Improved Branch-Cut-and-Price for Capacitated Vehicle Routing

The best performing exact algorithms for the Capacitated Vehicle Routing Problem are based on the combination of cut and column generation. Some authors could obtain reduced duality gaps by also using a restricted number of cuts over the Master LP variables, stopping separation before the pricing becomes prohibitively hard. This work introduces a technique for greatly decreasing the impact on the pricing of the Subset Row Cuts, thus allowing much more such cuts to be added. The newly proposed Branch-Cut-and-Price algorithm also incorporates and combines for the first time (often in an improved way) several elements found in previous works, like route enumeration and strong branching. All the instances used for benchmarking exact algorithms, with up to 199 customers, were solved to optimality. Moreover, some larger instances with up to 360 customers, only considered before by heuristic methods, were solved too.