Fig. 2. Relationship between groups of production phases.
2. Shrimp farm model
In practice, the primary objective of a shrimp farming operation can vary from maximizing total production, to minimizing downside risk, to meeting delivery
agreements, to maximize farm profits, or a combination of these objectives. For simplicity, we assume that the shrimp farmer operates to maximize long-run farm
profits subject to input constraints. Our shrimp farmer receives a fixed unit price for any amount of shrimp produced and can access all the resource inputs necessary to
expand farm size without limit. Shrimp reproduction and growth rates are assumed known and fixed. A single production technology is available to the farmer. The
cost of this technology is known and fixed. The farmer thus is left to make the following joint production decision. How large number of ponds should the farm
be? And with what frequency should the ponds be restocked each year?
2
.
1
. Production technology Adult shrimp, called spawners, are used to produce fertilized eggs. The spawning
shrimp are held in maturation tanks containing about 45 male and 35 female mature shrimp. Females produce an average of 0.053 spawnsday throughout the
year. At each spawning, free swimming larval shrimp called nauplii are released and moved immediately into hatchery tanks. In the hatchery tanks, the nauplii are fed
a special diet of algae and brine shrimp and allowed to grow until they reach a non-free swimming or post-larval stage. The post larval shrimp are reared in
nursery ponds until they form a carapace, then moved to growout ponds where they are reared to a marketable weight. The production technology and stocking
densities of the intensive shrimp operation described here are displayed in Table 1 and are largely based on the protocol developed at the Oceanic Institute in Hawaii
Wyban and Sweeney, 1991.
2
.
2
. Model equations Annual farm profit p is defined to be total revenue TR less total cost TC:
p = TR − TC
1 Total revenue is price per unit output multiplied by the quantity of shrimp
produced: TR = P × Q
2 Annual shrimp production Q is a function of number of growout ponds G, size
of the pond S, stocking density of the pond D, survival rate R, and number of cycles per year t.
Q = fG, S, D, R, t 3
Total annual cost of production TC include both fixed FC and variable costs VC:
TC = FC + VC 4
Costs include resource inputs, labor, and depreciated capital. Fixed and variable cost functions for an intensive shrimp farm operation were estimated by Tian
Table 1 Production technology for P. 6annamei
Growout Hatchery
Nursery Stage
Maturation Round concrete
Tank and pond Round earth
Round wooden tank Round fiberglass
pond pond
types tank
3250-l Tank and pond
0.08-ha 0.2-ha
8500-l size
75 Juveniles m
− 2
75 Nauplii l
− 1
Stocking density 1000 Post larvae
45 Male and 35 female m
− 2
adult shrimp tank
− 1
Spawning 0.053×365 per
female
− 1
year
− 1
frequency Spawning rate
55 555 Nauplii spawn
− 1
85 Survival rate
56 90
15 weeks Cycle duration
1 day 16 days
5 weeks Outdoor
Tank location Indoor
Outdoor Indoor
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
Kategori