Modeling optimal dietary pigmentation strategies in farmed Atlantic salmon: Application of mixed-integer non-linear mathematical programming techniques

The most important visual quality characteristic of Atlantic salmon is the red/pink flesh color. The primary source of this coloration in salmon is caused by deposition of relatively large amounts of pigments, such as astaxanthin, obtained from their diet. Astaxanthin is expensive, and in commercial farming practice, dietary color pigments comprises about 15–20% of the total feed cost. One important operational process in commercial fish farms is therefore to minimize pigment costs. Based on recent models on the effects of dietary pigment concentration and fish size on visual color perception of Atlantic salmon, this study has built a mathematical programming model designed to optimize dietary astaxanthin concentrations throughout the grow-out period that results in well-pigmented fish at minimum cost. We have applied a mixed-integer non-linear programming algorithm to solve this problem. Various managerial implications of applying optimization models in product quality management of farmed salmon are discussed.