a novel computer simulation model_design

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A novel computer simulation model for design andmanagement of re-circulating aquaculture systems

Ilan Halachmia,*, Yitzchak Simonb,

Rami Guetta

c

, Eric M. Hallerman

d

aInstitute of Agricultural Engineering, Agricultural Research Organization,

The Volcani Center, P.O. Box 6, Bet Dagan 50250, IsraelbAquaculture Department, Extension Service, Ministry of Agriculture, P.O. Box 28, Bet Dagan 50250, Israel

cFaculty of Agricultural Engineering, Technion Israel Institute of Technology, Haifa 32000, IsraeldDepartment of Fisheries and Wildlife Sciences, 150 Cheatham Hall,

Virginia Polytechnic Institute and State University, Blacksburg VA, 24061, USA

Received 23 February 2004; accepted 28 September 2004

Abstract

The aim of this study was to develop a simulation model for finding the optimal layout and

management regime for a re-circulating aquaculture system (RAS). The work plan involved: (1)

quantifying the effects of fish growth and management practices on production; (2) developing a

mathematical simulation model for the RAS, taking into account all factors that directly influence

system profitability; and (3) estimating the production costs and, hence, the profitability of an RAS.

The resulting model is process-oriented, following the flow of fish through the RAS facility, and

generates an animated graphic representation of the processes through which the fish passes as it

progress through the system. The simulation assesses the performance in terms of yearly turnover,

stocking density, tank utilization and biomass in process, and uses statistics to track the state of the

RAS and record changes that affect efficiency. The economic impact of system design and operation

was modeled to enable a user to anticipate how changes in design or operating practices, costs of

inputs, or price of products affect system profitability. The proposed approach overcomes difficulties

in characterizing RAS design and operation. The simulation approach allows all of the RASs

www.elsevier.com/locate/aqua-online

Aquacultural Engineering 32 (2005) 443464

Abbreviations: BW, fish body weight; CAD, Computer-assisted design; CS, Computer simulation; DGD,

Dynamic graphic display; DOE, Design of experiment; DXF, Drawing exchange format; I/O, Input/output; OO,

Object-oriented; PD, Probability distribution; RAS, Re-circulating aquaculture systems; SPL, simulation pro-

gramming language; SQP, sequential quadratic programming; VIS, Visual interactive simulation.

* Corresponding author. Tel.: +972 506 220 112; fax: +972 49 930 154.

E-mail address: [email protected] (I. Halachmi).

0144-8609/$ see front matter # 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.aquaeng.2004.09.010


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components such as equipment, biological processes (e.g., fish growth), and management practices to

be evaluated jointly, so that an initial design can be fine-tuned to produce an optimized system and

management regime suited to a specific fish farm within a reasonable time. The methodology was

executed step-by-step to design an optimal RAS that meets both economic and stocking-densitylimits. Optimal design specifications were presented for several case studies based on data from

Kibbutz Sde Eliahus RAS, in which Nile tilapia (Oreochromis niloticus) are raised in 20 concrete

raceways. Further research should include more extensive testing and validation of the integrated

model, which then should be disseminated to the aquaculture community.

# 2004 Elsevier B.V. All rights reserved.

Keywords: Re-circulating aquaculture systems (RAS); Computer simulation; Tilapia; Operations research;

Intensive aquaculture

1. Introduction

Despite an impressive record of recent growth (Timmons et al., 2001), there are

important constraints to the future growth of aquaculture, including limited availability of

high-quality water, and location factors related to site availability, soils suitable for pond

construction, and proximity to markets. Production of fish in re-circulating aquaculture

systems (RASs) addresses these constraints. RASs require less than 10% of the water and

much less land than do extensive pond systems to produce a given quantity of fish. RAS

technology reduces the effluent waste stream by a factor of 5001000 (Timmons et al.,

2001). Further, a RAS can place production on the doorstep of the consumer and candeliver a fresher, safer product at lower transportation costs (Timmons et al., 2001) and

with a high degree of product traceability (Smith, 1996; Jahncke and Schwarz, 2000).

RASs offer a high degree of environmental control and allow year-round production.

Operating a RAS requires intensive management of the many unit processes and/or

operations involved (Summerfelt, 1996; Libey and Timmons, 1996). Timmons et al. (2001)

listed several RAS ventures that failed, and poor management was the primary reason for

these failures. Because RAS is rather capital-intensive (ORourke, 1996), its profitability

relies on maximizing economic productivity per unit volume or rearing space. An

appreciable number of recently built RAS systems cannot reach production goals and,

therefore, cannot return the investment (Table 1). Hence, RAS must be optimized not onlyin an engineering sense, but also in biological and economic senses, in order to yield a

satisfactory return on investment.

I. Halachmi et al. / Aquacultural Engineering 32 (2005) 443464444

Table 1

Planned vs. actual yearly production (tonnes per year) for seven RAS facilities

Farma

A B C D E F G

Production planned 2000 100 200 20 2000 100 50

Actual production 1650 60 110 16 1500 70 25a Farms: A, B, C: tilapia farms in United States; D: tilapia research farm in United States; E: hybrid striped bass

farm in United States, F: Sde Eliahu tilapia farm in Israel, G: tilapia farm in Israel.


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The investment in a large RAS operation approaches the cost of a medium-sized factory,

e.g., a RAS system built in 1990 producing approximately three million pounds of tilapia

annually costs $9 million. While the designand daily management of a medium-sized factory

is supported by computer simulation (CS), that of RAS still relies on traditional methods andengineering rules-of-thumb. The burgeoning use of systems engineering techniques,

including computer simulation, has revolutionized the design and management of

manufacturing systems, telephone networks, banks, supermarkets, and other operations

(Gregor and Kosturiak, 1997; Hurrion, 1997; Law, 1990b; Chan, 1996; Galbraith and

Standridge, 1994; Chan and Tang, 1994; Hill et al., 1997; Halachmi, 2000, 2004; Halachmi

et al., 2001, 2002). Likewise, this study may be said to be a contribution to further revolution,

this time in the design of aquaculture systems. Although simulation may require skilled

manpower, physicalconstructionandrefittingof different layouts are usuallymoreexpensive.

Inourpresentcontext,simulationavoidsthedifficultiesof empiricalexperimentation withthe

RAS.Being flexible andfree from unimportantdetails, theiterative natureof modelingallows

isolation of a single parameter, with validation by means of any number of procedures (Pidd,

1989; Law and Kelton, 1991; Kleijnen and van Groenendaal, 1992; Banks, 1998). Recent

developments in computing power and simulation techniques have increased the power of

models, thereby enhancing their potential value for RAS design (Summerfelt, 1996;

McCallum et al., 2000; Rasmussen, 2002). Nevertheless, these techniques have not yet been

used to integrate engineering, biological and economic data in the design and management of

a complete, commercial-scale RAS. There is a clear need for improved design and

management of RASs, based on integrated biological, engineering, and economic modeling

of interactions among animals, facilities, and operators, and applicable to any farm or site.Systems engineering and CS techniques may provide the basis for identifying optimal

management practices, providing a practical tool that can be used daily.

1.1. Simulation in designing a RAS

Although simulation techniques have not been used to design complete re-circulating

aquaculture systems, simulation has been used to characterize various aspects of aquaculture

systems. Ellner et al. (1996) and Kochba et al. (1994) showed that simulation was useful for

investigating the production, transfer, and loss of inorganic nitrogen in pond systems. Jamu

and Piedrahita (2002) developed simulation models for organic matter and nitrogen inintegrated aquaculture systems. Singh et al. (1996) simulated the discharge of wastewater

heat from an RAS facility to determine optimum greenhouse size. Weatherley et al. (1993)

compared a continuous-time simulation language designed for solving time-dependent, non-

linear differential equations with analytical solutions of the unsteady-state mass-balance

equations for the transfer and removal of ammonia; they concluded that simulation is a

powerful tool for describing the dynamic behaviour of ammonia concentration. A general

discussion for the use of models in aquaculture science was presented by Ernst et al. (2000),

who developed decision support software for design and management planning that

simulates physical, chemical and biological unit processes. However, no one has yet

developed a complete stochastic simulation model of the entire system, including bothdiscrete and continuous processes and incorporating animation for use as a practical tool for

optimizing design and management of a specific RAS.

I. Halachmi et al. / Aquacultural Engineering 32 (2005) 443464 445


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1.2. Research problem and aim

Optimal design balances the need for adequate facility capacity against the wastefulness

of overcapacity. The necessary capacity of each RAS component (e.g., culture units, filters,feed storage, quarantine facility, hatchery tanks, and gas transfer facilities) depends on a

rather large number of engineering, production, and economic parameters. These include

stocking density, system carrying capacity, batch size, and batch arrival schedule, which

have to be operationally matched with harvest frequency, fish growth rate, fish weight at

market time, labor-related parameters, and other interconnected variables. The aim of

present study was to develop a simulation model for finding the optimal layout and

management regime for RASa model intended for research as well as practical

application. Although an optimal solution will reflect local conditions, the design

methodology, i.e., the model, should be universally applicable, adjustable to any farm or

site.

2. Methods

2.1. Modeling approach

We used ARENA 7, a simulation programming language (SPL) with Visual Interactive

Simulation (VIS), which is object-oriented (OO) and includes dynamic graphic display

(DGD). These recent developments in simulation techniques have increased the power ofmodeling and enhanced its potential value in RAS design. SPL facilitates the building of

executable computer models for carrying out simulation experiments (Pidd, 1989; Hlupic,

1997; van der Zee, 1997). VIS and DGD illustrate the outputs of simulation models and

alternative decision strategies (reviewed by Kirkpatrick and Bell, 1989; Bell, 1991). OO

promises benefits such as one-to-one mapping of real-world objects and improved

readability, maintainability, and extensibility of programs (Pidd, 1985). For all these topics,

there is a specialized literature (e.g., Law and McComas, 1990; Kleijnen and van

Groenendaal, 1992). The solution for coupling the drawing of RAS with the simulation

kernel was to load a Drawing Exchange Format (DXF) file containing a scale drawing of

the given RAS into the simulation software. A DXF file can be created by most CADsoftware (e.g., Anon., 1995, 1996). The integration of mathematical model, scale drawing

and computer simulation provides the integrated design tool required for designing and

managing a dynamic RAS system.

2.2. Data acquisition

The case study is based on data from Kibbutz Sde Eliahus RAS, in which Nile tilapia

(Oreochromis niloticus) are raised in 20 concrete raceways. This RAS has been working for

12 years. The planned turnover was 100 t/year, but the production actually achieved is less

than 70 t/year. The system comprises 10 small raceways of 17 m3

each for growth phase 1and 10 large raceways of 34 m3 each for growth phase 2. The fishes are placed into the

system at approximately 50 days of age and are kept in each growth phase for about 6575



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days. Grading is performed once a week, and the largest fish from the two oldest batches are

sent to market. The fish remaining in those two batches are pooled and continue growing

until the following week. The system usually occupies one worker, but once per week at the

grading time, an additional worker helps for half a day.The production data used in the model were obtained from January 2002 to May 2003.

The mean batch size was 4278 (289 S.D.) fingerlings. Mean initial body weight was80.9 29 g at entry. Body weight increased to 373 g within 137.35 21.4 days (Table 5).The target weight for market is 0.5 kg. Fish growth was determined periodically by 94

weight determinations over the experimental period. Mean fish weight at any given time

was characterized by the empirical equation:

Fish body weight g 0:175 t1:49 (1)

where t is fish age, measured in days. Curve fitting was performed with the MATLAB

software (Anon., 2001). The R2 obtained was 0.95 and, therefore, Eq. (1) was incorporatedinto the simulation model. Eq. (1) can be differentiated in order to obtain the fish growth

rate (g/day) at any given time, giving:

Fish growth rate g=day 0:2607 t0:49 (2)

Fitting of the curve described by Eq. (1) to the raw data is presented in Fig. 1. Growth

rate is a primary variable in the model, since it is on one hand related to water quality and

temperature, fish health and more aspects offish culture, and on the other hand the system

designparameters such as biomass balance, stocking density, feed, ammonia removal

and oxygen demandalso depends on growth rate. Besides, growth rate can be easily

measured in a commercial farm and consequently the model can be calibrated accordingly.

Step-wise regression and cross correlation analysis were used to quantify the effects of

five independent variables on the fish growth rate (Yg/day) with an R2 of 0.98:

Y 2:1081 0:0073X1 0:0078X2 1:374 105X3 0:01446X4

0:005X5 0:11781X6 (3)


Fig. 1. Fish growth measured in the experimental RAS and curve-fitting to 0.175 t1.49.


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where the independent variables were: X1 is final fish body weight (g) at market time, X2 is

initial fish body weight (g) when the fingerlings enter the RAS,X3 is batch size, i.e., number

offingerings entering the RAS,X4 is number of days in the RAS,X5 is season index (winter,

summer, autumn or spring), and X6 is mortality rate. The cross-correlation matrix (Table 2)

showed that all the independent variables had significant effects upon fish growth rate. By

definition,

YX1 X2

X4(4)

Applying different regression coefficients for only these three variables yielded

(R2

= 0.98):

Y 2:0403 0:0073X1 0:0078X2 0:01439X4: (5)

Final body weight (500 g) was a managerial parameter determined by demand in the

market. Initial body weight is influenced by seasonal availability; fingerings are produced

in an outside open pond, not an RAS. The number of days of growth used in the model was

based on the known character of this species and historic records from the farm.

The success of RAS depends not only on production variables but also on economic

variables. The incorporation of the economic variables and processes into the simulation

model enables RAS managers to quantify effects of changes in design or operation more

effectively. Costs and market prices, and returns on investment are presented in Tables 3and 4, respectively.

2.3. Development of the model

2.3.1. Modeling approach, level of detail and process logic

The RAS system was broken down into modules whose interactions produce the

systems behavior. Modules included culture tanks or raceways, filters, channels

connecting tanks, feed storage, waste storage, quarantine facility, marketing tank,

hatchery tanks, and gas transfer facilities. Additional components can be added to the

model as needed. The model is process-oriented, i.e., the flow of fish through the RASfacilities is tracked, and the processes through which these entities progress through the

RAS are represented graphically. Batches offish are the primary entities in the model, and


Table 2

Cross-correlation matrix: the impact of fish-related variables on growth ratea in simulation model

Y X1 X2 X3 X4 X5 X6

Y 1 0.64 0.14 0.60 0.49 0.34 0.43X1 0.64 1 0.45 0.60 0.14 0.27 0.32X2 0.14 0.45 1 0.26 0.33 0.39 0.23X3 0.60 0.60 0.26 1 0.15 0.47 0.29X4 0.49 0.14 0.33 0.15 1 0.36 0.30X5 0.34 0.27 0.39 0.47 0.36 1 0.42X6 0.43 0.32 0.23 0.29 0.30 0.42 1

a Variables: Y(g/day) = fish growth rate;X1: final fish body weight (g) at market;X2: initial fish body weight (g)

when fingerlings enter RAS;X3: batch size, number offingerings at entering the RAS;X4: number of days in RAS;

X5: season index (spring, summer, autumn or winter); and X6: mortality rate.


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each batch has seven unique attributes: species, number of fish, growth curve, batch

uniformity, initial body weight on entering the system, most recent tank entry time, and

target weight. When necessary, it is possible to add details regarding fish behavior,

mortality, and sensitivity to density.Logic modules mimic the instructions and logic control that are intrinsic to RAS

management (e.g., batch size = 5000 fish, market weight = 0.5 kg, delay before

grading = 3 days, on average, system carrying capacity = 55 kg per m3, pool batches of

fish from two tanks just before marketing). A meta-model of the inputoutput (I/O) data of

simulation enables a global optimum to be found and the integrated design methodology to

be completed. A detailed description of the meta-model technique was presented by

Halachmi et al. (2002).

2.3.2. Model variables and equations

The RAS simulation assesses performance in terms of yearly turnover (t/year, fish/year,

and kg m3 year1), stocking density, tank or raceway utilization, biomass in process in the

entire system and biomass in each cultivation unit, i.e., the so-called simulation responses.

The responses are calculated for as long as 50 years, and the simulated time-step is one day.

Factors can be changed between runs (e.g., system carrying capacity, fish species, reference

growth curve, facility allocation, and target weight for market) and between batches (e.g.,


Table 3

Variable costs and market prices

Transportation and marketing 0.135 $a/kg biomass

Insurance 0.090 $/kg biomassFingerlingsb 2.252 $/kg biomass

Feedc (conversion factor 1.21.6) 0.338 $/kg feed

Water (450 m3, replacement 7%/day) 11260 $/year

Oxygend 0.225 $/kg (Oxygen)

Energy (electricity) 15765 $/year

Laboure 90.090 $/day

Interestf 42792 $/year

Income (market price) 2.703 $/kg biomass

Since the system is 12 years old, the interest for the equipment was fully covered within 10 years. See Table 4

below.a Exchange rate: 1 USD (US Dollar) = 4.44 NIS (New Israeli Shekel, source: Bank of Israel, 8 December

2003).b Fingerling cost per year ($/year) is 2.252 ($/kg) number of fishes per year initial body weight (kg).c Average yearly feed cost is $0.338/kg turnover (kg/year) conversion factor. Conversion factor = 1.4.d One kilogram oxygen is provided to 1 kg of biomass. Therefore, yearly oxygen cost is 225 $/t (biomass).e Labour cost is $90/day 365day/year = 32850 $/year (constant).f Interest, $42792/year (constant), is the price paid for use of credit. Only building cost is taken into account.

Table 4

Return on investment (ROI)

Amount paid ($) Yearly interest Years Yearly return ($)Building 450450 7.0% 20 %42792Equipment 450450 7.0% 10 64134


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batch-size and time delay before grading). Animation represents the system graphically,

and reports the results as a set of statistics. The statistics track the state of the RAS during

the simulation, and records changes that affect RAS efficiency. The control variables are

listed below:

Fish-related variables System-related variables

1. Initial body weight 6. Time between successive

batch arrivals

2. Growth curve (weight gain in each

culture unit, based on stocking density,

fish species, local conditions,

water quality, feed, etc.)

7. Number of fish per batch

3. Growth period in each culture unit 8. Utilization of each culture unit4. Target weight in each culture unit 9. Grading time delay as a

result of labor constraints

5. Mortality 10. Actual growing days

11. Number of tanks and their

capacity (facility allocation)

Aspects of management regime that were analysed are: (1) time between fish batch

arrival (simulated range of 414 days), (2) purchase of smaller or larger fingerlings

(simulated range of 3580 g), (3) changes of batch size (simulated range of 35007000individuals), (4) variation of the growth curve between 2.4 g/day and 2.9 g/day in the 1st

phase and between 3.1 and 3.6 g/day in the 2nd phase, (5) addition of four to eight more

culture units, while keeping the same filter, and (6) choice of aquaculture systems (square

tank systems or big round tank systems; the simulated volume of a small tank at the first

growth phase varied between 17 and 20 m3, and the volume of a large tank for the second

phase between 34 and 40 m3).

The initial fish weight increment was 10 g, the batch size increment was 500 fish, and

the weight-gain step was 0.1 g/day, which resulted in 448,000 possible input combinations.

Therefore, the first step was to select the combination of parameters to be simulated in the

development of the model, i.e., to determine the design of experiment (DOE) (Banks,1998). The goal was to gain insight into the simulation model behavior while observing

relatively few factor combinations. In the first step of DOE, the feasible range for each

parameter (boundary) was determined through exploratory analysis with the newly

developed simulation model, with one factor being changed at a time. After fixing the

factor boundaries, we used a D-optimal design (Anon., 2001) in the second step; this

improves a starting design by making incremental changes to its elements. In the

coordinate exchange algorithm, the increments are the individual elements of the design

matrix (cordexch function in MATLAB, Anon., 2001) Using DOE, the number of

simulation runs needed was set to 3880.

Without animation (i.e., fish swimming on the computer screen while the user dialogboxes are updated), a simulation run of one combination took only 2.8 s on a 1.2 GHz PC.

Regression analysis of the inputoutput (I/O) data of the simulation gave the meta-model



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(Eq. (6)), defined as a model of the underlying simulation experiments, i.e., an

approximation of the simulations I/O transformation.

Turnover t=year 0:155 batch size

middle weight initial weight

weight gain at phase 1

number of small tanks5:818

0BBBBBBB@

1CCCCCCCA

(6)

where middle weight is the fish weight coming out of phase 1.

And since:

Number of fish per year batch size number of small tankstime between successive batch arrival

batch size number of small tanks

365 weight gain at phase 1

middle weight initial body weight(7)

Economics is an integral part of the model; each simulated scenario has an associated

cost. The yearly profit in the model is given by:

P p Tf F iBWfc Tff o T EL tr T i w (8)

where P is the yearly profit ($/year), p is the fish price ex factory ($/ton), T is the yearly

turnover (ton/year), f is the cost of the fingerlings ($/kg biomass), F is the number of fish

purchased per year; iBW is the initial body weight upon entry into the RAS (kg), fc is the

feed cost ($/ton),ff is the feed conversion factor, o is the cost of oxygen ($/ton), Eis the cost

of the energy for heating the water and electricity ($/year), L is the cost of the labor ($/

year), tris the transportation cost ($/ton), i is the interestthe price paid for use of credit ($/

year), and w is the cost of the water ($/year). Economic values are taken from Table 3. This

leads to the following constrained non-linear optimisation problems. Under stocking

density constraints of up to 55 kg m3 in phase 1 and 65 kg m3 in phase 2, we wish to

maximize yearly profit (P from Eq. (8) above):

max: P (9)

subjected to the following constraints:

Stocking density in phase 1 < 55 kg m3 (Constraint 1)Stocking density in phase 2 < 65 kg m3 (Constraint 2)3500 < batch size < 7000 (Constraints 3 and 4)35 g < initial body weight < 80 g (Constraints 5 and 6)2.4 g/day < weight gain in phase 1 < 2.9 g/day (Constraints 7 and 8)10 < number of small or large tanks < 14 (Constraints 9 and 10)17 m3 < small tank volume < 34 m3 (Constraints 11 and 12)34 m3 < large tank volume < 40 m3 (Constraints 13 and 14)



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The function (Eq. (9)) is convex and the constraints are linear functions; consequently,

KuhnTucker conditions are necessary and sufficient for global optimality. MATLAB uses

a sequential quadratic programming (SQP) method. In this method, a quadratic

programming (QP) sub-problem is solved at each iteration (Coleman et al., 1999).

2.3.3. Model verification and validation

The perfect model would be the real system itself (by definition, any model is a

simplification of reality, Kleijnen, 1995a). The modellers task, then, is to produce a

simplified, yet valid abstraction of the RAS of interest. In practice, the model should be

good enough to achieve the goals of model (Kleijnen, 1995b; Law, 1990a). We performed

full black-box validation (Pidd, 1992). Our working assumptions were: (1) The main

sources of validation information comprised the farm records, the owner of the given RAS,

and the operating data for the existing facilities; (2) It may be possible to test parts of the

model against parts of existing systems (white-box validation; see Pidd, 1992); and (3) It

is the modellers responsibility to ensure that the statistical distributions employed are

adequate for the intended RAS.

A number of steps were taken to verify that the model was a reasonable representation of

reality: (1) The RAS simulation repeatedly passed the face validity test; that is, several

people familiar with the farm found that the models animated display mimicked that of the

real system. (2) The RAS simulation was compared with real RAS measurements, using

familiar validation techniques: the correlated inspection approach, residual errors

examination, repeatability test, problem of initial transient, and time plot of important

variables. (3) Several consistency checks were performed, such as making incrementalincreases in the batch size (number of fish) and seeing that they led to reasonable and

steadily increasing values for the average yearly turnover. (4) The RAS simulation was

subjected to extreme condition tests, such as setting an extremely short time between batch

arrivals. Under such conditions, the RAS simulation still behaved reasonably. (5) The

model was implemented with the ARENA standard edition, a well-known OO language,

which contains pre-programmed modules that should reduce the likelihood of

programming error (Kelton et al., 1998). (6) The models operation was checked

interactively by means of ARENAs debugging capabilities, in order to examine the

attributes of any entity and the value of any variable during a run.

2.3.4. User interface and system animation

The display on the user-friendly interface (the computer screen) is designed to be

easily understood by the final users of the model. The same display incorporates direct

observations into the animated RAS and simultaneous examination of summary statistics.

In this way, the mathematical model is transformed into a communicative form, suitable for

use by non-experts. For instance, the proposed RAS layout configuration is animated in

Fig. 5. By simply looking at the animated fish circulating among animated cultivation

units, we can see whether there is enough capacity and enough raceways in that particular

RAS.

The simulation speed can be changed from very slow to allow detailed examination ofthe execution of control rules, to very fast for monitoring the development of production

bottlenecks. At maximum speed, with live animation, this model can simulate 1 year of



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activity in approximately 1 min; without live animation, 50 years can be simulated in less

than 2.8 s.

The basic mathematical model would lack the easily understood communication with the

user. This user-friendly interface solves these problems as well as making the mathematicalmodel (integrating fish behavior, RAS routines, feeding and grading procedures,

management practices, scale drawing, etc.) into a practical tool for designing a RAS. For

example,congestion during a particular time might be caused by management practices. This

congestion influences the physical design of each section in the RAS, and awareness of it in

advance could suggest a different management practice. Such congestion is not readily

identifiable from the reports, but is very apparent from the visual output of the model.

3. Results

3.1. Model validation

The result of this study is the simulation methodology itself. Validation of the

simulation model was pursued using several well-established approaches.

3.1.1. The correlated inspection approach

The system and the model were compared by running the model with historical system

input data, rather than samples from probability distributions, and then comparing the

outputs of the model and the system. Thus, the system and the model experience exactly thesame random variability of input, which should result in a statistically more valid

comparison (Law and Kelton, 1991: correlated inspection approach; Kleijnen et al.,

1998: trace-driven simulation). Table 5 compares real and model output data from 40 fish

batches by using the paired-tapproach, based on a fixed-sample-size procedure (Law and

Kelton, 1991). It can be seen (Table 5) that the average batch size measured in this

experiment is 4278 g and the average mortality rate is 3.7% (= 0.037). It can be seen that

when the model experienced the same random variability of inputs, the simulation

responses match the measured real system. Formally the paired-t approach quantifies the

distance of the average and STD of the simulation from reality; since in our case the

distance is zero and zero falls within the t-test interval, we can claim with 95% confidencethat model responses did not differ statistically from reality.

3.1.2. The problem of the initial transient

In the simulation literature, this problem is called the start-up problem or initial-data

deletion. The idea is to disregard a certain number of observations from the beginning of a

run. One simple and effective technique to determine the warm-up period is graphical

analysis. In Fig. 2, we display the time variation of the stocking density in the raceways.

Supply batches of 6500 fish arrived every 6 days, initial BW was 70.0 g, growth rate in

small raceways was 3.01 g/day (60 days in each growth phase); the simulated system

comprised 10 small and 10 large raceways which yielded 198 t/year (so-called proposedmanagement strategy A). In this case, at the beginning of the first year (t= 0), all the

raceways were empty and they were gradually filled, according to the availability of



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Table 5

Trace-driven simulation and validation

Batch

number

Batch

size

Initial

BWa

(g)

Last

BWb

(g)

Intervalc

(Days)

Mortality

rate

Growing time (days)

Small raceway Large raceway

Real Simulation Real Simulation

1 4000 80 418 119 0.000 91 91 28 28

2 3770 82 410 133 0.000 91 91 42 42

3 4000 78 411 136 0.000 87 87 49 49

4 4000 75 430 147 0.000 84 84 63 63

5 4000 85 455 145 0.038 89 89 56 56

6 4000 101 398 154 0.100 91 91 63 63

8 4050 106 427 133 0.000 84 84 49 49

9 4500 37 218 91 0.016 56 56 35 35

10 4500 41 345 119 0.018 77 77 42 42

11 4500 41 329 162 0.058 77 77 85 8512 4000 79 371 112 0.100 97 97 15 15

13 3850 96 406 133 0.000 81 81 52 52

14 4000 80 454 147 0.000 91 91 56 56

15 4100 56 344 112 0.000 90 90 22 22

16 4000 98 437 124 0.000 82 82 42 42

17 4200 92 331 133 0.067 63 63 70 70

18 4525 83 374 155 0.021 64 64 91 91

20 4500 65 281 112 0.018 84 84 28 28

21 4800 37 303 152 0.055 117 117 35 35

22 4500 26 350 168 0.061 140 140 28 28

23 4230 49 345 166 0.051 95 95 71 71

24 4500 32 348 203 0.050 168 168 35 35

25 4530 44 311 161 0.236 105 105 56 56

26 4480 70 379 127 0.069 85 85 42 42

27 4400 65 407 147 0.055 98 98 49 49

29 4000 82 421 154 0.000 112 112 42 42

30 4680 95 333 134 0.026 92 92 42 42

31 4640 88 346 126 0.034 91 91 35 35

32 4440 95 375 154 0.050 133 133 21 21

33 4100 127 327 119 0.028 58 58 61 61

34 4470 107 347 159 0.044 152 152 7 7

35 4700 131 368 131 0.029 82 82 49 49

36 4270 108 340 117 0.061 96 96 21 2137 4820 116 388 119 0.027 82 82 37 37

38 4135 119 456 140 0.028 96 96 44 44

39 4200 123 416 124 0.039 40 40 84 84

40 3900 105 402 114 0.026 56 56 58 58

Average 4278 80.9 373 137.35 0.037 91 91 46 46

STD 289 29 52 21.4 0.043 26 26 19 19

Observations from 40 typical fish batches-real system vs. simulation.a Initial BW: body weight (g) when the fish enter the RAS (approximately 50 days of age).b Last BW: body weight (g) at the last sampling before grading and pooling of large fish from two successive

batches.c Interval: time between initial BW and last BW samplings.


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fingerlings and of an empty raceway. It was found (Fig. 2) that the model had to run for a

simulated time of at least 2 years to achieve meaningful results. This took about 1 s of real

time.

In light of the warm-up period (2 years) suggested in Fig. 2, in this study, samples were

taken from simulated years 49 to 50, well after the warm-up period. By this time, the

influence of the initial conditions had disappeared and the system could be considered as

steady-state, enabling each run to be treated as an independent replication.

3.1.3. Time plots of important variables

Since the behavior of RAS varies with time, we needed an indication of how system

performance changes dynamically over time. Animation provides insight into short-term

dynamic behavior, but does not give an easily interpreted record of system performance

over the entire length of the simulation. A time plot can bridge the gap; for example, a plot

of stocking biomass against time (Fig. 3) provides information on which cultivation unit

has sufficient carrying capacity to accommodate the demands of a busy time. It was

observed that the cultivation unit has activity peaks every 60 days. This was attributed to

the farm routine of introducing a new batch every 6 days while operating 10 small racewaysand 10 large raceways. A small raceway (number 7 presented in Fig. 3) reaches its

maximum holding (1625-kg capacity) every 60 days and is immediately emptied to zero

holding until a new batch, weighing 455 kg (6500 fish 70 g), enters the system. A largeraceway (number 17 presented in Fig. 3) receives 1625 kg of biomass from a small raceway

and reaches its maximum holding (3250-kg capacity) also within 60 days. An empty unit

(zero biomass) retains that status for 1 day because of cleaning and grading activities.

Although each cultivation unit has a large variance (small tank range 01625 kg; large tank

range 03250 kg), a balancing management strategy potentially could result in a

synchronized system. Fig. 4 plots the biomass variable in the entire system at the same

period as shown for sampling units 7 and 17 in Fig. 3 (year 9). It can be observed in Fig. 4that stabilized biomass can be achieved, with 10 1 t in the small tanks and 23 2 t in thelarge tanks, which results in 33 3 t in the entire system. The bio-filter in the RAS under


Fig. 2. The problem of the initial transient; stocking density (kg/m3) in raceways 110 and 1120.


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study can handle daily variations up to 10 t without any problem. Hence, time plotsprovided an easy means to understand the long-term dynamic behavior of the system.

3.2. Case studies

The possibilities of interactive creative design are numerous, even for a single RAS.

Therefore, in order to illustrate the workings of the modeling methodology, its capability,and its scope within a given practical situation, three simple case studies were explored

using the infrastructure, management regime, and production data for an existing RAS

facility, Kibbutz Sde Eliahu.

Optimal RAS1. Keeping the existing 20 tanks, we estimated the optimal solution of:

production of 178 t/yr, batch size of 6518 fish arriving every 6 days, and


Fig. 3. Time plots offish biomass (kg) in raceways 7 and 17.

Fig. 4. Time plots offish biomass (t) in process: raceways 110, 1120, and the entire system.


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weight gain in phase 1 of 2.9 g/day (constraint 7). The active constraints

were: stocking density in phase 1 = 55 kg m3, initial body

weight = 80 g, and growth rate in phase 1 = 2.9 g/day. We noted that

optimal RAS 1 differed from the current situation in the frequency ofbuying fingerlings and the batch size.

Optimal RAS2. Allocating more tanks resulted in an optimal solution of: production of

265 ton/year, batch size of 7000 fish arriving every 5 days, weight gain in

phase 1 of 2.9 g/day, and 14 small tanks of 17 m3 each and 10.74 large

tanks of 35.40 m3, which we rounded upward (11 large tanks of 36 m3

each). The active constraints were: batch size = 7000, initial body weight

of 80 g, growth rate of 2.9 g/day, and number of small tanks = 14.

Optimal RAS3. We noted that the production bottleneck appeared to be fish growth rate.

Raising of fish growth rate from 2.9 g/day to 3.3 g/day resulted in an

optimal solution of: production of 304 t/year, batch size of 7000 fisharriving every 4 days, weight gain in phase 1 of 3.3 g/day, 14 small tanks

of 17 m3 each, and 10 large tanks of 34 m3 each. The active constraints

were: batch size = 7000, initial body weight of 80 g, and number of small

tanks = 14.

The above solutionsoptimal RASs 13were the results of the meta-model, i.e., from

solving Eq. (9), which we fine-tuned by using simulation (Table 6). The simulation of the

current situation (scenario 0, Table 6) resulted in an output of 72.24 t/year and losses of

$2164, which indeed is the current situation. However, raising the average growth rate from2.4 g/day to 3.2 g/day in the large raceways resulted in an output of 94.29 t/year and a profit

of $28,072 per year (scenario 1 in Table 6). Scenario 2 is the simulated mathematical solution

for RAS 1. This solution did not meet the design criteria of having an average stocking

density


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by farm routines (e.g., grading frequency, feeding via automated dispensers or manually,

water quality, nutrition, and environmental and management practices) that must be taken

into account when designing the layout of a RAS system. Theoretically, it is easy to design

a RAS that always has enough spacesimply make it too bigbut this is clearly a waste of

money. Optimal design balances the cost of inadequate capacity against the cost of excess

capacity. Since a RAS is a discrete-event dynamic system, such a balance will vary overtime, depending on equipment, fish growth, feeding and feed composition, farm

management practices, and other factors.


Fig. 5. Simulation of proposed management strategy A (batch size = 6500 fish arriving every 6 days, initialBW = 0.07 g, growth rate in small raceways = 3.01 g/day, 10 small and 10 large raceways) on 10 May 2006. The

clock at the top of picture shows the simulated time. To the left of the raceways, a fish icon represents an occupied

unit, i.e., a raceway full of fish (a batch). A number near a raceway is the current biomass value (kg) in that

raceway, while the graph to the left of the raceway tracks historical values during the preceding year. A schematic

layout drawing of the RAS is shown at the center of the computer screen. During the simulation run, all fish

batches are shown moving as in real life, only they were sped up. Vivid colors indicate the state of a fish batch: a

blue fish is in a growth mode, occupying a cultivation unit; a red green fish is in a transition state, swimming

between facilities (grading) or idle; a fish in a queue, waiting for an unavailable raceway, is red. On the left side of

the screen are current values of the run parameters: time between batch arrivals (6 days), grading delay (0 days),

batch size (6500 fish), initial body weight (0.070 kg), final weight at a each growing phase (kg) and weight gain

(kg/day). The graphs of stocking density, utilization (0.9), and biomass in process (32 t) are located at the bottom,

together with production measures: turnover (198 t/year) and 396,500 fish/year. A number near a graph is the

current value. The associated economic values are at the right side of the screen, accessible through a standard MS-

Windows functions, such as zooming in and out, or enlarging and moving a window.


17/22

Table 6

Selected simulation responses

Scenario Arrival interval

(days)

Batch size Initial BW (g) Phase 1 P

Growth,

days

Growth rate

(g/day)

Number of

small tanks

G

d

0 8 4278 80 79.9 2.1 10 1

1 8 4278 80 79.9 2.1 10 7

2 RAS 1 6 6500 80 58.6 2.9 10 5

3 7 6500 70 62.1 2.9 10 6

4 RAS 2 5 7000 80 58.6 2.9 14 4

5 RAS 3 4 7000 70 54.5 3.3 14 4

Stocking density (kg/m3) Utilization

Small tanks Large tanks Small tanks Large

0 41 (1.7) 47 (1.23) 0.98 (0.03) 0.99

1 41.04 (1.70) 46.44 (1.72) 0.99 0.992 RAS 1 61.19 (3.17) 69.23 (3.5) 0.97 0.97

3 54.78 (2.46) 63.79 (2.7) 0.89 0.89

4 RAS 2 52.73 (3.35) 64.46 (2.9) 0.61 0.79

5 RAS 3 57.12 (4.61) 71.50 (3.5) 0.69 0.87

Income ($/year) Costs ($a/year)

Fingerling Feed Oxygen Energy Labor Trans and Insb

0 201,077 26,810 35,189 21,783 15,766 32,883 16,757

1 261,550 34,873 45,771 28,335 15,766 32,883 21,796

2 RAS 1 530,921 70,789 92,911 57,516 15,766 32,883 44,243

3 455,025 53,086 79,629 49,294 15,766 32,883 37,919 4 RAS 2 686,605 91,547 120,156 74,382 15,766 32,883 57,217

5 RAS 3 858,541 100,163 150,245 93,009 15,766 32,883 71,545

a USD (US Dollar) = 4.44 NIS (New Israeli Shekel, source: Bank of Israel 8-Dec-03).b Trans & Ins: transportation and insurance ($/year).


18/22

The simplest type of design model is a scale drawing of the building. However, a scale

model is static; it cannot show how the various factors interact dynamically (Pidd, 1992).

Sometimes, mathematical models can solve a layout problem (Pidd, 1989). These models

apply techniques such as branch-and-bound, dynamic programming, queuing network,Markov chains or graph theorya source of easy-to-formulate but not so easy-to-solve

objective functions. While small (sometimes artificial) problems of finding a perfect

layout or routine can be solved by these techniques, large realistic problems often remain

intractable. Mathematical modeling has led to the development of spreadsheets aimed at

determining whether given production-management systems can prove profitable (Mozes

et al., 2001, 2002; Spradlin et al., 2000; Huntley et al., 2002), and of mass-balance

equations designed to estimate carrying capacity and required flow rates and bio-filter sizes

(Losordo and Hobbs, 2000). However, such simplifying equations need to be well

elaborated and validated on-site (Tomer and Wheaton, 1996) before they can credibly

support decisions regarding investment of the millions of dollars needed for construction

and management of large-scale commercial RAS facilities.

Simulation techniques offer a way of overcoming these disadvantages. Computer

simulation does not require the same degree of simplification as mathematical modeling.

The strength of simulation is its capability to deal with situations whose complexity

is too great for the mathematical approaches to handle. Simulation is applied in many

areas because of its flexibility, simplicity and realism (Kleijnen and Standridge, 1988).

In our context, it allows realistic modeling of the RAS, including the use of animation,

which provides a more natural approach for interfacing with the farmers expertise, and

allows introduction of all the factors that the farmer would like to integrate into hismodel.

The regression equations (Eqs. (3)(5)) are in agreement with the form of the equation

previously reported by Shnel et al. (2002), also regarding rearing of tilapia in RAS in the

Jordan Valley. However, the average growth rate was higher in the Sde Eliahus RAS, 2.4 g/

day compared with 1.4 g/day reported by Shnel et al. (2002). We did not find any additional

reports concerning the growth rate of tilapia under hot climate conditions as in Israel.

4.2. Simulation results

In practice, there exists a variety of RASs and, moreover, farmers may assume differentscenarios and select different design specifications based on different associated costs.

Hence, our contribution is the methodology that we developed in this study. Given the

conditions facing a real aquaculture enterprise, three optimal facility allocations were

determined. These examples demonstrated the models capabilities in the context of data

collected from the Sde Eliahu RAS. More data concerning fish growth curves under a

variety of conditions, economic risk factors, and additional design alternatives should be

introduced in order to further develop science-based, statistically valid models. That is, the

optimal solutions found in this study were appropriate for a specific RAS, but the

methodology developed in this research is universally applicable; the parameters can be

adjusted to any farm, site, or fish species.A fish growth-based simulation model, together with meta-model and optimisation

techniques, provided a useful integrated design methodology for RAS. The design focused



19/22

on optimal facility allocation, as related to fish batch size, stocking density, weight gain,

and management practices. The meta-model allowed a global optimum to be found for a

given set of boundary conditions. This use of the new design methodology and rigid design

specifications, formulated in terms of mathematical constraints, suggested that if thisdesign methodology had been developed previously, and if it had been applied prior to

installation, then the savings in building costs could have been significant while achieving

the same level of system performance and maintaining animal health and welfare (in terms

of stocking density).

Although the models analytical benefits are considerable, one other important

benefit is that the farmer gains the assurancebefore buildingthat the proposed

design will actually meet his specified requirements. Further advantages of the RAS

simulation include: (1) animal welfare: simulation allows experiments to be performed

without doing any harm to animals or to facilities. For example, one objective of a

simulation study may be to estimate the effects of extreme conditions, i.e., simulated

fish suffer no damage when they run out of oxygen or are flooded with ammonia in an

overloaded virtual RAS. (2) Lower costs: although simulation may require skilled

manpower, physical construction and refitting of different layouts are usually more

expensive. (3) Less time is needed to carry out an experiment, because it is often

possible to simulate weeks, months, or years in just a few seconds of computer time.

Consequently, a long-range strategy may be tested in a relatively short time. (4) Ease of

replication: whereas a real RAS rarely allows exact replication of experiments,

simulation does. (5) Simulation experiments allow factors that are uncontrollable in

reality to be controlled. This helps to focus our considerations more sharply. (6)Simulation yields a system-wide view of the effects of local changes. While the impact

of a change of a system component or process on the performance of that component

may be predicted easily, it might prove difficult to predict the impact of this change on

the performance of the overall system. For example, after increasing growth rate by

0.1 g/day with a variance of 0.3 g/day, it is easy to calculate the range of days of growth

needed to reach market size. However, it is more difficult to estimate the effect of

changes in standing biomass at any given time on the entire system, particularly on the

bio-filter. Similarly, changing a few tanks from 17 m3 to 25 m3, it is easy to predict the

new peak stocking density in these specific tanks, but estimating the effect on the

productivity of the entire RAS is difficult.Discrete-event simulation has some drawbacks for RAS modelling, implying the

following needs: (1) A new type of data collection is needed to deal with RAS behavior and

facility usage; it should not depend on any specific layout. Also, sophisticated statistical

tools are needed to study the stochastic nature of facility usage (e.g. Arsham, 1998). (2)

Heavy computations are required to obtain data analysis and visual simulation of many fish

batches. (3) Close collaboration is needed between aquaculture researchers and computer

scientists, who are usually not located in the same laboratory or RAS. This is necessary for

both model design and validation. Complex programming problems need to be solved. The

main limitation of simulation lies in its ad hoc character: we observe the simulation

responses only for the selected input combinations, i.e., there is no proof of the optimalityof a solution. This is why our methodology combines analytical/mathematical optimisation

(the meta-model).



20/22

5. Conclusions

The model combines simulation and optimization to overcome the difficulties that

characterize the RAS system. Simulation experiments allow fish behavior, equipment, andlayouts to be evaluated jointly. Hence, an initial design can be fine-tuned to produce a

balanced system, i.e., an optimal layout specific to a given RAS, within a reasonable time. By

implementing the suggested methodology, step-by-step, we designed an optimal RAS that

met both economic and stocking density needs. Application of the new methodology and

rigid specifications for 2025 raceways in a specific RAS in the simulation led to the

following findings: (1) The farm will build five more raceways in addition to the existing 20.

(2) The batch size will be 6500 fish arriving every 6, 5, or 4 days depending on the growth rate

achieved. (3) To support its peak loading, a small raceway should have a capacity of 1625 kg,

and a large one should carry up to 3250 kg. (4) The existing RAS design, with improved

management, can achieve the desired production. (5) The animation allowed a range of

personnel unfamiliar with RASs to appreciate how the new RAS would operate.

Additional data relevant to different species, water quality, feed components, cultivation

units, stocking density, etc., would make the model applicable in a wider range of cases.

The model is a discrete-event as well as continuous-process simulation. Clearly, the

programming of combined continuous and discrete event processes is a challenge

(Kleijnen and van Groenendaal, 1992) programmed in order to illustrate the capability to

deal with both in parallel. In the future, as needed, environmental impacts and other

continuous processes can be modeled in the same way. The economic part of the model is a

crucial part of the simulation. It is advised, in further research, to elaborate the ecumenicalaspects in the direction of developing an economical risk analysis model.

It would seem advisable to develop commercial software to enable persons with no

simulation or programming expertise to conduct simulation experiments.

Acknowledgements

The authors thank Michal Yanai, Shai Tabibian, and Noam Barak supervised by Prof.

Moshe Caspi from Ben-Gurion University for analyzing the data, their discussions on the

selection of variables describing fish growth rate, and for critical comments on themethodology. Special thanks are due to Mr. Ron Una, the manager of Sde Eliahus RAS, for

collecting the data and useful advice. E.M.H. was supported by the Commonwealth of

Virginia Aquaculture Initiative and by the USDACSREES Hatch Program.

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