A comparative study of theoretical model-based optimization and experimental design approaches for functional beverage formulation

Abstract

The demand for functional beverages offering specific health benefits beyond hydration has grown, while advancements in computer-aided food formulation introduce new approaches to reduce innovation costs in the food industry. Two case studies, a juice mixture and a plant-based beverage, were optimized using two approaches: one based on theoretical models (TMOs) and the other on experimental design (DoE). In both approaches, the objective function focused on maximizing the target property; in the first case study, it maximizes antioxidant content, whereas in the second case study, it maximizes protein content. The optimal juice formula based on the TMO approximation consisted of 14% apple, 44% grape, and 42% cranberry, whereas the DoE approach's formula comprised 28.5% apple, 32.2% grape, and 39.3% cranberry. Validation showed that TMO had a lower error rate of 2.0% in phenolic content compared to 13.7% from DoE. For the plant-based beverage, TMO estimated 74% rice, 16% peas, and 10% almonds, compared to DoE's 60%, 28%, and 12%, respectively. Total protein estimation errors were 14.5% for DoE and 4.2% for TMO. Overall, water activity estimation was most accurate for both cases (0.6% and 0.1%, respectively). Larger errors were observed in estimations of pH and acidity (20–24%) for the juices and in viscosity (22%) for the milk analogue. Sensory tests found no significant difference (p > 0.05) in consumer acceptance between the two approaches, with mean scores of 7.5 ± 1.2 (mix design) and 7.7 ± 1.9 (theoretical) for juices. Similarly, for the milk analogue, the values were 6.2 ± 2.5 (mix design) and 6.3 ± 2.4 (theoretical). Thus, although theoretical estimation has limitations in accuracy, it can produce acceptable, cost-effective formulations that consumers accept, saving time and resources.