Telmo Pinto

New constructive algorithms for leather nesting in the automotive industry

In this paper, we address one of the hardest two-dimensional cutting stock problems that can be found in industry. The problem is called the Leather Nesting Problem, and it consists in finding the best layouts for a set of irregular shapes within large natural leather hides with highly irregular contours, and which may have holes and quality zones. Here, we focus on a real case from the automotive industry, and in particular on the production of car seats. In this case, the irregular shapes that have to be cut from the hides are pieces of the car seats.The practical relevance of this problem, and the potential value of the savings that good solutions may generate, contrasts with the very small number of contributions that have been reported in the literature. In this paper, we aim to contribute to the efficient resolution of this problem by exploring in depth many new different constructive procedures. Our approaches rely on the computation of no-fit polygons, and try to use the information provided by these polygons as much as possible. Different strategies for sorting, selecting and placing the pieces, and for evaluating the placement of these pieces are proposed and discussed. We also report on an extensive set of computational experiments using real instances. To evaluate our approaches, we applied the real criteria used by companies operating in this sector. These experiments show that our approaches can generate very high quality layouts within the same time limits as those needed by human operators.

Variable Neighborhood Search for the Elementary Shortest Path Problem with Loading Constraints

In this paper, we address the elementary shortest path problem with 2-dimensional loading constraints. The aim is to find the path with the smallest cost on a graph where the nodes represent clients whose items may have different heights and widths. Beyond its practical relevance, this problem appears as a subproblem in vehicle routing problems with loading constraints where feasible routes have to be generated dynamically. To the best of our knowledge, there are no results reported in the literature related to this problem. Here, we explore a variable neighborhood search approach for this problem. The method relies on constructive heuristics to generate feasible paths, while improved incumbents are sought in different neighborhoods of a given solution through a variable neighborhood search procedure. The resulting variants of the algorithm were tested extensively on benchmark instances from the literature. The results are reported and discussed at the end of the paper.

Solving the Multiscenario Max-Min Knapsack Problem Exactly with Column Generation and Branch-and-Bound

Despite other variants of the standard knapsack problem, very few solution approaches have been devised for the multiscenario max-min knapsack problem. The problem consists in finding the subset of items whose total profit is maximized under the worst possible scenario. In this paper, we describe an exact solution method based on column generation and branch-and-bound for this problem. Our approach relies on a reformulation of the standard compact integer programming model based on the Dantzig-Wolfe decomposition principle. The resulting model is potentially stronger than the original one since the corresponding pricing subproblem does not have the integrality property. The details of the reformulation are presented and analysed together with those concerning the column generation and branch-and-bound procedures. To evaluate the performance of our algorithm, we conducted extensive computational experiments on large scale benchmark instances, and we compared our results with other state-of-the-art approaches under similar circumstances. We focused in particular on different relevant aspects that allow an objective evaluation of the efficacy of our approach. From different standpoints, the branch-and-price algorithm proved to outperform the other state-of-the-art methods described so far in the literature.

Variable neighborhood search algorithms for pickup and delivery problems with loading constraints

Abstract In this paper, we explore a capacitated vehicle routing problem with loading constraints and mixed linehauls and backhauls. The problem belongs to the subclass of pickup and delivery problems. To solve this problem, we describe a set of variable neighborhood search approaches whose shaking and local search phases rely on different neighborhood structures. Some of these structures were specially developed for this problem. All the strategies were implemented and exhaustively tested. The results of this computational study are discussed at the end of this paper.

A branch-and-price algorithm for the vehicle routing problem with 2-dimensional loading constraints

In this paper, we describe a branch-and-price algorithm for the capacitated vehicle routing problem with 2-dimensional loading constraints and a virtually unlimited number of vehicles. The column generation subproblem is solved heuristically through variable neighborhood search. Branch-and-price is used when it is not possible to add more attractive columns to the current restricted master problem, and the solution remains fractional. In order to accelerate the convergence of the algorithm, a family of valid dual inequalities is presented. Computational results are provided to evaluate the performance of the algorithm and to compare the different branching strategies proposed.

Exploring a Column Generation Approach for a Routing Problem with Sequential Packing Constraints

In this work we propose a computational study of a column generation based heuristic prototype for the vehicle routing problem with two-dimensional loading constraints. This prototype was recently proposed in literature (Pinto et al., 2013) and it relies in a column generation algorithm whose subproblem is relaxed. After solving the subproblem, the feasibility of the routes is verified using lower bounds and the classical bottom-left heuristic, enhanced with sequential constraints. For the infeasible routes, a simple route shortening process is applied, and the feasibility is tested again. The effectiveness of our approach is evaluated using benchmark instances from the literature.

Column generation based primal heuristics for routing and loading problems

Abstract In this paper, we explore a set of new heuristic strategies integrated within the column generation algorithm to solve the Capacitated Vehicle Routing Problem with 2-Dimensional Loading constraints. These heuristics rely on constructive procedures that iteratively build a solution using the solutions of a mixed integer linear programming model. The pricing subproblem is also heuristically solved, using strategies relying on variable neighborhood search algorithms proposed in literature. Column generation approaches for the 2L-CVRP are not quite explored. This paper aims to contribute with new strategies to tackle this problem. All the approaches were implemented and an exhaustive computational study is performed.

Variable neighborhood search for integrated planning and scheduling

In this paper, we consider the integrated planning and scheduling problem on parallel and identical machines. The problem is composed by two parts which are simultaneously solved in an integrated form. The first is the planning part, which consists in determining the jobs that should be processed in each period of time. The second is the scheduling part, which consists in assigning the jobs to the machines according to their release dates. We present new optimization approaches based on local search heuristics and metaheuristic methods based on variable neighborhood search using two neighborhood structures. Two different algorithms were implemented in the construction of initial solutions and combined with fifteen variants of the initial sequence of jobs. Computational experiments were performed with benchmark instances from the literature in order to assess the proposed methods.

Heuristic methods for the leather nesting problem in the automotive industry

In this paper, we address a real leather nesting problem (LNP) with holes and quality zones that arises in the automotive industry. We describe two approaches for the solution of the LNP. The first approach consists in a constructive heuristic, while the second relies on local search methods. The constructive heuristic is based on a simulation of the positioning of a piece so as to evaluate its fitness within the hide and within the current layout. The later approach suggested in this paper is based in a local search method whose neighbourhood structure operates on cutting patterns. In order to improve this procedure, we also describe an improvement of our constructive heuristic to apply it at each iteration of the local search procedure. The proposed methods were implemented and tested on real instances of the automotive industry. The obtained results for both heuristics illustrate the adequacy and the potential of the proposed approaches.

Models and advanced optimization algorithms for the integrated management of logistics operations

In this paper, we describe a set of algorithms regarding real combinatorial optimization problems in the context of transportation of goods. These problems consist in the combination of the vehicle routing problem with the two-dimensional bin-packing problem, which is also known as the vehicle routing problem with two-dimensional loading constraints. We also analyzed two related problems, namely the elementary shortest path problem and the vehicle routing problem with mixed linehaul and backhaul customers. In both problems, two-dimensional loading constraints are explicitly considered. Two column generation based approaches are proposed for the vehicle routing problem with two-dimensional constraints. The elementary shortest path problem with two-dimensional constraints is addressed due to its importance in solving the subproblem of the column generation algorithms. To the best of our knowledge, we contribute with the first approach for this problem, through different constructive strategies to achieve feasible solutions, and a variable neighborhood search algorithm in order to search for improved solutions. In what concerns the vehicle routing problem with mixed linehaul and backhaul customers and two-dimensional loading constraints, different variable neighborhood search algorithms are proposed. All the proposed methods were implemented and experimentally tested. An exhaustive set of computational tests was conducted, using, for this purpose, a large group of benchmark instances. In some cases, a large set of benchmark instances was adapted in order to assess the quality of the proposed models.