Distribution Network Design for Fixed Lifetime Perishable Products: A Model and Solution Approach

Algorithm 3

Lagrangian relaxation heuristic algorithm.

Step size = 2, Best upper bound = 10⁵⁵, best lower bound = −10⁵⁵, Iteration number = 1, non-improving

iteration = 0,

While iteration number < max iteration number

   Calculate lower bound;

   Calculate upper bound;

   If current upper bound < Best upper bound

     Best upper bound = Current upper bound;

   End

   If current upper bound < Best lower bound

     Best lower bound = −10⁵⁵;

   End

   If Current lower bound > Best lower bound and Best lower bound < Best upper bound

     Best lower bound = Current lower bound;

   End

   If number of consecutive non-improving iterations = 30

     Halve step size;

   End

   Update Lagrangian multipliers for all retailers;

   If min upper bound and best lower bound solutions are equal, or step size <10⁻⁷

     Go to Final step;

   End

   Iteration number = iteration number + 1;

End

Final step: Return solution;

Compute optimality gap ((UB−LB)/UB)∗100%