Árbók VFÍ/TFÍ - 01.06.1998, Qupperneq 316

314 Ritrýndar greinar
Forsberg (1996) proposes a multi-period linear programming model for long term plann-
ing of the stocking and harvesting of salmon. As Getz and Haight (1989), he uses the
Markov model to describe the size-structured growth of fish. Forsberg only formulates the
model but does not report any implementation or experience of real life situations and
empirical data. Also the linear programming model does not assure the feasibility of harvest-
ing, for example in case of full harvesting of each cage, or partial selective harvesting of
only the oldest animals in each cage (thinning from above). These harvesting practices can
probably only be represented by integer variables, as proposed in the following.
Description of salmon farm management practice
In our case of salmon farming in Atlantic Canada smolt is released into the pens in May
every year. The smolt is classified by size, and thereby quality, into 6 classes. The smolt
classes are 40-60 grams, 60-80, 80-100, 100-120, 120-140, and over 140 grams. Each
smolt class is grown separately so the pens, around 150 for each year-class in our case, can
be grouped accordingly into 6 pen or smolt quality classes.
Each year-class of fish is grown for 27 months, whereof it is harvested during the last 12
months, from September to August the following year. No transfer is made between pens,
and no splitting, so the same number of fish released as smolt is grown in each pen through-
out the whole period, from 16 to 27 months, except for the decrease in number by natural
mortality and partial harvesting.
The harvesting of each pen can be full or partial, in which case the largest fish is graed
out and selected for harvesting. The grading limit between the fish to harvest and the físh to
leave in the pen can be set anywhere in the size distribution of the pen, with an accuracy of
about 1 lbs.
In each pen, a size distribution of the fish evolves during the grow-out period. The size
classes used here are 8, i.e. smolt, 0-2 lbs, 2-4, 4-6, 6-8, 8-10, 10-12 and over 12 lbs. The
last 5 size classes are marketable, however
the price per kg usually increases by size.
The prices are also seasonal and the price
difference between size classes is not the
same through the year, see Fig. 1 which
shows the sales price of salmon in Canadian
dollars per kg, CAD/kg.
The feeding scheme is determined by the
farming company, according to the seasons
and the temperature of the sea, and is not a
variable in our optimization ntodels. The
transition probabilities of our growth models, see Table 1, which serves as an example, are
dependent on the feeding scheme and thus become time dependent, contrary to Leung et al.
(1990). The accumulated feeding cost per fish at any time is also determined by this given
feeding scheme, see Fig. 2.
Sep Oct Nov Dec
Feb Mar Apr May Jun Jul Aug
Fig 1. Sales price offanned salmon in Atlantic
Canada, in Canadian dollars/kg.