We address an assortment‐and‐cutting problem arising in the glass industry. The objective is to p... more We address an assortment‐and‐cutting problem arising in the glass industry. The objective is to provide minimum waste solutions that are robust against such raw material imperfections as those possibly occurring with float glass production technology. The stochastic realization of defects is modeled as a spatial Poisson point process. A mixed integer program in the classical vein of robust optimization is presented and tested on data taken from a real plant application. Defective final products must in any case be discarded as waste but, if a recourse strategy is adopted, faults in glass sheets can sometimes be recovered. Closed forms for the computation of faulty item probabilities are provided in simple cases, and obtained via Monte Carlo simulation in more complex ones. The computational results demonstrate the benefits of the robust approach in terms of the reduction of back‐orders and overproduction, thereby showing that recourse strategies can enable nonnegligible improvements...
In general, Integer Linear Programming problems are computationally hard to solve. The design of ... more In general, Integer Linear Programming problems are computationally hard to solve. The design of efficient algorithms for them often takes advantage from the analysis of the problem underlying mathematical structure. Starting from the problem of finding the maximum embedded reflected network submatrix of a matrix with entries in , this work deals with the equivalent problem of finding the maximum balanced induced subgraph of a signed graph (MBS, Max Balanced Subgraph). The contribution is twofold. In the first part of the work, a new heuristic for the MBS problem, the Cycle-Contraction Heuristic (CCH), has been proposed. The algorithm is based on a graph transformation rule that progressively reduces the lengths of cycles, preserving at the same time the feasibility of solutions for the MBS problem. CCH turns out to be more effective of the state-of-the-art heuristics. The efficiency and the effectiveness of CCH can be further improved by means of new rules of data reduction, i.e., ...
The paper describes models for scheduling the patterns that form a solution of a cutting stock pr... more The paper describes models for scheduling the patterns that form a solution of a cutting stock problem. We highlight the problem of providing the required final products with the necessary items obtained from the cut, choosing which pattern feeds which lot of parts. This problem can be solved prior to schedule cuts, or in an integrated way. We present integer programming models for both approaches.
We address a 1-dimensional cutting stock problem where, in addition to trimloss minimization, we ... more We address a 1-dimensional cutting stock problem where, in addition to trimloss minimization, we require that the set of cutting patterns forming the solution can be sequenced so that the number of stacks of parts maintained open throughout the process never exceeds a given s. For this problem, we propose a new integer linear programming formulation whose constraints grow quadratically with the number of distinct part types.
We address an assortment‐and‐cutting problem arising in the glass industry. The objective is to p... more We address an assortment‐and‐cutting problem arising in the glass industry. The objective is to provide minimum waste solutions that are robust against such raw material imperfections as those possibly occurring with float glass production technology. The stochastic realization of defects is modeled as a spatial Poisson point process. A mixed integer program in the classical vein of robust optimization is presented and tested on data taken from a real plant application. Defective final products must in any case be discarded as waste but, if a recourse strategy is adopted, faults in glass sheets can sometimes be recovered. Closed forms for the computation of faulty item probabilities are provided in simple cases, and obtained via Monte Carlo simulation in more complex ones. The computational results demonstrate the benefits of the robust approach in terms of the reduction of back‐orders and overproduction, thereby showing that recourse strategies can enable nonnegligible improvements...
In general, Integer Linear Programming problems are computationally hard to solve. The design of ... more In general, Integer Linear Programming problems are computationally hard to solve. The design of efficient algorithms for them often takes advantage from the analysis of the problem underlying mathematical structure. Starting from the problem of finding the maximum embedded reflected network submatrix of a matrix with entries in , this work deals with the equivalent problem of finding the maximum balanced induced subgraph of a signed graph (MBS, Max Balanced Subgraph). The contribution is twofold. In the first part of the work, a new heuristic for the MBS problem, the Cycle-Contraction Heuristic (CCH), has been proposed. The algorithm is based on a graph transformation rule that progressively reduces the lengths of cycles, preserving at the same time the feasibility of solutions for the MBS problem. CCH turns out to be more effective of the state-of-the-art heuristics. The efficiency and the effectiveness of CCH can be further improved by means of new rules of data reduction, i.e., ...
The paper describes models for scheduling the patterns that form a solution of a cutting stock pr... more The paper describes models for scheduling the patterns that form a solution of a cutting stock problem. We highlight the problem of providing the required final products with the necessary items obtained from the cut, choosing which pattern feeds which lot of parts. This problem can be solved prior to schedule cuts, or in an integrated way. We present integer programming models for both approaches.
We address a 1-dimensional cutting stock problem where, in addition to trimloss minimization, we ... more We address a 1-dimensional cutting stock problem where, in addition to trimloss minimization, we require that the set of cutting patterns forming the solution can be sequenced so that the number of stacks of parts maintained open throughout the process never exceeds a given s. For this problem, we propose a new integer linear programming formulation whose constraints grow quadratically with the number of distinct part types.
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