A note on “A LP-based heuristic for a time-constrained routing problem”
Muter, İbrahim and Birbil, Ş. İlker and Bülbül, Kerem and Şahin, Güvenç (2010) A note on “A LP-based heuristic for a time-constrained routing problem”. (Submitted)
Avella et al. (2006) [Avella, P., D'Auria, B., Salerno, S. (2006). A LP-based heuristic for a time-constrained routing problem. European Journal of Operational Research 173:120-124] investigate a time-constrained routing (TCR) problem. The core of the proposed solution approach is a large-scale linear program (LP) that grows both row- and column-wise when new variables are introduced. Thus, a column-and-row generation algorithm is proposed to solve this LP optimally, and an optimality condition is presented to terminate the column-and-row generation algorithm. We demonstrate that this optimality condition is incorrect and may lead to a suboptimal solution at termination. We identify the source of this error and discuss how the generic column-and-row generation algorithm proposed by Muter et al. (2010) may be applied to this TCR problem in order to solve the proposed large-scale LP correctly.
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