Analytical and empirical comparison of integer programming formulations for a partitioning-hub location-routing problem (original) (raw)
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In this paper we deal with a capacitated hub location problem arising in a freight logistics context; in particular, we have the need of locating logistics platforms for containers travelling via road and rail. The problem is modelled on a weighed multimodal network. We give a mixed integer linear programming model for the problem, having the goal of minimizing the location and shipping costs. The proposed formulation presents some novel features for modelling capacity bounds that are given both for the candidate hub nodes and the arcs incident to them; further, the containerised origin-destination (o − d) demand can be split among several platforms and different travelling modes. Note that here the network is not fully connected and only one hub for each o − d pair is used, serving both to consolidate consignments on less transport connections and as reloading point for a modal change. Results of an extensive computational experimentation performed with randomly generated instances of different size and capacity values are reported. In the test bed designed to validate the proposed model all the instances up to 135 nodes and 20 candidate hubs are optimally solved in few seconds by the commercial solver CPLEX 12.5.
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Less-than-truckload (LTL) freight transportation is a vital part of Canada's economy, with revenues running into billions of dollars and a cascading impact on many other industries. LTL operators have to deal with large volumes of shipments and uncertainty in demand patterns. In an industry that already has low profit margins, it is therefore vitally important to make good quality routing decisions without expending a lot of time. The optimization of such LTL freight networks results in large scale mathematical programming problems. In this paper, we present a novel Integer Linear Programming (ILP) formulation and heuristics for routing LTL freight. Experiments in collaboration with our industry partner indicate that our proposals can significantly lower routing costs for Canadian LTL operators. In addition, our approach can be useful for generating load plans on larger American LTL networks.
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The Generalized Vehicle Routing Problem (GVRP) is an extension of the Vehicle Routing Problem (VRP) defined on a graph in which the nodes (customers, vertices) are grouped into a given number of mutually exclusive and exhaustive clusters (nodesets). In this paper, an integer linear programming formulation of the GVRP with O(n 2) binary variables and O(n 2) constraints is presented. It is shown that, under specific circumstances, the proposed model reduces to the well-known routing problems. The computational performance of the models solved using a commercial code on test problems are also presented.
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.
Ordered median hub location problems with capacity constraints
Transportation Research Part C: Emerging Technologies, 2016
The Single Allocation Ordered Median Hub Location problem is a recent hub model introduced in [36] that provides a unifying analysis of a wide class of hub location models. In this paper, we deal with the capacitated version of this problem, presenting two formulations as well as some preprocessing phases for fixing variables. In addition, a strengthening of one of these formulations is also studied through the use of some families of valid inequalities. A battery of test problems with data taken from the AP library are solved where it is shown that the running times have been significantly reduced with the improvements presented in the paper. 1 Introduction Network design problems are among the most interesting models in combinatorial optimization. In the last years researchers have devoted a lot of attention to a particular member within this family, namely the hub location problem, that combines network design and location aspects of supply chain models, see the surveys [1, 7, 9]. The main advantage of using hubs in distribution problems is that they allow to consolidate shipments in order to reduce transportation costs by applying economies of scale; which are naturally incorporated to the models through discount factors. Hub location problems have been studied from different per-1 INTRODUCTION 2 spectives giving rise to a number of papers considering different criteria to be optimized: the minimization of the overall transportation cost (sum) (see [10, 6, 20, 27, 29, 30, 31]), the minimization of the largest transportation cost or the coverage cost ([4, 8, 24, 25, 26, 34, 40, 41]), et cetera. Apart from the choice of the optimization criterion, another crucial aspect in the literature on hub location, and in general on any location problem, is the assumption of capacity constraints. One can recognize that although this assumption implies more realistic models, the difficulty to solve them also increases in orders of magnitude with respect to their uncapacitated counterpart. In many cases new formulations are needed and a more specialized analysis is often required to solve even smaller sizes than those previously addressed for the uncapacitated versions of the problems. For this reason, capacitated versions of hub location problems have attracted the interest of locators in the last years, see [2, 5, 11, 13, 14, 15, 16, 20, 29]. In the same line, we also mention some other references related with congestion at hubs, as congestion acts as a limit on capacity, see [17, 18, 28]. An interesting version of hub location model is the Capacitated Hub Location Problem with Single Allocation (CSA-HLP), see [11, 13, 20]. In this context, single allocation means that incoming and outgoing flow of each site must be shipped via the same hub. In contrast to single allocation models, where binary variables are required in the allocation phase, multiple allocation allows different delivery patterns which in turns implies the use of continuous variables simplifying the problems. The CSA-HLP model incorporates capacity constraints on the incoming flow at the hubs coming from origin sites or even simpler, on the number of non-hub nodes assigned to each hub. The inclusion of capacity constraints make these models challenging from a theoretical point of view. Regarding its applicability we cite one example described in Ernst at al. [20] based on a postal delivery application, where a set of n postal districts (corresponding to postcode districts represented by nodes) exchange daily mail. The mail between all the pairs of nodes must be routed via one or at most two mail consolidation centers (hubs). In order to meet time constraints, only a limited amount of mail could be sorted at each sorting center (mail is just sorted once, when it arrives to the first hub from origin sites). Hence, there are capacity restrictions on the incoming mail that must be sorted.
Location-Routing Models for Two-Echelon Freight Distribution System Design †
2011
In this paper, we address the decision problem of designing a two-echelon freight distribution system. The problem is modeled as a two-echelon location-routing problem, which arises when considering, within the same decision process, the location of facilities on two adjacent echelons of a distribution system, together with the routing of vehicles at both echelons. We describe the issues, set up the general problem class, and study its basic variant, proposing and comparing three mixed-integer programming formulations, aimed at defining the locations and numbers of two types of capacitated facilities, the sizes of two different vehicle fleets, and the related routes. The computational evaluation and comparisons are performed on a large set of instances inspired by two-tiered City Logistics system settings with various numbers and relative distributions of potential locations for the two types of facilities.
Location-Routing Models for Designing a Two-Echelon Freight Distribution System
2011
In this paper, we address the decision problem of designing a two-echelon freight distribution system for an urban area. The scope of the paper is twofold. At first it describes a two-level distribution system focusing on its structure, components and related decision problems. Then the problem arising in this context is formulated as a two- echelon location-routing problem. Three mixed integer programming models will be proposed, aimed at defining location and number of two kinds of capacitated facilities, size of two different vehicle fleets and related routes. An instance generator has been developed and results of proposed models on a wide set of small and medium instances are reported, comparing their performances in terms of quality of solution and computation times.
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.