A comparison of formulations for a three-level lot sizing and replenishment problem with a distribution structure.

•We study a three-level lot sizing problem with a distribution structure.•We develop or extend 13 different MIP formulations for the problem.•We analyze the relationships between the linear relaxation of these formulations.•We performs numerical experiments with balanced and unbalanced networks, and with or without production capacity.•We introduce several KPIs to measure the performance of the formulations.