Abstract

Abstract
Cutting and packing problems are challenging combinatorial optimization problems that have many relevant industrial applications and arise whenever a raw material has to be cut into smaller parts while minimizing waste, or products have to be packed, minimizing the empty space. Thus, the optimal solution to these problems has a positive economic and environmental impact. In many practical applications, both the raw material and the cut parts have a rectangular shape, and cutting plans are generated for one raw material rectangle (also known as plate) at a time. This is known in the literature as the (two-dimensional) rectangular cutting problem. Many variants of this problem may arise, led by cutting technology constraints, raw-material characteristics, and different planning goals, the most relevant of which are the guillotine cuts. The absence of the guillotine cuts imposition makes the problem harder to solve to optimality. Based on the Floating-Cuts paradigm, a general and flexible mixed-integer programming model for the general rectangular cutting problem is proposed. To the best of our knowledge, it is the first mixed integer linear programming model in the literature for both non-guillotine and guillotine problems. The basic idea of this model is a tree search where branching occurs by successive first-order non-guillotine-type cuts. The exact position of the cuts is not fixed, but instead remains floating until a concrete small rectangle (also known as item) is assigned to a child node. This model does not include decision variables either for the position coordinates of the items or for the coordinates of the cuts. Under this framework, it was possible to address various different variants of the problem. Extensive computational experiments were run to evaluate the model's performance considering 16 different problem variants, and to compare it with the state-of-the-art formulations of each variant. The results confirm the power of this flexible model, as, for some variants, it outperforms the state-of-the-art approaches and, for the other variants, it presents results fairly close to the best approaches. But, even more importantly, this is a new way of looking at these problems which may trigger even better approaches, with the consequent economic and environmental benefits. © 2022 Elsevier Ltd

Abstract

Abstract

Abstract
With the advent of mass customization and product proliferation, the appearance of hybrid Make-toStock(MTS)/Make-to-Order(MTO) policies arise as a strategy to cope with high product variety maintaining satisfactory lead times. In companies operating under this reality, Sales and Operations Planning (S&OP) practices must be adapted accordingly during the coordinated planning of procurement, production, logistics, and sales activities. This paper proposes a novel S&OP decision-making framework for a flow shop/batch company that produces standard products under an MTS strategy and customized products under an MTO strategy. First, a multi-objective mixed-integer programming model is formulated to characterize the problem. Then, a matrix containing the different strategies a firm in this context may adopt is proposed. This rationale provides a business-oriented approach towards the analysis of different plans and helps to frame the different Pareto-optimal solutions given the priority on MTS or MTO segments and the management positioning regarding cost minimization or service level orientation. The research is based on a real case faced by an electric cable manufacturer. The computational experiments demonstrate the applicability of the proposed methodology. Our approach brings a practical, supply chain-oriented, and mid-term perspective on the study of operations planning policies in MTS/MTO contexts.