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

Towards an IT-based Planning Process Alignment: Integrated Route and Location Planning for Small Package Shippers

To increase the efficiency of delivery operations in small package shipping (SPS), numerous optimization models for routeand location planning decisions have been proposed. This operations research view of defining independent problems hastwo major shortcomings: First, most models from literature neglect crucial real-world characteristics, thus making themuseless for small package shippers. Second, business processes for strategic decision making are not well-structured in mostSPS companies and significant cost savings could be generated by an IT-based support infrastructure integrating decisionmaking and planning across the mutually dependent layers of strategic, tactical and operational planning. We present anintegrated planning framework that combines an intelligent data analysis tool, which identifies delivery patterns and changesin customer demand, with location and route planning tools. Our planning approaches extend standard Location Routing andVehicle Routing models by crucial, practically relevant characteristics like the existence of subcontractors on both decisionlevels and the implicit consideration of driver familiarity in route planning

Facility Location Problem of Beverage Distribution Considering Time Window and Land Use Plan Using GIS

As the boundaries and population of urban areas expand, beverage distributors may seek to expand the capacity in their distribution centers. As a result, they may need to add new locations or increase the utilization of their existing center. This paper investigates the facility location problem through network space, considering traversable truck roads, thereby providing a strategic decision for identifying a depot location in consideration of vehicle routings from a real application. For the analysis, a geospatial tool, which is embedded in the commercial software ArcMap®, was used for routing and calibrating the model. Ten candidates from commercial and industrial zones in the cities of Fargo, West Fargo, and Moorhead were considered for future distribution centers. The candidate locations were analyzed to determine which site minimizes the total transportation costs and travel miles in consideration of time window, vehicle capacity, heterogeneous vehicle types, land use plan, and hours-of-service. Most attractive candidates are close to the intersections of major highways. From the analysis, the study recommends locating a distribution center at three alternatives based on the average ranking method. This study can be used by distributors as they consider new locations and extra depots to support strategic planning to deal with mid-term and long-term growth of demand in beverage markets. This study provides a ready-to-use example of how to adopt state-of-the-art spatial technology and operations research using Geographic Information Systems (GIS), and bring it to state-of-practice

Metodología para crear rutas alimentadoras en sistemas de transporte masivo

Se propone una metodología para identificar rutas alimentadoras en zonas no conectadas para un sistema de transporte masivo, con el fin de aumentar la cobertura del servicio y mejorar el nivel de ocupación del sistema. La metodología propuesta consta de dos etapas: 1) estructurar escenarios de áreas no conectadas al sistema de transporte y 2) combinar técnicas heurísticas y exactas para resolver el problema de rutas alimentadoras. La metodología considera dentro de sus restricciones la duración de la ruta y la capacidad del vehículo alimentador. Para su modelamiento se establece una analogía entre los problemas del transporte de pasajeros y el problema de localización y ruteo, Location Routing Problem (LRP), que usualmente es aplicado a problemas de transporte de mercancías. La metodología de solución propuesta es una matheurística que combina las heurísticas Lin-Kernighan-Helsgaun (LKH) y ahorros con el algoritmo de ramificación y corte, Branch-and-Cut, aplicado sobre un modelo lineal entero mixto de partición de conjuntos (Set Partitioning) para LRP. Esta propuesta metodológica es validada con casos de prueba reales del sistema de transporte masivo de la ciudad de Pereira (Megabús), donde se consideran algunas zonas no conectadas del Área Metropolitana Centro Occidente, localizada en el eje cafetero colombiano

Reliable Location-Routing Design Under Probabilistic Facility Disruptions

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The Two-Echelon Capacitated Vehicle Routing Problem

Multi-echelon distribution systems are quite common in supply-chain and logistic systems. They are used by public administrations in their transportation and traffic planning strategies as well as by companies to model their distribution systems. Unfortunately, the literature on com- binatorial optimization methods for multi-echelon distribution systems is very poor. The aim of this paper is twofold. Firstly, it introduces the family of Multi-Echelon Vehicle Routing Problems. Second, the Two-Echelon Capacitated Vehicle Routing Problem, is presented. The Two-Echelon Capacitated Vehicle Routing Problem (2E-CVRP) is an extension of the classical VRP where the delivery passes through intermediate depots (called satellites). As in the classical VRP, the goal is to deliver goods to customers with known demands, minimizing the total delivery cost while considering vehicle and satellites capacity constraints. A mathematical model for 2E-CVRP is presented and some valid in- equalities given, which are able to significantly improve the results on benchmark tests up to 50 customers and 5 satellites. Computational re- sults under different realistic scenarios are presented

Solving the Capacitated Location Routing Problem by a Cooperative Lagrangean Relaxation - Granular Tabu Search Heuristic

International audienceMost of the time in a distribution system, depot location and vehicle routing are interdependent, and recent studies have shown that the overall system cost may be excessive if routing decisions are ignored when locating depots. The location-routing problem (LRP) overcomes this drawback by simultaneously tackling location and routing decisions. This paper presents a cooperative metaheuristic to solve the LRP with capacitated routes and depots. The principle is to alternate between a depot location phase and a routing phase, exchanging information on the most promising edges. In the first phase, the routes and their customers are aggregated into supercustomers, leading to a facility-location problem, which is then solved by a Lagrangean relaxation of the assignment constraints. In the second phase, the routes from the resulting multidepot vehicle-routing problem (VRP) are improved using a granular tabu search (GTS) heuristic. At the end of each global iteration, information about the edges most often used is recorded to be used in the following phases. The method is evaluated on three sets of randomly generated instances and compared with other heuristics and a lower bound. Solutions are obtained in a reasonable amount of time for such a strategic problem and show that this metaheuristic outperforms other methods on various kinds of instances

Solving the Capacitated Location-Routing Problem by a Cooperative Lagrangean Relaxation-Granular Tabu Search Heuristic

International audienceMost of the time in a distribution system, depot location and vehicle routing are interdependent, and recent studies have shown that the overall system cost may be excessive if routing decisions are ignored when locating depots. The location-routing problem (LRP) overcomes this drawback by simultaneously tackling location and routing decisions. This paper presents a cooperative metaheuristic to solve the LRP with capacitated routes and depots. The principle is to alternate between a depot location phase and a routing phase, exchanging information on the most promising edges. In the first phase, the routes and their customers are aggregated into supercustomers, leading to a facility-location problem, which is then solved by a Lagrangean relaxation of the assignment constraints. In the second phase, the routes from the resulting multidepot vehicle-routing problem (VRP) are improved using a granular tabu search (GTS) heuristic. At the end of each global iteration, information about the edges most often used is recorded to be used in the following phases. The method is evaluated on three sets of randomly generated instances and compared with other heuristics and a lower bound. Solutions are obtained in a reasonable amount of time for such a strategic problem and show that this metaheuristic outperforms other methods on various kinds of instances

Formulation and a two-phase matheuristic for the roaming salesman problem: Application to election logistics

In this paper we investigate a novel logistical problem. The goal is to determine daily tours for a traveling salesperson who collects rewards from activities in cities during a fixed campaign period. We refer to this problem as the Roaming Salesman Problem (RSP) motivated by real-world applications including election logistics, touristic trip planning and marketing campaigns. RSP can be characterized as a combination of the traditional Periodic TSP and the Prize-Collecting TSP with static arc costs and time-dependent node rewards. Commercial solvers are capable of solving small-size instances of the RSP to near optimality in a reasonable time. To tackle large-size instances we propose a two-phase matheuristic where the first phase deals with city selection while the second phase focuses on route generation. The latter capitalizes on an integer program to construct an optimal route among selected cities on a given day. The proposed matheuristic decomposes the RSP into as many subproblems as the number of campaign days. Computational results show that our approach provides near-optimal solutions in significantly shorter times compared to commercial solvers