Years of globalization, outsourcing and cost cutting have increased supply chain vulnerability calling for more effective risk mitigation strategies. In our research, we analyze supply chain disruptions in a production setting. Using a bilevel optimization framework, we minimize the total production cost for a manufacturer interested in finding optimal disruption mitigation strategies. The problem constitutes a convex network flow program under a chance constraint bounding the manufacturer's regrets in disrupted scenarios. Thus, in contrast to standard bilevel optimization schemes with two decision-makers, a leader and a follower, our model searches for the optimal production plan of a manufacturer in view of a reduction in the sequence of his own scenario-specific regrets. Defined as the difference in costs of a reactive plan, which considers the disruption as unknown until it occurs, and a benchmark anticipative plan, which predicts the disruption in the beginning of the planning horizon, the regrets allow measurement of the impact of scenario-specific production strategies on the manufacturer's total cost. For an efficient solution of the problem, we employ generalized Benders decomposition and develop customized feasibility cuts. In the managerial section, we discuss the implications for the risk-adjusted production and observe that the regrets of long disruptions are reduced in our mitigation strategy at the cost of shorter disruptions, whose regrets typically stay far below the risk threshold. This allows a decrease of the production cost under rare but high-impact disruption scenarios.