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In this research we consider the problem of accelerating the convergence ofcolumn generation (CG) for the weighted set cover formulation of thecapacitated vehicle routing problem with time windows (CVRPTW). We adapt twonew techniques, Local Area (LA) routes and Graph Master (GM) to these problems.LA-routes rely on pre-computing all lowest cost elementary sub-routes, calledLA-arcs, where all customers but the final customer are localized in space.LA-routes are constructed by concatenating LA-arcs where the final customer ina given LA-arc is the first customer in the subsequent LA-arc. To construct thelowest reduced cost elementary route during the pricing step of CG we apply aDecremental State Space Relaxation/time window discretization method over time,remaining demand, and customers visited; where the edges in the associatedpricing graph are LA-arcs. To accelerate the convergence of CG we use anenhanced GM approach. We map each route generated during pricing to a stricttotal ordering of all customers, that respects the ordering of customers in theroute; and somewhat preserves spatial locality. Each such strict total orderingis then mapped to a multi-graph where each node is associated with a tuple ofcustomer, capacity remaining, and time remaining. Nodes are connected byfeasible LA-arcs when the first/last customers in the LA-arc are less/greaterthan each intermediate customer (and each other) with respect to the totalorder. The multi-graph of a given route can express that route and other"related" routes; and every path from source to sink describes a feasibleelementary route. Solving optimization over the restricted master problem overall multi-graphs is done efficiently by constructing the relevant nodes/edgeson demand.

Graph Master and Local Area Routes for Efficient Column Generation for the Capacitated Vehicle Routing Problem with Time Windows