Formulations and exact solution approaches for a coupled bin-packing and lot-sizing problem with sequence-dependent setups

We study bin-packing and lot-sizing decisions in an integrated way. Such a problem appears in several manufacturing settings where items first need to be cut and next assembled into final products. One of the main novelties of this research is the modeling of the complex setup operations in the cutting process, which is modeled using a bin-packing formulation. More specifically, we consider the operation regarding the insertion or removal of the knives in the cutting process. Since this operation depends on the number of items cut in the current cutting process and in the previous one, the number of insertions and removals is sequence-dependent. The setups in the lot-sizing problem related to the production of the final products are also sequence-dependent. To deal with such a problem, two compact formulations are proposed. The sequence-dependent setups in the bin-packing problem are modeled in two different ways: based on known constraints from the literature, and based on the idea of micro-periods and a phantom cutting process. Due to the dependency in the setups decisions, the resulting formulations are mixed-integer nonlinear mathematical models. In order to deal with the sequence-dependent cutting and production setups, different polynomial-sized sets of subtour elimination constraints are employed to the coupled problem. A computational study is conducted in order to analyze the impact of the proposed approaches to model sequence-dependent setups, as well as the different subtour elimination strategies to solve the coupled bin-packing and lot-sizing problem, via an automatic-Benders decomposition algorithm.