A Multiperiod Vehicle Lease Planning for Urban Freight Consolidation Network

Algorithm 2

Overall solution procedure for .

PROC(MVLPUC)

begin

(1) Initialize the necessary parameters and Lagrange multipliers (i.e., , , ,

   , , and );

(2) Initialize where represents the number of consecutive iterations for

   which the best lower bound has not been improved;

   repeat

(3)    Solve the Lagrangian problem , and let be the resulting objective value;

      if     then

(4)     Set and ;

     else

(5)    Set

      end

(6)   Find a feasible solution by (CH) where represents the

     feasible solution to at iteration ;

     if   (TSH)-activating conditions are satisfied   then

(7)    Update by (TSH);

      end

(8)   Let be the objective value of the solution for ;

(9)   if     then

(10)    Set , and set where represents

         the best feasible solution searched until iteration ;

      end

      if     then

(11)    Set and ;

    end

(12)   Update by the subgradient optimization procedure (refer to Section 3.3);

(13)   Set ;

   until   the aforementioned termination conditions (i.e., , or ) are met;

end