A note on ‘A LP‐based heuristic for a time‐constrained routing problem’

In their paper, investigate a time‐constrained routing problem. The core of the proposed solution approach is a large‐scale linear program that grows both row‐ and column‐wise when new variables are introduced. Thus, a column‐and‐row generation algorithm is proposed to solve this linear program optimally, and an optimality condition is presented to terminate the column‐and‐row generation algorithm. We demonstrate by using Lagrangian duality that this optimality condition is incorrect and may lead to a suboptimal solution at termination.