all and extension along is feasible do
(9)	Extend along arc and create label ;
(10)	if is not dominated by any label in then
(11)	Set ;
(12)	Discard the labels in which are dominated by ;
(13)	end if
(14)	Set and ;
(15)	end for
(16)	end while
(17)	Return the route with minimum reduced cost defined by labels in .