In this project, Vehicle Routing Problem (VRP) is studied. VRP is an NP-hard combinatorial optimization problem. It appears in a large number of real world situations, such as transportation of people and products, delivery services, garbage collection etc. It can be applied everywhere, for vehicles, trains, plains; that is why Vehicle Routing Problem is of great practical importance in real life. The Vehicle Routing Problems (VRPs) are the ones concerning the distribution of goods between depots and customers. In particular, the solution of VRP calls for the determination of a set of routes, each performed by a single vehicle that starts and ends at its own depot, such that all requirements of the customers are fulfilled, all operational constraints
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It appears in a large number of practical situations, such as transportation of people and products, delivery services, garbage collection etc. It can be applied everywhere, for vehicles, trains, planes etc. that is why Vehicle Routing Problem is of great practical importance in real life. The vehicle Routing Problems (VRPs) are the ones concerning the distribution of goods between depots and customers. The distribution of goods concerns, in a given time period, of a set of customers by a set of vehicles, which are located in one or more depots, are operated by a set of crews (drivers) and perform their movements by using an appropriate road network. In particular, the solution of VRP calls for the determination of a set of routes, each performed by a single vehicle that starts and ends at its own depot, such that all requirements of the customers are fulfilled, all operational constraints are satisfied, and the global transportation cost is minimized. VRPs are multi-objective in nature and these objectives are conflicting (preventing simultaneous optimization) in general. It means that one objective is optimized at the cost of other objective. Today, exact VRP methods have a size limit of 50-100 orders depending on the VRP variant and the time-response requirements. Consequently, current research concentrates on approximate algorithms that are capable of finding high quality solutions in …show more content…
Here vertex 0 corresponds to the depot and vertices i = 1…n corresponds to customers. A nonnegative cost, cij, is associated with each edge (i,j) ∈ E and represents the travel cost spent to go from vertex i to vertex j. If G is a directed graph, the cost matrix c is asymmetric, and the corresponding problem is called asymmetric CVRP (ACVRP) on the other hand if cij = cji for all (i, j) ∈ E, then the problem is called symmetric CVRP (SCVRP), and the edge set E is generally replaced by a set of undirected edges. In several practical cases, the cost matrix satisfies the triangle inequality. Each customer i (i = 1 . . . n) is associated with a known nonnegative demand, di, to be delivered, and the depot has a fictitious demand do = 0.A set of K identical vehicles, each with capacity C, is available at the
It appears in a large number of practical situations, such as transportation of people and products, delivery services, garbage collection etc. It can be applied everywhere, for vehicles, trains, planes etc. that is why Vehicle Routing Problem is of great practical importance in real life. The vehicle Routing Problems (VRPs) are the ones concerning the distribution of goods between depots and customers. The distribution of goods concerns, in a given time period, of a set of customers by a set of vehicles, which are located in one or more depots, are operated by a set of crews (drivers) and perform their movements by using an appropriate road network. In particular, the solution of VRP calls for the determination of a set of routes, each performed by a single vehicle that starts and ends at its own depot, such that all requirements of the customers are fulfilled, all operational constraints are satisfied, and the global transportation cost is minimized. VRPs are multi-objective in nature and these objectives are conflicting (preventing simultaneous optimization) in general. It means that one objective is optimized at the cost of other objective. Today, exact VRP methods have a size limit of 50-100 orders depending on the VRP variant and the time-response requirements. Consequently, current research concentrates on approximate algorithms that are capable of finding high quality solutions in …show more content…
Here vertex 0 corresponds to the depot and vertices i = 1…n corresponds to customers. A nonnegative cost, cij, is associated with each edge (i,j) ∈ E and represents the travel cost spent to go from vertex i to vertex j. If G is a directed graph, the cost matrix c is asymmetric, and the corresponding problem is called asymmetric CVRP (ACVRP) on the other hand if cij = cji for all (i, j) ∈ E, then the problem is called symmetric CVRP (SCVRP), and the edge set E is generally replaced by a set of undirected edges. In several practical cases, the cost matrix satisfies the triangle inequality. Each customer i (i = 1 . . . n) is associated with a known nonnegative demand, di, to be delivered, and the depot has a fictitious demand do = 0.A set of K identical vehicles, each with capacity C, is available at the