Planning optimization considering various uncertainties has attracted increasing attention in the process industry. In existing studies, the uncertainty is often described with a time-invariant distribution function during the entire planning horizon, which is a questionable assumption. In particular, for long-term planning problems, the uncertainty tends to vary with time, and it usually increases when a model is used to predict the parameter (e.g., price) far into the future. In this paper, time-varying uncertainties are considered in robust planning problems with a focus on a poly(vinyl chloride) (PVC) production planning problem. Using the stochastic programming techniques, a stochastic model is formulated and then transformed into a multiperiod mixed-integer linear programming model by chance-constrained programming and piecewise linear approximation. The proposed approach is demonstrated on industrial-scale cases originating from a real-world PVC plant. The comparisons show that the model considering varying uncertainty is superior in terms of robustness under uncertainties.