A Column Generation Algorithm for the Resource-Constrained Order Acceptance and Scheduling on Unrelated Parallel Machines

Algorithm 1 The procedure of the proposed column generation.

 Step 1: implement the proposed constructive heuristic to obtain a feasible solution

 Step 2: initialize the RLMP with the solution obtained by the constructive heuristic

 Step3: set the number of consecutive iterations of failing to find a column with positive reduced cost to be 0, i.e.,

 Step 4: while is less than a specified number , do

 Step 4.1: solve the RLMP and get the dual solution

 Step 4.2: define the subproblems by the current dual solution and solve them by the proposed DE algorithm

 Step 4.3: If there exist columns with positive reduced cost, do

  Add new columns to the RLMP;

 Else

 End

 End

 Step 5: convert the RLMP model to an IP model

 Step 6: solve the IP model by CPLEX

 Step 7: output the solution