3. The calculated constants are shown in Table 3 Leiman, 1995. It can be seen that as stocking densities decrease from 1100 to 40 shrimpm
2
, the k values decrease from 0.022 to 0.009day, while the W
inf
values increase from 4.1 to 44.9 g. Using Eq. 3 and the constants from Table 3, we can construct Fig. 2.
While Fig. 1 is an idealized representation, Fig. 2 is based upon limited real data. We can see that Fig. 2 gives an excellent facsimile of Fig. 1.
The total water surface area of the pondstanks for each production stage can now be calculated with the following equations and Eq. 1.
Ii = Oi Si 100 4
Ai = Ii SDi 5
where: Ii is input or stocking population of shrimp in phase i; Oi is output or transferharvest population of shrimp in phase i; Si is shrimp alive by the
end of rearing period in phase i 100 refers to the shrimp alive at stocking time of phase i ; Ai is water surface area of individual pondtank in phase i
m
2
; SDi is stocking density of shrimp in phase i shrimpm
2
. Ni = [t
th
i − t
s
i + t
d
i ]t
pd
6 where: Ni is number of pondstanks in phase i integer c ; t
th
i is transfer harvest time in phase i weeks; t
s
i is stocking time in phase i weeks; t
d
i is down period between cycle in phase i weeks; t
pd
is period between product deliveries weeks = lfrequency of delivery.
4. Optimization
Setting the market size to be 50 shrimpkg and the amount of shrimp produced every other week to be 2000 kg of shrimp, Eqs. 4 – 6 are used to calculate the
water surface area required. In Eq. 6, Ni is the number of shrimp tanks and must therefore be an integer; t
d
i is the rest period between production cycles used for maintenance and repair and it can be increased so that Ni is an integer.
It can be seen from Fig. 2 that tanks stocked at initial densities of 1100, 550 and 100 shrimpm
2
will reached their CSC biomass at days 21, 42 and 63, respectively. Shrimp in pondstanks stocked at 40 shrimpm
2
grow at the maxi- mum biological growth rate attainable under the environmental and feeding
regimes. The total water surface area needed by the production system can be calculated
using Eqs. 1 and 4 – 6 with appropriate rest periods. The results are shown in Table 4 and Fig. 3. Fig. 3 shows that while the water surface area required
declines from the single-stage through the four-stage production systems, the greatest reduction occurs between a single-stage and a two-stage system. Fig. 3
also shows that the most efficient system is a two-stage system consisting of an initial stocking rate of 550 shrimpm
2
and in which the shrimp are redistributed on day 42 to a density of 40 shrimpm
2
.
251 J
.- K
. Wang
, J
. Leiman
Aquacultural
Engineering
22 2000
243 –
254
Table 4 Possible phase configurations with rearing period and stocking density in each phase for the design case study
Phase configu- Phase category
Rearing p- Stocking den-
Rearing pe- Rearing period
Stocking den- Stocking den-
Configuration Stocking den-
No. of phases Rearing pe-
riod of phase eriod of phase
sity of phase a No.
sity of phase c sity of phase d
riod of phase sity of phase b
ration of phase d
days shrimpm
2
shrimpm
2
c days b days
a days shrimpm
2
shrimpm
2
42–63 63–154
1100.00 443.95
69.02 0–21
26.43 1
21–42 a, b, c, d
4 Multiphase
Multiphase 0–42
42–63 63–154
– 550.00
69.02 26.43
3 b, c, d
2 –
21–63 63–154
3 1100.00
Multiphase –
80.72 26.43
3 a, c, d
0–21 –
– 42–154
1100.00 443.95
– 21–42
27.61 a, b, d
0–21 4
Multiphase 3
– Multiphase
0–63 63–154
– –
100.00 26.43
2 c, d
– 5
– 42–154
– 550.00
– 27.61
6 Multiphase
2 b, d
– 0–42
– 21–154
100.00 –
– –
32.29 a, d
7 Multiphase
2 0–21
8 –
1-Phase 0–154
– –
40.00 1
d –
–
5. Discussion
