As already mentioned, there are difficulties in using the associated relaxed linear program, since there are many linearly dependent columns that cannot be simultaneously in a base when using the simplex method to solve the model. We could also develop a procedure that attempts to explore the similarity of this problem with the reduction of distinct patterns. For the minimization of tool switches problem, we can explore the idea of aggregating simple tasks, that is, tasks that require a small number of tools.
As a consequence, we could reduce the size of the instance and, hopefully, we would require a lower computational effort to solve the problem. The challenge is to define the aggregation procedure so that the solution of the modified instance is also optimal for the original one. There are cases where the aggregation of tasks is not possible simply because there are no simple tasks in the instance.
In these cases, we plan to verify whether the transformation of the minimization of tool switches problem in a generalized traveling salesman problem would not be an interesting alternative to be explored, since the number of nodes of the transformed problem does not grow much in these cases.
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We also intend to develop a decomposition procedure that reduces the original instance into a set of smaller-sized instances. The way we plan to decompose the problem is by duplicating tools. Another problem we have started studying is the packing of items in a multi-compartmentized truck with the objective of minimizing the handling of the cargo along the delivery route. For this multi-compartmentized vehicle loading problem, we now intend to take into account load balancing constraints and fragility.
An idea to explore is the possibility of shelf loading in each compartment. These are some of our future research plans.
 Combinatorial Optimization on Gate Model Quantum Computers: A Survey
We hope to be able to contribute to the improvement of some production processes to contribute a little to the consolidation of research groups in this area as well as in related areas, and to promote scientific and technological development as well as the training of human resources in the field of operations research. Many of the results derived were obtained in collaboration with colleagues from many places and universities, graduate students, and my thesis advisor, Professor Gabriel Bitran.
I must thank all of them for their discussions, support, advise, and friendship. A method for solving the minimisation of the maximum number of open stacks problem. Published in CD Acta de Trabajos , ref. A method for solving the minimisation of the maximum number of open stacks problem within a cutting process. Computers and Operations Research , 31 14 : ISSN: DI Analysis of the uncapacitated dynamic lot size problem. Published by INPE, ref. Approximation methods for the uncapacitated lot size problem. Management Science , 30 9 : Published in the proceedings.
Computational complexity of the capacitated lot size problem. Management Science , 28 10 : Sloan WP No. Deterministic approximations to stochastic production problems. Operations Research , 32 5 : A pattern reduction procedure in a one-dimensional cutting stock problem by grouping items according to their demands. Journal of Computational Interdisciplinary Sciences , 1 2 : ISSN Resolution of the unidimensional cutting stock problem with usable leftover. The one-dimensional cutting stock problem with usable leftovers - a heuristic approach. European Journal of Operational Research , 3 : The usable leftover one-dimensional cutting stock problem - a priority in use heuristic.
Accepted, International Transactions in Operational Research, Um sistema de planejamento agregado de estoques. O problema CPM com investimento. Published in the Proceedings, vol. Published in the Proceedings, p. ISSN , 16 p. A linear programming approach to the cutting-stock problem. Operations Research , 9 : Computing partitions with applications to the knapsack problem.
ACM , pp.
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Published in the proceedings in CD. Published in the proceedings in CD, p. Abstract, p. Proceedings of the V Oficina, p. Campos, SP. On the minimization of open stack problem.
Technical Report, ref. Industrial pattern-sequencing problems: some complexity results and new local search models.
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Connections between cutting-pattern sequencing, VLSI design, and flexible machines. Computers and Operations Research , 29 12 : Linear gate assignment: a fast statisticalmechanics approach.
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A partial representation technique for subset sums. Extended abstract published, Vol. Published in CD,p. Published in CD, p. Algoritmos paralelos para o problema da mochila. Comments on parallel algorithms for the knapsack problem. Parallel Computing , 28 10 : Short Communication. An optimal and scalable parallelization of the two-list algorithm for the subset-sum problem.
Metaheuristic Research for Solving Combinatorial Optimization Problems
European Journal of Operational Research , 2 : Theoretical Computer Science , : Observations on optimal parallelizations of two-list algorithm. Parallel Computing Short Communication , 36 : Production scheduling of assembly fixtures in the aeronautical industry. A planar solution procedure for linear diophantine equations.
Louis meeting, St. A polynomial approximation scheme for the subset sum problem. Discrete Applied Mathematics , 57 : Aggregation and computational complexity of lot size problems. Published in the proceedings, p. EOQ systems: the case of an increase in purchase cost. Journal of the Operational Research Society , 41 7 : A search strategy for the one-size assortment problem.
European Journal of Operational Research , 74 : On a pattern sequencing problem in the wood industry. Proceedings, p. A heuristic procedure for solving a pattern sequencing problem in the wood cut industry.
Published in the Proceedings in CD. Minimization of open orders - polynomial algorithms for some special cases. Pesquisa Operacional , 16 1 : Abstract published. On a pattern sequencing problem to minimize the maximum number of open stacks. European Journal of Operational Research , : A transformation for solving a pattern sequencing problem in the wood cut industry.
Pesquisa Operacional , 17 1 : An exact algorithm for the tree case of the minimization of open orders problem. A note on generating solutions of a pattern sequencing problem to minimize the maximum number of open orders. A note on the minimization of the number of cutting cycles problem.
Published in the proceedings in CD , arq, p. Proceedings in CD, p. Abstract Book, p. A collapsing arc heuristic for solving a patterns sequencing problem. Bounds for a problem of sequencing patterns. Pesquisa Operacional , 19 2 : A heuristic to solve a pattern sequencing problem based on partial orderings. ISSN x. II, p. Um modelo linear para o problema da mochila compartimentada. Published in CD, arq. Checkerboard patterns: proposals for its generation.
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An integrated cutting stock and sequencing problem. Refinements on an enumeration scheme for solving a pattern sequencing problem. International Transactions in Operations Research , 11 : A hybrid heuristic to reduce the number of different patterns in cutting stock problems. Computers and Operations Research , 33 9 : Linear models for one-group two-dimensional guillotine cutting problems. International Journal of Production Research , 44 17 : A note on linear models for two-group and three-group two-dimensional guillotine cutting problems.
International Journal of Production Research , 46 21 : Linear and non-linear models for one-, two- and three-group and two-stage two-dimensional guillotine cutting problems. Published in the proceedings, Vol. III, p. The minimization of tool switches problem as a network flow problem with side constraints. A new proposal for solving the minimization of the maximum number of open stacks problem.
Conference Program and Abstract Book, p. The minimization of open stacks problem: a review of some properties and their use in pre-processing operations. An improved partial ordering scheme for solving the minimization of tool switches problem. Performance evaluation of some heuristics based on partial ordering for solving the minimization of tool switches problem. Um algoritmo exato para o problema da mochila.
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Two very general discrete structures with strong algorithmic properties are matroids and submodular functions, which can be found in a surprising and steadily growing number of applications. Numerous results have already been discovered for such algorithmically important mathematical structures. However, partially due to upcoming research areas, like online algorithms and submodular function maximization, many new open questions arose in the context of classical discrete structures. We believe that substantial progress in such emerging areas is tightly linked to deeper mathematical insights.
At IFOR we therefore have a strong interest in the study of discrete structures, in particular poly- matroids and submodular functions, and their various applications. Our interest in this context covers a wide range of problems, including submodular function maximization, network coding, online algorithms, constrained spanning trees, Steiner Tree relaxations, multiobjective optimization, and matroid secretary problems.
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Network optimization is a classic research focus in Combinatorial Optimization, and an important reason for the widespread use of Combinatorial Optimization in various application areas. Network optimization has many facets, and at IFOR we are interested in a diverse set of network optimization problems. In particular, we study network design problems like generalized spanning tree problems, the Steiner Tree problem, design of failure-resilient networks, Furthermore, we have a particular interest in problems related to network robustness.