We introduce a problem where a fleet of vehicles is available to visit suppliers offering various products at different prices and quantities, with the aim to select a subset of suppliers so to satisfy products demand at the minimum traveling and purchasing costs. Vehicles have a predefined capacity and pairs of products may be incompatible to be carried simultaneously on a same vehicle. We call this problem the multi-vehicle traveling purchaser problem with pairwise incompatibility constraints. We show how a three-index one-commodity flow formulation for the problem is easy to implement with a common MILP solver, but highly nonefficient when solving large size instances. We concentrate on a formulation using connectivity constraints to exclude subtours and introduce a branch-and-cut framework using a preprocessing routine and the separation of different valid inequalities. We also propose a four-step heuristic based on the solution of different subproblems and use it to provide an initial feasible solution. We run computational tests on a large set of instances with up to 50 suppliers, 100 products, and 20% of crossed incompatibility between products. Results show that two different streamlined versions of the proposed exact method largely outperform the plain solution by the commercial solver Cplex 12.3. Also, the heuristic approach is observed to be rather effective and efficient providing a valid solving alternative. © 2014 Wiley Periodicals, Inc. NETWORKS, 2014

]]>In this article, we study the (*k,c*)-coloring problem, a generalization of the vertex coloring problem where we have to assign *k* colors to each vertex of an undirected graph, and two adjacent vertices can share at most *c* colors. We propose a new formulation for the (*k,c*)-coloring problem and develop a Branch-and-Price algorithm. We tested the algorithm on instances having from 20 to 80 vertices and different combinations for *k* and *c*, and compare it with a recent algorithm proposed in the literature. Computational results show that the overall approach is effective and has very good performance on instances where the previous algorithm fails. © 2014 Wiley Periodicals, Inc. NETWORKS, 2014

We consider 2-facility location problems with equity measures, defined on networks. The models discussed are, the variance, the mean of absolute weighted deviations, the maximum weighted absolute deviation, the sum of absolute weighted differences, and the range. We give new algorithmic results for these models in the 2-facility case. © 2014 Wiley Periodicals, Inc. NETWORKS, Vol. 65(1), 1–9. 2015

]]>We study the problem of minimizing the profile of a graph and develop a solution method by following the tenets of scatter search. Our procedure exploits the network structure of the problem and includes strategies that produce a computationally efficient and agile search. Among several mechanisms, our search includes path relinking as the basis for combining solutions to generate new ones. The profile minimization problem (PMP) is NP-Hard and has relevant applications in numerical analysis techniques that rely on manipulating large sparse matrices. The problem was proposed in the early 1970s but the state-of-the-art does not include a method that could be considered powerful by today's computing standards. Extensive computational experiments show that we have accomplished our goal of pushing the envelope and establishing a new standard in the solution of the PMP. © 2014 Wiley Periodicals, Inc. NETWORKS, Vol. 65(1), 10–21. 2015

]]>The flow-capturing problem (FCP) consists of locating facilities to maximize the number of flow-based customers that encounter at least one of these facilities along their predetermined travel paths. The FCP literature assumes that if a facility is located along (or “close enough” to) a predetermined path of a flow of customers, that flow is considered captured. However, existing models for the FCP do not consider targeted users who behave noncooperatively by changing their travel paths to avoid fixed facilities. Examples of facilities that targeted subjects may have an incentive to avoid include weigh-in-motion stations used to detect and fine overweight trucks, tollbooths, and security and safety checkpoints. This article introduces a new type of flow-capturing model, called the “evasive flow-capturing problem” (EFCP), which generalizes the FCP and has relevant applications in transportation, revenue management, and security and safety management. We formulate deterministic and stochastic versions of the EFCP, analyze their structural properties, study exact and approximate solution techniques, and show an application to a real-world transportation network. © 2014 Wiley Periodicals, Inc. NETWORKS, Vol. 65(1), 22–42. 2015

]]>In this article, we deal with the polyhedral description and the resolution of the directed general routing problem (DGRP) and the stacker crane problem (SCP). The DGRP, in which the service activity occurs both at some of the nodes and at some of the arcs of a directed graph, contains a large number of important arc and node routing problems as special cases, including the SCP. We describe large families of facet-defining inequalities for the DGRP. Furthermore, a branch-and-cut algorithm for these problems is presented. Extensive computational experiments over different sets of DGRP and SCP instances are included. These results show that our algorithm is among the best solution procedures proposed for both problems. © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 65(1), 43–55. 2015

]]>In this article, we propose a generic decomposition scheme for the maximum concurrent flow problem. This decomposition scheme encompasses many models, including, among many others, the classical path formulation and the less studied tree formulation, where the flows of commodities sharing a same source vertex are routed on a set of trees. The pricing problem for this generic model is based on shortest-path computations. We show that the tree-based linear programming formulation can be solved much more quickly than the path or the aggregated arc-flow formulation. Some other decomposition schemes can lead to even faster resolution times. Finally, an efficient strongly polynomial-time combinatorial algorithm is proposed for the single-source case. © 2014 Wiley Periodicals, Inc. NETWORKS, Vol. 65(1), 56–67. 2015

]]>We present an alternative linear programming formulation of the maximum concurrent flow problem (MCFP) termed the triples formulation. The standard formulations in the literature are the edge-path and node-edge formulations, which are known to be equivalent due to the Flow Decomposition Theorem. We present algorithms for deriving a triples solution from an edge-path solution and vice versa, and hence show that all three formulations are equivalent. Our new formulation leads to more compact linear programs than either the edge-path or node-path formulations. We show that the triples formulation often has half the number of rows and half the number of columns compared to the node-edge formulation. We report computational results comparing the solution times using the three formulations and the state-of-the-art linear programming solver CPLEX on a set of popular problem instances from the literature and a set of instances defined on random geometric graphs. The results indicate that the triples formulation can be solved more efficiently than the other two. We found that the CPLEX linear programming solvers solved 89% of the MCFP instances in our computational study faster with the triples formulation than it did with the other two formulations, typically two to four times faster than the node-edge formulation when available computer memory allowed both to be solved. The triples formulation appears to be particularly well suited for problem instances defined on dense graphs; on average, CPLEX solved these types of problems in our study 10 times faster with the triples formulation. © 2014 Wiley Periodicals, Inc. NETWORKS, Vol. 65(1), 68–87. 2015

]]>In this article, we present a comparative study of several strategies that can be applied to achieve the so-called elementary lower bound in vehicle routing problems, that is, the bound obtained when all positive-valued variables in an optimal solution of the linear relaxation of the set-partitioning formulation correspond to vehicle routes without cycles. This bound can be achieved by solving the resource-constrained elementary shortest path problem—an -hard problem—as the pricing problem in a column generation algorithm, but several other strategies can be used to ultimately produce the same lower bound in less computational effort. State-of-the-art algorithms for vehicle routing problems rely on the quality of this lower bound to either bound the size of the search tree in a branch-and-price algorithm or the complexity of an enumeration procedure used to limit the number of variables in the set-partitioning model. We consider several strategies for imposing elementarity that involve *ng*-paths, strong degree constraints, and decremental state-space relaxation. We compare the performance of these strategies on some selected instances of the vehicle routing problem with time windows. © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 65(1), 88–99. 2015