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Mathematical models for optimizing production chain planning in salmon farming



The salmon farming production chain is structured in four consecutive phases: freshwater, seawater, plant processing, and distribution and marketing. The phases interact in a pull manner, freshwater stocks fish to meet seawater's demand, seawater produces to meet plant processing biomass demand, and the processing plant produces to satisfy consumers' demand. Freshwater planning decisions are in regard to which freshwater center the fish should be located depending on the state of development of the fish. The goal is to satisfy seawater's demand while minimizing costs. In the seawater phase, the fish are first placed in seawater centers, and then sent to the processing plant as they approach suitable harvest conditions. The goal of seawater is to maximize harvested biomass while satisfying processing plant's demand. This paper presents two mixed-integer linear programming models—one for the freshwater phase and another for the seawater phase. These models are designed in such a way that the production planning is well integrated and more efficient and incorporates the requirements of the farm operator's freshwater and seawater units (biological, economic, and health-related constraints) ensuring that production in both phases is better coordinated. The development of the two models was based on the farming operations of one of the main producer farms in Chile. Preliminary evaluations of the models indicate that they not only succeed in enforcing constraints that are difficult to be met by manual planning but also led to more effective results in terms of the objectives set out.