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This article introduces a Mixed-Integer Linear Programming model for cost optimization in multi-product multi-line production scheduling. This model considers discrete time windows and includes realistic constraints. The NP completeness of the problem is proven. A novel scheme based on embedding bounds is applied to speed up convergence. The model is tested on 16 input configurations of a real case study from the top Uruguayan grain production facility. The numerical results show that the model significantly improves the outcome of the current ad hoc heuristic planning, reducing on average 10% the overall production costs; and that the introduction of the embedded bounds-based scheme reduces significantly the elapsed time, on average by 22%.

The problem addressed in this paper attempts to efficiently solve a network design with redundant connections, often used by telephone operators and internet services. This network connects customers with one master node and sets some rules that shape its construction, such as number of customers, number of components and types of links, in order to meet operational needs and technical constraints. We propose a combinatorial optimization problem called CmTNSSP (Capacitated m Two-Node-Survivable Star Problem), a relaxation of CmRSP (Capacitated m Ring Star Problem). In this variant of CmRSP the rings are not constrained to be cycles; instead, they can be two node connected components. The contributions of this paper are (a) introduction and definition of a new problem (b) the specification of a mathematical programming model of the problem to be treated, and (c) the approximate resolution thereof through a GRASP metaheuristic, which alternates local searches that obtain incrementally better solutions, and exact resolution local searches based on mathematical programming models, particularly Integer Linear Programming ones. Computational results obtained by developed algorithms show robustness and competitiveness when compared to results of the literature relative to benchmark instances. Likewise, the experiments show the relevance of considering the specific variant of the problem studied in this work.

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