Table 2 Identity equations and constraints
Hatchery Maturation
Nursery Stage
Growout Juvenile shrimp
Market shrimp Post larval
Product Nauplii
shrimp N
g
= y
4
G
g
ay
3
R
3
H
g
= y
3
N
g
y
2
R
2
G
g
M
g
= y
2
H
g
y
1
Number per group same cycle
Total number N = N
g
+ D
n
b H = H
g
+ D
h
d M = M
g
+ D
m,
G y
2
= S
2
D
2
y
1
= U
1
Q
1
M
1
Output per pond or tank y
4
= S
4
D
4
y
3
= S
3
D
3
Y
2
= y
2
t
2
R
2
H Y
1
= y
1
t
1
M Y
3
= y
3
t
3
R
3
N Q = y
4
t
4
R
4
wG Output per year
Y
3
B Y
2
QBY
3
Y
2
B Y
1
Y1\0 Ouput constraints
1993 and are as follows. Fixed cost FC as a function of the number of maturation tanks M, hatchery tanks H, nursery ponds N and growout ponds
G is:
FC
c
= 35.8140 + 5.9768M + 3.0964H + 6.0632N + 6.9669G − 0.0014M
2
− 0.0023H
2
− 0.0130N
2
− 0.0097G
2
5 Variable cost VC as a function of the number of maturation tanks M,
hatchery tanks H, nursery ponds N and growout ponds G, and their respec- tive number of cycles per year t
1
, t
2
, t
3
, and t
4
is: VC = 0.3653 + 0.0494Mt
1
+ 6.3216 + 0.4534Ht
2
+ 22.6640 + 2.0046Nt
3
+ 61.1774 + 19.8060Gt
4
10
3
6 The identity equations Table 2 provide the linking relationships between the
four stages of production. Definitions of the model variables can be found in Appendix A.
2
.
3
. Data 6alues The model was parameterized using the data displayed in Table 3.
3. Model scenarios
The size of a closed-farm operation is indicated by the area devoted to produc- ing marketable product, or the number of growout ponds on the facility. In a
continuous, year-around operation, each growout pond will be restocked every four months with the output juveniles produced by a dedicated group of nursery
ponds. Those nursery ponds in turn are stocked with postlarvae from the hatchery tanks which in turn are stocked with nauplii produced in the maturation tanks. A
depiction of the flow of intermediate product between tanks is shown in Fig. 2.
Three model scenarios were developed to capture a plausible range of farm sizes for evaluating scale economies in shrimp production and are described in Section
3.1 – Section 3.3.
3
.
1
. Growout ponds are stocked and har6ested weekly A shrimp farm with as few as 16 growout ponds can harvest marketable shrimp
weekly. Each pond will be restocked and harvested three times per year for a total of 48 harvests, about one per week. A production schedule is displayed in Fig. 3.
3
.
2
. Growout ponds are stocked and har6ested biweekly A shrimp farm with as few as eight growout ponds can harvest marketable
shrimp every other week. Each pond will be restocked and harvested three times per year for a total of 24 harvests, twice per month. A production schedule is displayed
in Fig. 4.
Table 3 Shrimp farm data
Value Variable
Variable description Price of shrimp kg
− 1
P 10
Shrimp weight at harvest kg shrimp
− 1
W 0.023
75 Hatchery tank stocking density nauplii l
− 1
D
2
1000 D
3
Nursery pond stocking density, postlarvae m
− 2
D
4
75 Growout pond stocking density, juvenile m
− 2
Broodstock culling interval months 3
L
1
Nauplii per female per spawn M
1
55 555 Number of female spawners per maturation tank
Q
1
35 Q
2
Number of male spawners per maturation tank 45
R
2
0.56 Survival rate in hatchery
Survival rate in nursery 0.85
R
3
R
4
0.9 Survival rate in growout
Hatchery tank volume l S
2
3250 0.08
S
3
Nursery pond area ha Growout pond area ha
S
4
0.2 t
1
48 Number of maturation cycles per tank per year cycles year
− 1
Hatchery cycles per tank per year cycles year
− 1
t
2
18 t
3
Nursery cycles operated per pond per year cycles year
− 1
9 3
Growout cycles operated per pond per year cycles year
− 1
t
4
U
1
1.59 Spawns per female spawns month
− 1
Harvest shrimp weight g 23
W Nauplii per tank nauplii cycle
− 1
103 055 y
1
243 750 Postlarvae per tank postlarvae cycle
1
y
2
Juvenile per pond juvenile cycle
1
800 000 y
3
150 000 Shrimp per pond adult shrimp cycle
1
y
4
Fig. 3. Closed-market operational system production schedule — growout ponds are stocked weekly.
Fig. 4. Closed-market operational system production schedule — growout ponds are stocked biweekly.
3
.
3
. Growout ponds are stocked and har6ested e6ery
8
weeks A shrimp farm with as few as two growout ponds will allow for a harvest of
23 g shrimp every 8 weeks. At this rate, the ponds must be restocked and harvested three times per year for a total of six harvests, or one every 2 months.
A production schedule is displayed in Fig. 5.
3
.
4
. Parameter 6alues for the model scenarios The parameter values for the three stocking and harvesting scenarios, once per
week, biweekly, and every 8 weeks, are shown in Table 4.
4. Results and discussions
