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Two-echelon vehicle routing problems in city logistics : approaches based on exact methods of mathematical optimization

Abstract : The main focus of this thesis is to develop mathematical optimization based exact methods to solve vehicle routing problems in two-level distribution systems. In such a system, the first level involves trucks that ships goods from a distribution center to intermediate depots called satellites. The second level involves city freighters that are loaded with goods at satellites and deliver the customers. Each customer must be visited once. The two-echelon vehicle routing problem seeks to minimize the total transportation cost in such a distribution system.The first chapter gives an overview of the branch-and-cut-and-price framework that we use throughout the thesis.The second chapter tackles the Two-Echelon Capacitated Vehicle Routing Problem. We introduce a new route based formulation for the problem which does not use variables to determine product flows in satellites. We propose a new branching strategy which significantly decreases the size of the branch-and-bound tree. Most importantly, we suggest a new family of satellite supply inequalities, and we empirically show that it improves the quality of the dual bound at the root node of the branch-and-bound tree. Experiments reveal that our algorithm can solve all literature instances with up to 200 customers and 10 satellites. Thus, we double the size of instances which can be solved to optimality.The third chapter tackles the Two-Echelon Vehicle Routing Problem with Time Windows. We consider the variant with precedence constraints at the satellites: products should be delivered by an urban truck to a satellite before loading them to a city freighter. This is a relaxation of the synchronisation variant usually considered in the literature. We consider single-trip and multi-trip variants of this problem. In the first one, city freighters start from satellites and do a single trip. In the second one, city freighters start from a depot, load product at satellites, and do several trips. We introduce a route based formulation that involves an exponential number of constraints to ensure precedence relations. A minimum-cut based algorithm is proposed to separate these constraints. We also show how these constraints can be taken into account in the pricing problem of the column generation approach. Experiments show that our algorithm can solve to optimality instances with up to 100 customers. The algorithm outperforms significantly another recent approach proposed the literature for the single-trip variant of the problem. Moreover, the “precedence relaxation” is exact for single-trip instances.The fourth chapter considers vehicle routing problems with knapsack-type constraints in the master problem. For these problems, we introduce new route load knapsack cuts and separation routines for them. We use these cuts to solve to optimality three problems: the Capacitated Vehicle Routing Problem with Capacitated Multiple Depots, the standard Location-Routing Problem, and the Vehicle Routing Problem with Time Windows and Shifts. These problems arise when routes at first level of the two-level distribution system are fixed. Our experiments reveal computational advantage of our algorithms over ones from the literature.
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Guillaume Marques. Two-echelon vehicle routing problems in city logistics : approaches based on exact methods of mathematical optimization. Automatic Control Engineering. Université de Bordeaux, 2020. English. ⟨NNT : 2020BORD0199⟩. ⟨tel-03097659⟩

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