Árbók VFÍ/TFÍ - 01.06.1998, Blaðsíða 315
Optimization Models of Aquaculture Operations 313
approaches that have been proposed in the literature, see Forsberg (1996), however
implementations in real life situations have not been reported.
The sludy covers only salmon, which is the most important species to the North-Atlantic
fish farming. The methodology presented here has a general approach so it should be poss
ible to adapt the research results of this paper to other species.
Economic Analvsis of Aquaculture Production: Hatch and Tai (1997) provide a recent
review of the literature on aquaculture production economics and farm management, with
the focus on salmon, trout, catfish and shrimp. Bjorndal (1988) contributes with an eco-
nomical analysis deriving qualitative results regarding the optimal harvesting time for a
year-class of farmed fish. One of the underlying assumptions is that all físh weigh the sante.
Size difference, and selective harvesting, are only briefly addressed. Arnason (1992) extends
the economic analysis by Bjorndal to involve the interdependent questions of what feeding
schedule to adopt and when to harvest. Talpaz and Tsur (1982) use a gantma distribution
function to represent the variability of fish size, and propose that selective harvesting with
thinning from above is preferable.
Contmon to all these bio-economic analysis references is that, as ntuch as they help to
understand and give insight with qualitative results, they are not based on empirical data
from real life operations, and they do not provide the individual farming companies with
operational management tools.
Mathcniatical Programming Approaches: Recent reviews of the literature on systems
modeling and information technology in aquaculture are found in Cacho (1997) and El-Gay-
ar (1997). Varvarigos and Horne (1986) discuss the use of linear programming for planning
fish farming business and analyze the skills needed, the data requirements and the strengths
and usefulness of LP models. Bala and Satter (1989) present a combination of a system
dynamics model and a linear programming model. Pelot and Cyrus (1997) use a linear
programming rnodel for a large-scale scallop hanging culture operation to determine the
optimal duration for each stage of the grow-out process.
In Shaftel and Wilson (1990) and Wilson et al. (1991), a mixed integer linear programm-
ing model is used to optintize harvesting and restocking in a single enclosure. The integer
variables assure that fish is placed in the enclosure only when it is empty. As in all refer-
ences mentioned above, all animals placed in the enclosure at a certain time are assunted to
be of the same size through Ihe grow-out period. Clayton, E.R. (1995) extends the work by
Wilson and Shaftel to the multi-enclosure case, and optimizes the allocation of tanks to each
echelon of fish, however the size variation within an age-class is still not addressed.
Markov Model Approaches: A Markov model to describe the size-structured growth of
farmed fish was first proposed by Sparre (1976). He formulates a linear programming model
and a dynamic programming to optimize the harvesting and discusses the shortcomings of
both. In Leung and Shang (1989), Leung et al. (1990) and Leung et al. (1993), the Markov
process approach and dynamic programming is used to study optimal decision rules for
stocking and harvesting shrimp and prawn. The analysis is restricted to the operation of a
single pond without any resource constraints, and a constant growth structure throughout the
year.