Collaborative operations planning is a key element of modern supply chains. We introduce the collaborative multi-level lot-sizing problem with cost synergies. This arises if producers can realise reductions of their costs by providing more than one product in a specific time horizon. Since producers are typically not willing to reveal critical information, we propose a decentralised mechanism, where producers do not have to reveal their individual items costs. Additionally, a Genetic Algorithms-based centralised approach is developed, which we use for benchmarking. Our study shows that this approach comes very close to the a central plan, while in the decentralised one no critical information has to be shared. We compare the results to a myopic upstream planning approach, and show that these results are almost 12% worse than the centralised ones. All solution approaches are assessed on available test instances for problems without cost synergies. For the biggest available instances, the proposed centralised mechanism improves the best known solutions on average by 10.8%. The proposed decentralised mechanism can be applied to other problem classes, where collaborative decision makers aim for good plans under incomplete information.