Risk shaping in production planning problem with pricing under random yield.

•Presented a risk shaping model for production planning problem under random yield.•Used Conditional Value-at-Risk as the risk measure.•Developed an efficient solution method for the presented nonconvex model.•The presented model can incorporate risk thresholds of decision makers.•The presented model can be used for obtaining efficient frontiers.•Characterized the set of saddle points by KKT conditions.