To efficiently meet demand in a production system, the lot-sizing problem determines a production plan that minimizes the overall costs, optimizes the use of the available resources, and satisfies demand requirements. Nonetheless, uncertainties in the production environment directly affect the quality and feasibility of the production plans. In fact, demand can be highly volatile and influenced by multiple factors such as age, life-cycle, economic context, reference groups, culture, festive season. To increase the robustness of the production plan to unforeseen uncertainties, one could rely on the robust optimization methodology that offers ease and flexibility to account for uncertain parameters. In the light of the robust approaches, an adaptive robust uncapacitated lot-sizing model is proposed to deal with demand uncertainty. It offers a production plan that can be updated when demand information unfolds over time. Numerical experiments demonstrate that the adaptive model can outperform the static model, while marginal additional computational effort is required to obtain a robust production plan. The results also indicate that the proposed approach is a better alternative for production planning within a system that is flexible for changes in the lot size at each period.