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We consider the problem of accelerating column generation (CG) for logisticsoptimization problems using vehicle routing as an example. Without loss ofgenerality, we focus on the Capacitated Vehicle Routing Problem (CVRP) via theaddition of a new class of dual optimal inequalities (DOI) that incorporateinformation about detours from the vehicle routes. These inequalities extendthe Smooth-DOI recently introduced in the literature for the solution ofcertain classes of set-covering problems by CG. The Detour-DOI introduced inthis article permit low cost swap operations between items on a given activeroute with items near to other items on that route to estimate (and bound) thevalues of the dual variables. Smooth-DOI in contrast only permit low cost swapoperations between nearby items. The use of Detour-DOI permits a fasterconvergence of CG without weakening the linear programming relaxation. We thenargue that these DOI can also be conveniently applied to single sourcecapacitated facility location problems. These problems have been shown to beequivalent to a broad class of logistics optimization problems that include,for example telecommunication network design and production planning. Theimportance of developing vastly more efficient column generation solvers cannotbe overstated. Detour-DOI, which permit large numbers of columns to beexpressed with a finite set of variables, contributes to this importantendeavor.

Detour Dual Optimal Inequalities for Column Generation with Application to Routing and Location