Instances of "New formulations and a matheuristic for the multi-product multi-period inventory lot sizing with supplier selection problem"

This research considers the multi-product, multi-period inventory lot-sizing with supplier selection problem, which is a well known complex combinatorial optimization problem proven to be NP-hard. We address the problem from a modeling viewpoint, thus we propose three new mixed integer programming formulations. The first formulation takes advantage of a disaggregated set of constraints, the second one improves a facility location problem (FLP) formulation which is known to have good linear relaxation, but scales poorly and finally a variant of the FLP formulation that, through an auxiliary variable, reduces the size of the decisions variables in the model. Furthermore, we prove that the decision variable related to the production quantity from a supplier in any period always has integer values. Although we present exact mathematical formulations, we take advantage of the properties of the problem and propose a two-phase matheuristic for this problem. The performance of the proposed exact and approximated methodologies is evaluated by comparing them against the traditional formulation and the original FLP formulation using the literature benchmark instances. The new formulations and the matheuristic outperform the previous proposed formulations from the literature in solution quality, computational time, and in some cases scalability.

The original instances from Basnet & Leung (2005) are those that do not have the N1 and N2 labels, which correspond to the instances proposed in Cardenas-Barrón et al. (2021).