Locating Depots for Capacitated Vehicle Routing

We study a location-routing problem in the context of capacitated vehicle routing. The input is a set of demand locations in a metric space and a fleet of k vehicles each of capacity Q. The objective is to locate k depots, one for each vehicle, and compute routes for the vehicles so that all demands are satisfied and the total cost is minimized. Our main result is a constant-factor approximation algorithm for this problem. To achieve this result, we reduce to the k-median-forest problem, which generalizes both k-median and minimum spanning tree, and which might be of independent interest. We give a (3+c)-approximation algorithm for k-median-forest, which leads to a (12+c)-approximation algorithm for the above location-routing problem, for any constant c>0. The algorithm for k-median-forest is just t-swap local search, and we prove that it has locality gap 3+2/t; this generalizes the corresponding result known for k-median. Finally we consider the "non-uniform" k-median-forest problem which has different cost functions for the MST and k-median parts. We show that the locality gap for this problem is unbounded even under multi-swaps, which contrasts with the uniform case. Nevertheless, we obtain a constant-factor approximation algorithm, using an LP based approach.Comment: 12 pages, 1 figur

Modeling a four-layer location-routing problem

Distribution is an indispensable component of logistics and supply chain management. Location-Routing Problem (LRP) is an NP-hard problem that simultaneously takes into consideration location, allocation, and vehicle routing decisions to design an optimal distribution network. Multi-layer and multi-product LRP is even more complex as it deals with the decisions at multiple layers of a distribution network where multiple products are transported within and between layers of the network. This paper focuses on modeling a complicated four-layer and multi-product LRP which has not been tackled yet. The distribution network consists of plants, central depots, regional depots, and customers. In this study, the structure, assumptions, and limitations of the distribution network are defined and the mathematical optimization programming model that can be used to obtain the optimal solution is developed. Presented by a mixed-integer programming model, the LRP considers the location problem at two layers, the allocation problem at three layers, the vehicle routing problem at three layers, and a transshipment problem. The mathematical model locates central and regional depots, allocates customers to plants, central depots, and regional depots, constructs tours from each plant or open depot to customers, and constructs transshipment paths from plants to depots and from depots to other depots. Considering realistic assumptions and limitations such as producing multiple products, limited production capacity, limited depot and vehicle capacity, and limited traveling distances enables the user to capture the real world situations

Combining heuristics with simulation and fuzzy logic to solve a flexible-size location routing problem under uncertainty

The location routing problem integrates both a facility location and a vehicle routing problem. Each of these problems are NP-hard in nature, which justifies the use of heuristic-based algorithms when dealing with large-scale instances that need to be solved in reasonable computing times. This paper discusses a realistic variant of the problem that considers facilities of different sizes and two types of uncertainty conditions. In particular, we assume that some customers’ demands are stochastic, while others follow a fuzzy pattern. An iterated local search metaheuristic is integrated with simulation and fuzzy logic to solve the aforementioned problem, and a series of computational experiments are run to illustrate the potential of the proposed algorithm.This work has been partially supported by the Spanish Ministry of Science (PID2019-111100RB-C21/AEI/10.13039/501100011033). In addition, it has received the support of the Doctoral School at the Universitat Oberta de Catalunya (Spain) and the Universidad de La Sabana (INGPhD-12-2020).Peer ReviewedPostprint (published version

Stochastic Dynamic Vehicle Routing in the Euclidean Plane: The Multiple-Server, Capacitated Vehicle Case

In a previous paper [12], we introduced a new model for stochastic and dynamic vehicle routing called the dynamic traveling repairman problem (DTRP), in which a vehicle traveling at constant velocity in a Euclidean region must service demands whose time of arrival, location and on-site service are stochastic. The objective is to find a policy to service demands over an infinite horizon that minimizes the expected system time (wait plus service) of the demands. We showed that the stability condition did not depend on the geometry of the service region (i.e. size, shape, etc.). In addition, we established bounds on the optimal system time and proposed an optimal policy in light traffic and several policies that have system times within a constant factor of the lower bounds in heavy traffic. We showed that the leading behavior of the optimal system time had a particularly simple form which increases much more rapidly with traffic intensity than the system time in traditional queues (e.g. M/G/1). In this paper, we extend these results in several directions. First, we propose new bounds and policies for the problem of m identical vehicles with unlimited capacity and show that in heavy traffic the system time is reduced by a factor of 1/m2 over the single server case. Policies based on dividing the service region into m equal subregion

Stochastic and dynamic vehicle routing in the Euclidean plane with multiple capacitated vehicles

"March 13, 1991."Includes bibliographical references (p. 34-36).Supported by the National Science Foundation. DDM-9014751 Supported by a grant from the Draper Laboratories and the UPS Foundation.Dimitris J. Bertsimas, Garrett van Ryzin

Location and Routing Problems of Debris Collection Operation after Disasters with Realistic Case Study

AbstractDebris removal after disasters presents challenges unique to each disaster. The transportation routing as well as disposal sites issue will be the subject of this study. The uniqueness of debris collection operation is due to the limited access from one section to the other, as a result of the blocked access by debris. Therefore a new constraint i.e. access possibility constraint was added to the classical L-CARP. Case studies on a test network and on realistic instances based on estimates of debris due to likely large scale natural disaster in Tokyo Metropolitan Area have also been reported under various scenarios

The Bi-objective Periodic Closed Loop Network Design Problem

© 2019 Elsevier Ltd. This manuscript is made available under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International licence (CC BY-NC-ND 4.0). For further details please see: https://creativecommons.org/licenses/by-nc-nd/4.0/Reverse supply chains are becoming a crucial part of retail supply chains given the recent reforms in the consumers’ rights and the regulations by governments. This has motivated companies around the world to adopt zero-landfill goals and move towards circular economy to retain the product’s value during its whole life cycle. However, designing an efficient closed loop supply chain is a challenging undertaking as it presents a set of unique challenges, mainly owing to the need to handle pickups and deliveries at the same time and the necessity to meet the customer requirements within a certain time limit. In this paper, we model this problem as a bi-objective periodic location routing problem with simultaneous pickup and delivery as well as time windows and examine the performance of two procedures, namely NSGA-II and NRGA, to solve it. The goal is to find the best locations for a set of depots, allocation of customers to these depots, allocation of customers to service days and the optimal routes to be taken by a set of homogeneous vehicles to minimise the total cost and to minimise the overall violation from the customers’ defined time limits. Our results show that while there is not a significant difference between the two algorithms in terms of diversity and number of solutions generated, NSGA-II outperforms NRGA when it comes to spacing and runtime.Peer reviewedFinal Accepted Versio