A branch-and-cut algorithm for the partitioning-hub location-routing problem (original) (raw)
Related papers
2008
We introduce the Partitioning-Hub-Location-Routing Problem (PHLRP), a hub location problem involving graph partitioning and routing features. PHLRP consists of partitioning a given network into sub-networks, locating at least one hub in each sub-network and routing the traffic within the network at minimum cost. This problem finds applications in deployment of an Internet Routing Protocol called Intermediate System-Intermediate System (ISIS), and strategic planning of LTL ground freight distribution systems. We introduce three Integer Programming (IP) formulations for solving PHLRP. We compare, both analytically and empirically, these formulations with each other in order to identify the best-performing one among the three.
A Branch and Cut method for the Capacitated Location-Routing Problem
2006
Recent researches in the design of logistic networks have shown that the overall distribution 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. The aim of this paper is to propose an exact approach based on a Branch-and-Cut algorithm for solving the LRP with capacity constraints on depots and vehicles. The proposed method is based on a zero-one linear model strengthened by new families of valid inequalities. The computational evaluation on three sets of instances (34 instances in total), with 5-10 potential depots and 20-88 customers, shows that 26 instances with five depots are solved to optimality, including all instances with up to 40 customers and three with 50 customers.
A branch and cut algorithm for hub location problems with single assignment
Mathematical Programming, 2005
The hub location problem with single assignment is the problem of locating hubs and assigning the terminal nodes to hubs in order to minimize the cost of hub installation and the cost of routing the traffic in the network. There may also be capacity restrictions on the amount of traffic that can transit by hubs. The aim of this paper is to investigate polyhedral properties of these problems and to develop a branch and cut algorithm based on these results.
A branch-and-price algorithm for combined location and routing problems under capacity restrictions
Operations Research/ Computer Science Interfaces Series, 2009
We investigate the problem of simultaneously determining the location of facilities and the design of vehicle routes to serve customer demands under vehicle and facility capacity restrictions. We present a set-partitioning-based formulation of the problem and study the relationship between this formulation and the graph-based formulations that have been used in previous studies of this problem. We describe a branch-and-price algorithm based on the set-partitioning formulation and discuss computational experience with both exact and heuristic variants of this algorithm.
Location-Routing Problems with Distance Constraints
Transportation Science, 2007
An important aspect of designing a distribution system is determining the locations of the facilities. For systems in which deliveries are made along multiple stop routes, the routing problem and location problem must be considered simultaneously. In this paper, a set-partitioning-based formulation of an uncapacitated location-routing model with distance constraints is presented. An alternate set of constraints is identified that significantly reduces the total number of constraints and dramatically improves the linear programming relaxation bound. A branch and price algorithm is developed to solve instances of the model. The algorithm provides optimal solutions in reasonable computation time for problems involving as many as 10 candidate facilities and 100 customers with various distance constraints.
Capacitated Hub Routing Problem in Hub-and-Feeder Network Design: Modeling and Solution Algorithm
2015
In this paper, we address the Bounded Cardinality Hub Location Routing with Route Capacity wherein each hub acts as a transshipment node for one directed route. The number of hubs lies between a minimum and a maximum and the hub-level network is a complete subgraph. The transshipment operations take place at the hub nodes and flow transfer time from a hub-level transporter to a spoke-level vehicle influences spoketo- hub allocations. We propose a mathematical model and a branch-and-cut algorithm based on Benders decomposition to solve the problem. To accelerate convergence, our solution framework embeds an efficient heuristic producing high-quality solutions in short computation times. In addition, we show how symmetry can be exploited to accelerate and improve the performance of our method.
Capacitated Bounded Cardinality Hub Routing Problem: Model and Solution Algorithm
arXiv (Cornell University), 2017
In this paper, we address the Bounded Cardinality Hub Location Routing with Route Capacity wherein each hub acts as a transshipment node for one directed route. The number of hubs lies between a minimum and a maximum and the hub-level network is a complete subgraph. The transshipment operations take place at the hub nodes and flow transfer time from a hub-level transporter to a spoke-level vehicle influences spoketo-hub allocations. We propose a mathematical model and a branch-and-cut algorithm based on Benders decomposition to solve the problem. To accelerate convergence, our solution framework embeds an efficient heuristic producing high-quality solutions in short computation times. In addition, we show how symmetry can be exploited to accelerate and improve the performance of our method.
The hub location and routing problem
European Journal of Operational Research, 1995
In this paper, we consider the hub location and routing problem in which the hub locations and the service types for the routes between demand points are determined together. Rather than aggregating the demand for the services, flows from an origin to different destination points are considered separately. For each origin-destination pair, one-hub-stop, two-hub-stop and, when permitted, direct services are considered. In the system considered, the hubs interact with each other and the level of interaction between them is determined by the two-hub-stop service routes. A mathematical formulation of the problem and an algorithm solving the hub location and the routing subproblems separately in an iterative manner are presented. Computational experience with four versions of the proposed algorithm differing in the method used for finding starting solutions is reported.
A hub location problem with fully interconnected backbone and access networks
Computers & Operations Research, 2007
This paper considers the design of two-layered fully interconnected networks. A two-layered network consists of clusters of nodes, each defining an access network and a backbone network. We consider the integrated problem of determining the access networks and the backbone network simultaneously. A mathematical formulation is presented, but as the linear * Corresponding author 1 programming relaxation of the mathematical formulation is weak, a formulation based on the set partitioning model and column generation approach is also developed. The column generation subproblems are solved by solving a series of quadratic knapsack problems. We obtain superior bounds using the column generation approach than with the linear programming relaxation. The column generation method is therefore developed into an exact approach using the Branch-and-Price framework. With this approach we are able to solve problems consisting of up to 25 nodes in reasonable time. Given the difficulty of the problem, the results are encouraging.