چکیده

The vehicle routing problem (VRP) is a wellknown combinatorial optimisation problem and holds a central place in
logistics management. Many exact, heuristic and metaheuristic approaches have been proposed to solve VRP. An important
variant of the VRP arises when a fleet of vehicles is fixed and characterised by different capacities for distribution
activities. The problem is known as the heterogeneous fixed fleet VRP (HFFVRP). The HFFVRP is a natural generalisation
of the VRP with several vehicle types, each type being defined by a capacity, a fixed cost and a cost per distance
unit, and can cover more practical situations in transportation. This problem consists of determining a set of vehicle trips
of minimum total length in which a set of customers is to be satisfied in the demand constraints using identical vehicles
with limited capacity. If open routes instead of closed ones are considered in the HFFVRP, the problem becomes a heterogeneous
fixed fleet Open VRP (HFFOVRP) which has numerous applications in industrial and service problems. In this
paper, a bone route algorithm which uses the tabu search as an improved procedure is utilised to solve the HFFOVRP.
The proposed algorithm was tested empirically on a 24 of generated VRPs, and compared with elite ant system and ant
colony system. In all cases, the proposed algorithm finds the bestknown solutions within a reasonable time.
