Two process designs for the separation section of a flexible dimethyl ether and methanol polygeneration plant are presented, as well as an optimization method which can determine the optimal design under market uncertainty quickly and to global optimality without loss of model fidelity. The polygeneration plant produces a product mixture that is either mostly dimethyl ether or mostly methanol depending on market conditions by using a classic two-stage dimethyl ether production catalytic reaction route in which the second stage is bypassed when the market demand is such that methanol production is more favorable than dimethyl ether. The downstream distillation sequence is designed to purify the products to desired specifications despite the wide variability in feed condition that corresponds to the upstream reaction system operating either in DME-rich or methanol-rich mode. Because the optimal design depends on uncertain market conditions (realized as the percentage of the time in which the plant operates in either DME-rich or methanol-rich mode), this uncertainty is considered in the formulation of the optimal design problem. The results show that using one set of flexible distillation columns for two different objectives is superior to the “traditional” approach of using two different sets of distillation columns which are each optimized for one specific operating condition. Different approaches to design under uncertainty were considered, with a scenario-based two-stage stochastic formulation with a uniform distribution of the uncertain parameter recommended as the preferred formulation.