Multi-Response Optimization and Quality Assessment of Whey Yogurt Using a Constrained Mixture Design

The valorization of whey, a major dairy-processing by-product, represents an important strategy for improving resource efficiency, supporting sustainable dairy production, and diversifying fermented dairy products. However, increasing whey incorporation into yogurt may affect gel stability and water retention during storage. This study aimed to develop and optimize a whey yogurt formulation using a constrained mixture-design approach, with milk, liquid whey, and skim milk powder (SMP) as formulation components. Twenty-two randomized experimental runs were conducted, including 13 formulations in the first batch and nine repeated formulations in a second batch. The mixture design was constrained to 40–100% milk, 0–50% whey, and 0–10% SMP, with the components summing to 100%. A multi-response approach was applied to evaluate syneresis, water-holding capacity (WHC), and pH after 1, 7, and 14 days of refrigerated storage, together with total phenolic content (TPC) and microbiological quality. The experimental data were analyzed using Design-Expert software (Version 13, Stat-Ease Inc., Minneapolis, MN, USA)), and mixture models were evaluated using analysis of variance and model-adequacy statistics. Numerical optimization was performed using a desirability-function approach, with minimization of syneresis and maximization of WHC as the principal optimization objectives. TPC was evaluated as a supplementary response but was not included in the final optimization because an adequate predictive model was not established. During storage, pH decreased, indicating progressive post-acidification, while syneresis and WHC varied among formulations and storage periods. The optimized formulation consisted of 52.665% milk, 38.948% whey, and 8.388% SMP, with an overall desirability of 0.754. The predicted syneresis and WHC values were 52.337 mL/100 mL and 48.442% on day 1, 53.231 mL/100 mL and 48.902% on day 7, and 50.913 mL/100 mL and 52.329% on day 14, respectively, while the predicted pH values were 4.361, 4.273, and 4.154. The numerical optimum was further evaluated using two independent confirmation runs, showing reasonable agreement between the predicted and experimental syneresis and pH values. TPC results showed considerable variation among the formulations, reflecting differences in the phenolic content of the developed yogurts, while microbiological analysis showed variable results among the experimental runs. Overall, the findings demonstrate the applicability of constrained mixture-design methodology for balancing whey utilization with yogurt physical stability and highlight the potential of liquid whey valorization as a sustainable strategy for fermented dairy product development.