In food supply chain planning, the trade-off between expected profit and risk is emphasized by the perishable nature of the goods that it has to handle. In particular, the risk of spoilage and the risk of revenue loss are substantial when stochastic parameters related to the demand, the consumer behavior, and the spoilage effect are considered. This paper aims to expose and handle this trade-off by developing risk-averse production planning models that incorporate financial risk measures. In particular, the performance of a risk-neutral attitude is compared to the performance of models taking into account the upper partial mean and the conditional value-at-risk. Insights from an illustrative example show the positive impact of the risk-averse models in operational performance indicators, such as the amount of expired products. Furthermore, through an extensive computational experiment, the advantage of the conditional value-at-risk model is evidenced, as it is able to dominate the solutions from the upper partial mean for the spoilage performance indicator. These advantages are tightly related to a sustainable view of production planning, and they can be achieved at the expense of controlled losses in the expected profit.