Shrimp size, density, growth rate and mortality
enter the first production stage and is reduced each time the shrimp are transferred to subsequent stages.
The advantages of multi-stage production systems have been well identified by Cao and Jiang 1990, Fast 1991, Sandifer et al. 1991, Sturmer et al. 1991,
Samocha and Lawrence 1992, Stern and Letellier 1992. In general, these authors feel that a multi-stage shrimp production system can improve stock inventory
control and disease treatment, reduce predator damage and feed waste, alleviate the difficulty of monitoring survival rate, provide more efficient use of land, and
potentially lead to increased numbers of crops per year.
On the other hand, Stern and Letellier 1992 reported increased shrimp stress in a multi-stage production system due to the transfer of animals which may cause
increased mortality. Let us assume that identical mechanical oxygenation and pumping efficiencies
prevail and that biological efficiencies such as growth rate, mortality rate, feed conversion ratio, and final average weight of shrimp produced are constants that
do not vary in the production systems under consideration. The annual operating cost of a shrimp production system is then approximately a function of the number
of shrimp produced, since the number of shrimp targeted for production will dictate the number of postlarvae required, feed and electrical costs, and other expenses.
The annual operating cost per kg of shrimp produced, therefore, should not vary with the number of stages in a production system. Thus, the financial return of a
multi-stage shrimp production system, given the above assumptions, must be approximately a function of land and construction costs Chong, 1990. If we
further assume that construction cost is proportional to the water surface area of the specific system, we can then compare the expected financial returns of shrimp
production systems by comparing their land use efficiency.
By adopting the above simplifying assumptions, the problem of optimizing a multi-stage shrimp production system is reduced to the following:
Min
j
A
pr
j,i =
i
[N j,iA j,i] 1
where: A
pr
j,i is total water surface area of pondstanks in phase configuration j and phase i m
2
; N j,i is number of pondstanks in phase configuration j and phase i integer c ; A j,i is water surface area of individual pondtank in phase
configuration j and phase i m
2
.