Research Article

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 .