This paper develops a new mathematical model to study location-routing problem with simultaneous pickup and delivery under the risk of disruption. A remarkable number previous studies have assumed that network components ( e.g. , routes, production factories, depots, etc.) are always available can permanently serve customers. assumption is no longer valid when faces disruptions such as flood, e...

Manufacturers, who re-supply a large number of customers, continually struggle with the question of how to formulate a replenishment strategy. The purpose of this paper is to determine the optimal set of routes for a group of vehicles in the transportation network under defined constraints – which is known as the Vehicle Routing Problem (VRP) – delivering new items, and resolving the invent...

Multi-depot Location-Routing Problem (MDLRP) is about finding the optimal number and locations of depots while allocating customers to depots and determining vehicle routes to visit all customers. In this study we propose a nested Lagrangian relaxation-based method for the discrete uncapacitated MDLRP. An outer Lagrangian relaxation embedded in subgradient optimization decomposes the parent pro...

In this paper, we address the Two-Echelon Vehicle Routing Problem (2E-VRP) in which freight is delivered from depots to intermediary satellites, from where it is delivered to customers. Different from other multi-level problems, the focus in 2E-VRP is on the global routing costs of the overall network. 2E-VRP has been recently introduced and, to our knowledge, there are no studies of the impact...

In contrast to the classical location-allocation models, the location-routing problem (LRP) integrates vehicle routing and scheduling aspects in the location planning process. A survey and classification scheme of location-routing is e.g. proposed by [3] and [2]. This paper presents a LRP of a company which distributes finished cars. This LRP is decomposed into two steps. In the first step a se...