Optimal stocking in intensive aquaculture under sinusoidal temperature, price and marketing conditions

When the environmental and/or market conditions of an intensive aquacultural operation vary with time, maximization of profit may require a time dependent fish stocking rate. A simplified stocking problem is formulated where temperature, market price and/or market demand change sinusoidally over the annual cycle. The fish biomass sustaining-capacity is limited by the water treatment equipment, and is expressed in terms of maximum feeding rate per unit volume of culture tanks.It is demonstrated that under such conditions, sinusoidal stocking rates produce good sub-optimal solutions. A critical element of the solution is the time delay (phase-shift) between the constraining (restricting) conditions (temperature and market), and the stocking cycle. Furthermore, if the solutions for two individual conditions have very different time delays, a combination of the two conflicting restrictions is likely to produce poor returns.