A computer-implemented method for routing shipments according to criticality includes accessing an initial solution to an optimization problem of routing multiple shipments to multiple locations using multiple vehicles, the initial solution including multiple loads such that each shipment is routed within exactly one load and a global cost across all loads is minimized, the initial solution being generated independent of the criticality of the shipments. Into each of one or more critical loads in a current solution, one or more non-critical shipments are inserted that are within a neighborhood of the critical load, a critical load being a load containing at least one critical shipment. One or more local search operations are executed to improve the initial solution, the operations including at least one of: (a) splitting each of one or more selected critical loads in a current solution into two new critical loads; (b) for each of one or more selected critical load pairs in a current solution, move a sequence of stops from one critical load in the pair to the other critical load in the pair and / or swap two sequences of stops between the critical loads in the pair; and (c) for each of one or more selected critical loads in a current solution that are indirect critical loads having at least one in-transit stop, break up the indirect critical load into a plurality of new direct critical loads having no in-transit stops and execute operation (b) on each of one or more selected critical load pairs, each selected critical load pair including at least one new direct critical load.