Abstract
This paper deals with a split delivery vehicle routing problem, which is a modification of a vehicle routing problem. It consists in delivery routes optimization in communications network containing initial city of all routes and a given number of places, which is necessary to include in delivery routes, where a customer can be served by more than one vehicle. The objective is to find a set of vehicle routes that serve all the customers and the total distance traveled is minimized. The split delivery vehicle routing problem is NP hard, therefore we present a solution approach by three heuristics, and a metaheuristics called Ant colony optimization (ACO).
Highlights
Vehicle routing problem (VRP) is a classical problem in operations research
In most VRPs it is assumed that the demand of a customer is given and is less than or equal to the capacity of a vehicle and that each customer has to be served by exactly one vehicle, i.e., there is a single-visit assumption
As the split delivery vehicle routing problem is NP hard, for the large problem the solution of the model cannot be obtained for acceptable computer time consumption
Summary
Vehicle routing problem (VRP) is a classical problem in operations research. It consists in delivery routes optimization in communications network containing depot of all routes and a given number of cities, which is necessary to include in delivery routes. The condition is that the sum of demands of the cities on the route should be less than or equal to the capacity of vehicle. It is obvious that when a customer’s demand exceeds the vehicle capacity it is necessary to visit that customer more than once. The inequality (5) defines variable ui, which represents the demand on the route k from the city 1 to the city i This condition has the anti-cycling effect – it prevents creating the sub-cycles in the solution. The condition (7) means that demand on the route k does not exceed the vehicle capacity V. Otherwise the city is not deleted from the set M, and city has the demand pk ϭ qk Ϫ V, the route is closed and the method continues by the step 1 (starting (2) the new route).
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