Mathematical principles of production management and robust layout design: Part III. 2500-ton/year fish farming in marine net cages

Fish production in marine netcages is expanding rapidly in many parts of the world. Nevertheless, production planning and layout design tools still rely on rule of thumb, spreadsheets, local experience and practices handed down through the generations. An integrated model (queuing, optimization and simulation were linked together) was developed. The solution finds the values of decision variables to maximize yearly production.The concept was that a single netcage can be seen as a “server” in which neither a “queue” (over-holding of fish), nor an idle netcage is allowed. A marine fish farm can then be seen as a queuing network, and a queuing network-based management model was developed.Growth data of 40 batches of fish, each batch comprising on average 180,000 fish (std 50,000), were recorded over an experimental period of 4 years.The model inputs were (1) the empirical fish growth rates (2) the given space for netcages, (3) preferred netcage holes, netcage depth and netcage diameter, (4) fingerling supply limitations, (5) market timing, and (6) Preferred market-size fish at the farm gate. The model outputs were: (7) optimal fingerling arrival frequency, (8) optimal number of fingerlings in a batch, (9) number of days in each culture netcage, (10) grading and sorting criteria along the production line, and (11) optimal facility allocation (number of netcages for each growing phase). Model validity was statistically tested and was not rejected within the 95% confidence level. The model application results with 4 netcages in the 1st growing phase, 8 netcages in the 2nd growing phase and 16 netcages in the 3rd growing phase (so called “4,8,16 layout”) gave the following optimal operating parameters: arrival of a batch every 30 days; 122 days in each successive growth phase. The optimal values satisfied the biomass density criterion of less than 25kgm−3 and the netcage utilization criterion of never below 99%. Expected production was 2403tonyear−1 (vs. the current 686tonyear−1). The enterprise owners decided to adopt the model results and the system is now being built according to the 4,8,16 design.