The optimization community has made significant progress in solving vehicle routing problems (VRPs) to optimality using sophisticated branch-cut-and-price (BCP) algorithms. VRPSolver is a BCP algorithm with excellent performance in many VRP variants. However, its complex underlying mathematical model makes it hardly accessible to routing practitioners. To address this, VRPSolverEasy provides a Python interface to VRPSolver that does not require any knowledge of mixed integer programming modeling. Instead, routing problems are defined in terms of familiar elements, such as depots, customers, links, and vehicle types. VRPSolverEasy can handle several popular VRP variants and arbitrary combinations of them. History: Accepted by Ted Ralphs, Area Editor for Software Tools. This paper has been accepted for the INFORMS Journal on Computing Special Issue on Software Tools for Vehicle Routing. Funding: This work was supported by Faperj [Grant E-26/202.887/2017] and Conselho Nacional de Desenvolvimento Científico e Tecnológico [Grant 305684/2022-1]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0103 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0103 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Abstract In this article, we propose graph‐based models for several vehicle routing problems with intermediate stops: the capacitated multi‐trip vehicle routing problem with time windows, the multi‐depot vehicle routing problem with inter‐depot routes, the arc routing problem with intermediate facilities under capacity and length restrictions and the green vehicle routing problem. In these models, the set of feasible routes is represented by a set of resource constrained paths in one or several graphs. Intermediate stops are supported by the possibility to define negative resource consumption for some arcs. The models that we propose are then solved by VRPSolver, which implements a generic branch‐cut‐and‐price exact algorithm. Thus, a simple parameterization enables us to use several state‐of‐the‐art algorithmic components: automatic stabilization by dual price smoothing, limited‐memory rank‐1 cuts, reduced cost‐based arc elimination, enumeration of elementary routes, and hierarchical strong branching. For each problem, we numerically compare the proposed methodology with the best exact approach found in the literature. State‐of‐the‐art computational results were obtained for all problems except one.

We introduce and motivate several variants of the bin packing problem where bins are assigned to time slots, and minimum and maximum lags are required between some pairs of items. We suggest two integer programming formulations for the general problem: a compact one and a stronger formulation with an exponential number of variables and constraints. We propose a branch-cut-and-price approach that exploits the latter formulation. For this purpose, we devise separation algorithms based on a mathematical characterization of feasible assignments for two important special cases of the problem: when the number of possible bins available at each period is infinite and when this number is limited to one and time lags are nonnegative. Computational experiments are reported for instances inspired from a real-case application of chemical treatment planning in vineyards, as well as for literature instances for special cases of the problem. The experimental results show the efficiency of our branch-cut-and-price approach, as it outperforms the compact formulation on newly proposed instances and is able to obtain improved lower and upper bounds for literature instances. Summary of Contribution: The paper considers a new variant of the bin packing problem, which is one of the most important problems in operations research. A motivation for introducing this variant is given, as well as a real-life application. We present a novel and original exact branch-cut-and-price algorithm for the problem. We implement this algorithm, and we present the results of extensive computational experiments. The results show a very good performance of our algorithm. We give several research directions that can be followed by subsequent researchers to extend our contribution to more complex and generic problems.

Major advances were recently obtained in the exact solution of Vehicle Routing Problems (VRPs). Sophisticated Branch-Cut-and-Price (BCP) algorithms for some of the most classical VRP variants now solve many instances with up to a few hundreds of customers. However, adapting and reimplementing those successful algorithms for other variants can be a very demanding task. This work proposes a BCP solver for a generic model that encompasses a wide class of VRPs. It incorporates the key elements found in the best recent VRP algorithms: ng-path relaxation, rank-1 cuts with limited memory, and route enumeration; all generalized through the new concept of “packing set”. This concept is also used to derive a new branch rule based on accumulated resource consumption and to generalize the Ryan and Foster branch rule. Extensive experiments on several variants show that the generic solver has an excellent overall performance, in many problems being better than the best existing specific algorithms. Even some non-VRPs, like bin packing, vector packing and generalized assignment, can be modeled and effectively solved.

ISP networks are taking a leap forward thanks to emerging technologies such as Software Defined Networking (SDN) and Network Function Virtualization (NFV). Efficient algorithms considered too hard to be put in practice on legacy networks now have a second chance to be considered again. In this context, we rethink the ISP network dimensioning problem with protection against Shared Risk Link Group (SLRG) failures. We consider a path-based protection scheme with a global rerouting strategy in which, for each failure situation, we may have a new routing of all the demands. Our optimization task is to minimize the needed amount of bandwidth. We develop a scalable mathematical model that we handle using the Column Generation technique. We show the effectiveness of our methods and demonstrate the feasibility of our approach using Mininet.

Primal heuristics have become essential components in mixed integer programming (MIP) solvers. Extending MIP-based heuristics, our study outlines generic procedures to build primal solutions in the context of a branch-and-price approach and reports on their performance. Our heuristic decisions carry on variables of the Dantzig–Wolfe reformulation, the motivation being to take advantage of a tighter linear programming relaxation than that of the original compact formulation and to benefit from the combinatorial structure embedded in these variables. We focus on the so-called diving methods that use reoptimization after each linear programming rounding. We explore combinations with diversification-intensification paradigms such as limited discrepancy search, sub-MIP, local branching, and strong branching. The dynamic generation of variables inherent to a column generation approach requires specific adaptation of heuristic paradigms. We manage to use simple strategies to get around these technical issues. Our numerical results on generalized assignment, cutting stock, and vertex-coloring problems set new benchmarks, highlighting the performance of diving heuristics as generic procedures in a column generation context and producing better solutions than state-of-the-art specialized heuristics in some cases.

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We consider a variant of the freight railcar flow problem. In this problem, we need 1) to choose a set of transportation demands between stations in a railroad network, and 2) to fulfill these demands by appropriately routing the set of available railcars, while maximizing the total profit. We formulate this problem as a multi-commodity flow problem in a large space-time graph. Three approaches are proposed to solve the Linear Programming relaxation of this formulation: direct solution by an LP solver, a column generation approach based on the path reformulation, and a ``column generation for extended formulations'' approach. In the latter, the multi-commodity flow formulation is solved iteratively by dynamic generation of arc flow variables. Three approaches have been tested on a set of real-life instances provided by one of the largest freight rail transportation companies in Russia. Instances with up to 10 millions of arc flow variables were solved within minutes of computational time.

The bin packing problem with conflicts consists of packing items in a minimum number of bins of limited capacity while avoiding joint assignments of items that are in conflict. Our study demonstrates that a generic implementation of a branch-and-price algorithm using specific pricing oracle yields comparatively good performance for this problem. We use our black-box branch-and-price solver BaPCod, relying on its generic branching scheme and primal heuristics. We developed a dynamic programming algorithm for pricing when the conflict graph is an interval graph, and a depth-first-search branch-and-bound approach for pricing when the conflict graph has no special structure. The exact method is tested on instances from the literature where the conflict graph is an interval graph, as well as harder instances that we generated with an arbitrary conflict graph and larger number of items per bin. Our computational experiment report sets new benchmark results for this problem, closing all open instances of the literature in one hour of CPU time.

We consider both branch-and-cut and column-generation approaches for the problem of finding a minimum-cost assignment of jobs with release dates and deadlines to unrelated parallel machines. Results are presented for several variants both with and without constraint programming. Among the variants, the most effective strategy is to combine a tight and compact, but approximate, mixed integer programming (MIP) formulation with a global constraint testing single machine feasibility. Instances with up to nine machines and 54 jobs have been solved. All the algorithms have been implemented in the Mosel modeling and optimization language.