Publicação
Models for multi-depot routing problems
| Resumo: | In this dissertation we study two problems. In the first part of the dissertation we study the multi-depot routing problem. In the multi-depot routing problem we are given a set of depots and a set of clients and the objective is to find a set of routes with minimum total cost, one for each depot, such that each route starts and ends at the same depot and all clients are visited in one and only one route. The requirement that routes must start and end at the same depot is modeled by so-called path elimination constraints. We present a formulation which includes a newly developed set of multi-cut path elimination constraints and a branch-and-cut algorithm based on the new formulation that it is able to solve both asymmetric and symmetric instances with up to 300 clients and 60 depots. Additionally, we present other approaches to model path elimination constraints, including a formulation which provides linear programming relaxation values which are close to the optimal value in the instances tested. In the second part of the dissertation we study the Hamiltonian p-median problem. In the Hamiltonian p-median we are given a set of nodes and the objective is to find p circuits with minimum total cost such that each node is in one and only circuit. We propose a formulation based on the concept of acting depot which attributes the role of artificial depot to p of the nodes. This formulation is a non-straightforward adaptation of the new model proposed for the multidepot routing problem and it is based on a novel idea in which the standard arc variables are split into three cases depending on whether none or exactly one of its endpoints is an acting depot. We present a branch-and-cut algorithm based on the new formulation which is able to solve asymmetric instances with up to 171 nodes and symmetric instances with up to 100 nodes. |
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| Autores principais: | Santos, Daniel |
| Assunto: | multi-depot routing Hamiltonian p-median integer linear programming projection branch-and-cut |
| Ano: | 2019 |
| País: | Portugal |
| Tipo de documento: | tese de doutoramento |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade de Lisboa |
| Idioma: | inglês |
| Origem: | Repositório da Universidade de Lisboa |
| Resumo: | In this dissertation we study two problems. In the first part of the dissertation we study the multi-depot routing problem. In the multi-depot routing problem we are given a set of depots and a set of clients and the objective is to find a set of routes with minimum total cost, one for each depot, such that each route starts and ends at the same depot and all clients are visited in one and only one route. The requirement that routes must start and end at the same depot is modeled by so-called path elimination constraints. We present a formulation which includes a newly developed set of multi-cut path elimination constraints and a branch-and-cut algorithm based on the new formulation that it is able to solve both asymmetric and symmetric instances with up to 300 clients and 60 depots. Additionally, we present other approaches to model path elimination constraints, including a formulation which provides linear programming relaxation values which are close to the optimal value in the instances tested. In the second part of the dissertation we study the Hamiltonian p-median problem. In the Hamiltonian p-median we are given a set of nodes and the objective is to find p circuits with minimum total cost such that each node is in one and only circuit. We propose a formulation based on the concept of acting depot which attributes the role of artificial depot to p of the nodes. This formulation is a non-straightforward adaptation of the new model proposed for the multidepot routing problem and it is based on a novel idea in which the standard arc variables are split into three cases depending on whether none or exactly one of its endpoints is an acting depot. We present a branch-and-cut algorithm based on the new formulation which is able to solve asymmetric instances with up to 171 nodes and symmetric instances with up to 100 nodes. |
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