baseline scenario, the average weekly incremental
growth in the high growth rate scenario is about 8%
higher.
As expected, a faster growth rate will lead to an
improvement in profitability. The overall net revenue is
estimated to increase by 44% when compared to the
baseline scenario. The production schedule in Fig. 4
indicates that changes in growth rate have similar effects
on the optimal managerial schedule as changes in
survival rate in the sense that larger shrimp will be
targeted. The optimal harvest size is now predominantly
in the 26/30 (count per pound) size class, with a 2-week
increase in the average length of the production cycle.
The overall fixed cost falls 13%, while the overall
variable cost rises 2% (this increase is mainly due to
added feeding necessary for growing larger shrimp).
Together, it causes a 7% drop in the overall production
cost. Therefore, the increase in overall net revenue is
largely due to the fact that the assumed increased growth
rate allows the farm to capture the price premium for
larger shrimp. The results also indicate that the average
return from a typical cycle in the high growth rate
scenario would increase about 75% when compared to
that in the baseline scenario (Table 2). Therefore,
although not as pronounced as the case of increased
survival rate, enhancing shrimp growth can also
significantly improve the profitability of this shrimp
farm as long as the added cost (such as using improved
seedstocks with enhanced growth rate) can be adequately
compensated. Furthermore, since either a high growth
rate or a high survival rate would imply a high biomass
which in turn may depress growth and result in a lower
growth rate. The results of the alternate high growth rate
and high survival rate scenarios suggest that the
negative effect of biomass on growth might not be so
significant.
3.3. Price seasonality
While this farm faces a rather stable price throughout
the year due to the markets it is presently serving, it
would be worthwhile to investigate how this farm would
fare if it chooses to enter a market with seasonal pricing.
In this seasonal price scenario, we captured the monthly
ex-vessel shrimp price from the Northern Gulf (Alabama,
Louisiana, and Mississippi) for the year 2002 into
the scheduling model. To be consistent in our
comparison, we also created a constant price scenario
whereby the price is assumed to be the annual average
for the year 2002. Except for the price, the other
assumptions of these two scenarios are identical with the
baseline scenario.
The production schedule for the constant price and
seasonal price scenarios are presented in Figs. 5 and 6,
respectively. We can see that although all shrimp would
be harvested in the size class of 41/50 (count per pound),
the arrangement of the production schedule has
substantially altered in order to capture certain niche
seasonal markets. The results indicate that by capturing
the variation in seasonal pricing of shrimp, the farm now
can obtain $0.23 more for every pound of shrimp
produced when compared to what can be secured under
the constant price scenario. As a result, there is a 46%
increase in the overall net revenue. It also indicates that
overall fixed cost increase by 1% and overall variable
cost by 3%. Overall, the average net revenue from a
single production cycle increases by 41% (Table 3). The
comparative results clearly demonstrate that when
seasonal price is applicable, ignoring the effect of
price seasonality would result in a sizable loss in
potential profit.
The price adopted in these two scenarios is lower
than what the farm currently can be received. Hence, the
results also indicate that with lower price growing
smaller shrimp would be more profitable. Comparing
Figs. 5 and 6 to Figs. 2–4, it implies that it might not be
efficient to restock the growout pond immediately even
if the preparation for a new crop is completed. This may
be caused by slow incremental growth at certain periods
due to the cold temperature or the expected low price
when the shrimp is ready for market. Therefore, using an
appropriate resting period between two production
cycles can be rather critical when faced with seasonal
pricing.
The above comparison suggests that the economic
value of information about seasonal price can be
substantial for this shrimp farm, if seasonal price
becomes relevant.
3.4. Labor force constraints
In practice, due to the limitation of labor force and
facility capacity, usually there are restrictions on the
frequency of harvests and stockings within a certain
assessment period. The current practice of the shrimp
farm under our investigation allows at most 3 harvests
(stockings) to occur within one week. In order to
investigate how this constraint would affect the optimal
managerial schedule and economic performance, the
following two scenarios are examined: (1) a “no
constraint” scenario where