An extended goal programming model for the multiobjective integrated lot-sizing and cutting stock problem

Lot sizing and cutting stock problems generally arise in manufacturing as a two stage connected process. Although these two problems have been addressed separately by many authors, recently, inspired by practical applications, some studies have emerged analyzing their integration. The mono-objective version of the integrated lot-sizing and cutting stock problem can be considered as an enhancement that minimizes the global production cost. However, it does not include the multiple criteria that can arise from the inclusion of multiple stakeholders in a modern, distributed manufacturing process.

This paper aims to introduce a new extended goal programming model for the integrated lot-sizing and cutting stock problem which models the arising multiple criteria by a set of goals representing the interests of different stakeholders in the manufacturing process. This formulation allows for the consideration of the balance between the conflicting goals of multiple stakeholders and the cost efficiency of the overall process. In order to efficiently solve the proposed model, a column generation based heuristic procedure is applied. The trade-offs among the various criteria related to the problem are assessed, and a series of computational experiments are performed. The computational results compare individual criteria weighting schemes and evaluate the goals’ sensitivity using performance profiles and time-to-target plots methodologies.