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

2 Realopt - Reformulations based algorithms for Combinatorial Optimization
LaBRI - Laboratoire Bordelais de Recherche en Informatique, IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
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. We first tackle the Two-Echelon Capacitated Vehicle Routing Problem. We introduce a new route based formulation, a new branching strategy, and new valid inequalities for the problem. Experiments reveal that our algorithm can solve all literature instances. Then, we tackle 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. We introduce a route based formulation that involves an exponential number of constraints to ensure precedence relations. 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. At last, we consider vehicle routing problems with knapsack-type constraints in the master problem. We present some families of valid inequalities. We use these inequalities 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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Submitted on : Thursday, December 10, 2020 - 5:59:46 PM
Last modification on : Wednesday, November 3, 2021 - 5:55:45 AM
Long-term archiving on: : Thursday, March 11, 2021 - 8:57:21 PM

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• HAL Id : tel-03052822, version 1

### Citation

Guillaume Marques. Two-echelon vehicle routing problems in city logistics : approaches based on exact methods of mathematical optimization. Operations Research [cs.RO]. Université de Bordeaux, 2020. English. ⟨tel-03052822⟩

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