Exact Solution of Combined Cutting Stock and Scheduling Problems
The combination of cutting and packing with scheduling has been addressed recently by various authors considering both one- and two-dimensional instances. These problems consist essentially in finding the cutting plan that minimizes a function of the wastage and tardiness related to the items delivery given a set of due dates (and possibly release dates). As shown by other authors, some of these models may not be exact due to the definition of the time periods on which they rely. In this paper, we explore an exact and compact assignment formulation for the combined cutting stock and scheduling. The model is general in the sense that it applies to instances with any level of demand per item. To strengthen the model, we resort to knapsack-based inequalities derived using dual-feasible functions. Up to now, these functions have been used mainly to derive lower bounds for cutting and packing problems. Different computational experiments performed on benchmark instances illustrate their potential as an effective cutting plane tool.
This work was supported by FEDER funding through the Programa Operacional Factores de Competitividade - COMPETE and by national funding through the Portuguese Science and Technology Foundation (FCT) in the scope of the project PTDC/EGE-GES/116676/2010.
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