Aquaculture is an important industry in certain coastal areas. Focusing on the farming of salmon and trout, an operational planning problem arises with the goal of allocating a supply of fish to the demand that is expressed through customer orders. This paper provides a conceptual model of such a planning problem and defines a corresponding bi-objective mathematical programming model. The problem is novel with respect to the structure of fish transport and the rules for satisfying customer orders with respect to fish size, quality, certification, and health status. Computational experiments have been conducted to gain further insight into the use of the provided model to provide support for planners who are involved in operational decision-making. The results indicated that the bi-objective optimization model can be useful in situations where a supply is insufficient to cover all of the demand within a given planning horizon.