A route decomposition approach for the single commodity Split Pickup and Split Delivery Vehicle Routing Problem

We address a single commodity Pickup and Delivery Vehicle Routing Problem from the literature. A network of customer nodes is given with both travel times costs. fleet vehicles limited capacity exploited to satisfy node demands, set routes must be found such that vehicle capacities are never exceeded, each route does not exceed time resource, cost minimized. The demands pickup delivery can split, visited more than once. provide new theoretical insights. propose formulation where decomposed into sequences simpler substructures called clusters, mitigating combinatorial explosion feasible solutions. introduce valid inequalities, design branch-and-price algorithm, exploiting ad hoc pricing routines branching strategies, embedding rounding heuristic speed up pruning. An extensive experimental analysis shows our method offer simultaneously modelling flexibility computational effectiveness previous attempts Our investigation opens also interesting insights use decomposition strategies.