An integrated approach to the two-dimensional bin packing problem and production planning with minimization of maximum and total order spread

In this research, we address the two-dimensional bin packing problem combined with minimizing the maximum and total order spread. This integrated problem acquires greater relevance in make-to-order production contexts, in which the establishment of an optimized production schedule is as important as the efficient use of raw materials. Assuming a planning horizon divided into a finite quantity of production periods and that purchase orders are made up of item sets, the spread of an order is defined by the difference in periods between the start and end of order processing. By making these considerations, production planning gains greater operational and logistical quality, mitigating the occurrence of other possible costs, such as expenses associated with inventory and order delivery. We formulate the problem as an integer linear program, restricted to the case in which items are arranged in non-exact 2-stage guillotine cutting patterns. We apply lexicographic optimization as a strategy to determine the priority of terms in the objective function. Computational experiments carried out with benchmark instances demonstrate the effectiveness of the proposed approach, producing results superior to those reported in the literature. In particular, the model was able to increase the number of instances resolved to optimality, in addition to significantly reducing the computational time required to obtain the solutions.