1,720,994 research outputs found
Replication Data for: Exact decomposition approaches for a single container loading problem with stacking constraints and medium-sized weakly heterogeneous items
No full textThis repository contains the code for all algorithms discussed in the paper "Exact decomposition approaches for a single container loading problem with stacking constraints and medium-sized weakly heterogeneous items" by Maxence Delorme and Joris Wagenaar
Mathematical models and decomposition methods for the multiple knapsack problem
Full text linkWe consider the multiple knapsack problem, that calls for the optimal assignment of a set of items, each having a profit and a weight, to a set of knapsacks, each having a maximum capacity. The problem has relevant managerial implications and is known to be very difficult to solve in practice for instances of realistic size. We review the main results from the literature, including a classical mathematical model and a number of improvement techniques. We then present two new pseudo-polynomial formulations, together with specifically tailored decomposition algorithms to tackle the practical difficulty of the problem. Extensive computational experiments show the effectiveness of the proposed approaches
Bin packing and cutting stock problems: Mathematical models and exact algorithms
No full textWe review the most important mathematical models and algorithms developed for the exact solution of the one-dimensional bin packing and cutting stock problems, and experimentally evaluate, on state-of-the art computers, the performance of the main available software tools
Logic based Benders' decomposition for orthogonal stock cutting problems
Full text linkWe consider the problem of packing a set of rectangular items into a strip of fixed width, without overlapping, using minimum height. Items must be packed with their edges parallel to those of the strip, but rotation by 90° is allowed. The problem is usually solved through branch-and-bound algorithms. We propose an alternative method, based on Benders' decomposition. The master problem is solved through a new ILP model based on the arc flow formulation, while constraint programming is used to solve the slave problem. The resulting method is hybridized with a state-of-the-art branch-and-bound algorithm. Computational experiments on classical benchmarks from the literature show the effectiveness of the proposed approach. We additionally show that the algorithm can be successfully used to solve relevant related problems, like rectangle packing and pallet loading
Exact algorithms for a parallel machine scheduling problem with workforce and contiguity constraints
Full text linkWe address a real-world scheduling problem where the objective is to allocate a set of tasks to a set of machines and to a set of workers in such a way that the total weighted tardiness is minimized. Our case study encompasses four types of constraints: precedence, resource, eligibility, and contiguity. While the first three constraints are common in the scheduling literature, contiguity constraints, which can be defined as a form of precedence constraints that requires both a predecessor and its successor to be processed on the same machine with no intermediate jobs in-between (but idle time is allowed), have never been studied in the literature. We present four exact methods to solve the problem: two methods use integer linear programming, one uses constraint programming, and one uses a combinatorial Benders’ decomposition. We introduce method-specific strategies to model the contiguity constraints for each of the proposed methods. We empirically evaluate, through an extensive set of computational experiments, the performance of the four methods on a heterogeneous dataset composed of real, realistic, and random instances, and outline that every method offers a competitive advantage on a targeted subset of instances. We also show that our algorithms can be generalized to solve related scheduling problems with contiguity constraints
Bounds and heuristic algorithms for the bin packing problem with minimum color fragmentation
Full text linkIn this paper, we consider a recently introduced packing problem in which a given set of weighted items with colors has to be packed into a set of identical bins, while respecting capacity constraints and the number of available bins, and minimizing the total number of times that colors appear in the bins. We review exact methods from the literature and present a fast lower bounding procedure that, in some cases, can also provide an optimal solution. We theoretically study the worst-case performance of the lower bound and the effect of the number of available bins on the solution cost. Then, we computationally test our solution method on a large benchmark of instances from the literature: quite surprisingly, all of them are optimally solved by our procedure in a few seconds, including those for which the optimal solution value was still unknown. Thus, we introduce additional harder instances, which are used to evaluate the performance of a constructive heuristic method and of a tabu search algorithm. Results on the new instances show that the tabu search produces considerable improvements over the heuristic solution, with a limited computational effort
Arcflow formulations and constraint generation frameworks for the two-bar charts packing problem
Full text linkWe consider the two-bar charts packing (2-BCPP), a recent combinatorial optimization problem whose aim is to pack a set of one-dimensional items into the minimum number of bins. As opposed to the well-known bin packing problem, pairs of items are grouped to form bar charts, and a solution is only feasible if the first and second items of every bar chart are packed in consecutive bins. After providing a complete picture of the connections between the 2-BCPP and other relevant packing problems, we show how we can use these connections to derive valid lower and upper bounds for the problem. We then introduce two new integer linear programming (ILP) models to solve the 2-BCPP based on a non-trivial extension of the arcflow formulation. Even though both models involve an exponential number of constraints, we show that they can be solved within a constraint generation framework. We then empirically evaluate the performance of our bounds and exact approaches against an ILP model from the literature and demonstrate the effectiveness of our techniques, both on benchmarks inspired by the literature and on new classes of instances that are specifically designed to be hard to solve. The outcomes of our experiments are important for the packing community because they indicate that arcflow formulations can be used to solve targeted packing problems with precedence constraints and also that some of these formulations can be solved with constraint generation
Integer Linear Programming for the Tutor Allocation Problem: A practical case in a British University
Full text linkIn the Tutor Allocation Problem, the objective is to assign a set of tutors to a set of workshops in order to maximize tutors’ preferences. The problem is solved every year by many universities, each having its own specific set of constraints. In this work, we study the tutor allocation in the School of Mathematics at the University of Edinburgh, and solve it with an integer linear programming model. We tested the model on the 2019/2020 case, obtaining a significant improvement with respect to the manual assignment in use and we showed that such improvement could be maintained while optimizing other key metrics such as load balance among groups of tutors and total number of courses assigned. Further tests on randomly created instances show that the model can be used to address cases of broad interest. We also provide meaningful insights on how input parameters, such as the number of workshop locations and the length of the tutors’ preference list, might affect the performance of the model and the average number of preferences satisfied
BPPLIB: a library for bin packing and cutting stock problems
Full text linkThe bin packing problem (and its variant, the cutting stock problem) is among the most intensively studied combinatorial optimization problems. We present a library of computer codes, benchmark instances, and pointers to relevant articles for these two problems. The library is available at http://or.dei.unibo.it/library/bpplib. The computer code section includes twelve programs: seven are directly downloadable from the library page, while for the remaining five we provide addresses where they can be obtained or downloaded. Some of the codes for which we provide an original C++ implementation need an integer linear programming solver. For such cases, the library provides two versions: one that uses the commercial solver CPLEX, and one that uses the freeware solver SCIP. The benchmark section provides over six thousands instances (partly coming from the literature and partly randomly generated), together with the corresponding solutions. Instances that are difficult to solve to proven optimality are included. The library also includes a BibTeX file of more than 150 references on this topic and an interactive visual tool to manually solve bin packing and cutting stock instances. We conclude this work by reporting the results of new computational experiments on a number of computer codes and benchmark instances
An Improved Arcflow Model for the Skiving Stock Problem
Full text linkBecause of the sharp development of (commercial) MILP software and hardware components, pseudo-polynomial formulations have been established as a viable tool for solving cutting and packing problems in recent years. Constituting a natural (but independent) counterpart of the well-known cutting stock problem, the one-dimensional skiving stock problem (SSP) asks for the maximal number of large objects (specified by some threshold length) that can be obtained by recomposing a given inventory of smaller items. In this paper, we introduce a new arcflow formulation for the SSP applying the idea of reflected arcs. In particular, this new model is shown to possess significantly fewer variables as well as a better numerical performance compared to the standard arcflow formulation
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