In this paper we present a new variant of the classical Vehicle Routing Problem – the Fleet Size and Mix Vehicle Routing Problem with Backhauls (FSMVRPB). An ILP formulation of the FSMVRPB is presented. Optimal solutions for small size instances are produced and upper and lower bounds are generated for larger ones. In this paper we also propose a Set Partitioning Problem (SPP) based heuristic. ...

Abstract In the classic Vehicle Routing Problem (VRP) a fleet of of vehicles has to visit a set of customers while minimising the operations’ costs. We study a rich variant of the VRP featuring split deliveries, an heterogeneous fleet, and vehiclecommodity incompatibility constraints. Our goal is twofold: define the cheapest routing and the most adequate fleet. To do so, we split the problem in...

This paper proposes a bus line capacity optimization design model considering the scale of multiple vehicles, which is achieved by minimizing system operating costs and user costs. The proposed takes into account difference passenger demand in different periods, can get optimal headway delivery reserve plan. In order to prove that method effectively minimize cost, we solved numerical example co...

This paper presents a hybrid evolutionary algorithm (HEA) to solve heterogeneous fleet vehicle routing problems with time windows. There are two main types of such problems, namely the fleet size and mix vehicle routing problem with time windows (F) and the heterogeneous fixed fleet vehicle routing problem with time windows (H), where the latter, in contrast to the former, assumes a limited ava...

In this paper, we propose a new routing problem to model a highly relevant planning task in small package shipping. We consider the Prize-Collecting Vehicle Routing Problem with Non-Linear cost (PCVRPNL) in its single and multi-depot version, which integrates the option of outsourcing customers to subcontractors instead of serving them with the private fleet. Thereby, a lower bound on the total...

287 Numerous organizations are involved in distributing goods and materials. When shipping alternatives exist, the selection of the appropriate shipping alternative (mode) for each shipment may result in significant cost savings. This paper describes a highly flexible dispatching system that selects the shipping mode to be used for each shipment while minimizing the overall shipping costs. Mult...