This paper addresses a multi-stage and multi-period supply chain network design problem in which multiple commodities should be produced through different subsequent levels of manufacturing processes. The problem is formulated as a two-stage stochastic program under stochastic and highly time-variable demands. To deal with the stochastic demands, a Latin Hypercube Sampling method is applied to generate a fan of scenarios and then, a backward scenario reduction technique reduces the number of scenarios. Weighted mean-risk objectives by using different risk measures and minimax objective are examined to obtain risk-averse and robust solutions, respectively. Computational results are presented on a real-life case study to illustrate the applicability of the proposed approaches. To compare these different decision-making situations, a simulation approach is used. Furthermore, by several test problems, the performance of the stochastic model is investigated and the scenario generation method is evaluated in terms of in-sample and out-of-sample stability. Finally, sensitivity analysis on main parameters of the problem is performed to drive some managerial insights.