Mathematical principles of production management and robust layout design: Part II. Upscaling to a 1000-ton/year recirculating aquaculture system (RAS)

Abstract

The design and management of a recirculating aquaculture system (RAS) is crucial for the farm's economic survival. In a previous paper (Part I of this study), a model was developed. The current paper extends the principles developed in Part I by (1) addressing a larger-scale RAS, (2) addressing the layout positioning problem, (3) integrating a robust 6σ design into the optimization problem. A queuing model and a solvable nonlinear constrained optimization problem including the 6σ robust design were developed and validated. The design criteria were: (1) turnover ≥1000ton/year, (2) 7 days quarantine, i.e., at least 7 days between arrivals of two successive fish batches, (3) fish biomass density ≤55kg/m3, (4) three growth phases, (5) neither fish-sorting nor batch-splitting events allowed, and (6) a robust design to accommodate two species—seabream and seabass grouper, with different growth rates. Decision variables were: (1) number of culture tanks, (2) fingerling arrival frequency, (3) number of fingerlings per batch, (4) number of days in a growth phase, (5) timing of grading and sorting criteria on the production lines, (5) standing biomass in the entire system, which is the actual biomass load on the biofilters, (6) feed amount per day.The optimal layout was: 13 culture tanks in each of the three growth phases (39 tanks total). Optimal parameters included: arrival frequency—a single fish batch into the system every 7 days, 91 days in each phase; growth up to 77, 233, and 468g in successive growth phases. Optimal values satisfied the criteria of biomass density below 50kg/m3 and culture tank utilization above 99%. Expected production was 1000ton/year. The proposed layout can accommodate different fish species—here, seabream and grouper—under the same culture volume, density, and schedule, but with different growth rates. Increasing the desired biomass density from 50 to 60kg/m3 advances expected production to 1335ton/year. The numerical values reflect local aquatic conditions, but the proposed methodology can be applied anywhere.