A multi-period production and inventory planning problem of a manufacturer with a fixed proportions production system in a three-stage supply chain consisting of a raw material supplier, a manufacturer and customers is studied under the uncertain demand environment. The interval uncertainty set is used to model market demand uncertainties, and the joint chance constraint is adopted to describe the service level requirement of the manufacturer. An affinely adjustable robust production and inventory optimization model with a joint chance constraint is developed based on the linear decision rule for the fixed proportions production system. Furthermore, the developed robust optimization model is equivalently transformed into a tractable linear programming model. Considering the moderating effect of uncertain disturbance coefficient between model robustness and the conservatism of the solution, an uncertain disturbance coefficient optimization algorithm is proposed, which can effectively improve the total profit of the manufacturer with the fixed proportions production system and satisfy the pre-specified service level. Numerical examples show that the operation scheme obtained based on the proposed model can effectively cope with the changes in the balance degree of supply and demand, and can satisfy the pre-specified service level with a higher profit.