Developing a decision support system for sustainable cage aquaculture

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Environmental Modelling & Software 24 (2009) 694–702

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Environmental Modelling & Software

journal homepage: www.elsevier .com/locate/envsoft

Developing a decision support system for sustainable cage aquaculture

Halmar Halide a,b,*, A. Stigebrandt c, M. Rehbein a, A.D. McKinnon a

a Australian Institute of Marine Science, PMB3, MC, Townsville 4810, Australiab Physics Department, Hasanuddin University, Jl. Perintis Kemerdekaan Km. 10, 90245 Makassar, Sulawesi Selatan, Indonesiac Earth Sciences Centre/Oceanography, University of Gothenburg, P.O. Box 460, SE-S-40530 Gothenburg, Sweden

a r t i c l e i n f o

Article history:Received 12 March 2008Received in revised form23 October 2008Accepted 24 October 2008Available online 5 December 2008

Keywords:Decision supportSustainable cage aquaculturesSite selectionHolding capacityEconomic appraisal

* Corresponding author. Physics Department, HasaKemerdekaan Km. 10, 90245 Makassar, Sulawesi Sela433803; fax: þ62 411 585188.

E-mail addresses: [email protected] (H. Halide), [email protected] (M. Rehbein), d.mckinnon@aims

1364-8152/$ – see front matter � 2008 Elsevier Ltd.doi:10.1016/j.envsoft.2008.10.013

a b s t r a c t

A decision support system to assist cage aquaculture managers is presented. The system enablesmanagers to perform four essential tasks: (i) site classification, (ii) site selection, (iii) holding capacitydetermination, and (iv) economic appraisal of an aquaculture farm at a given site. Based on measure-ments of water and substrate qualities, hydrometeorology and socioeconomic factors, a cage aquaculturesite is classified into three categories – poor, medium, and good. With this information, the AHP(analytical hierarchy process) tool is used to evaluate the best site from several alternatives. A simplifiedversion of the Modelling-On growing-Monitoring (MOM), SMOM, is developed and applied to determinehow much fish can be grown on site without harming the environment. The simplified model has beencalibrated against MOM, compared with other carrying capacity models and validated with farm data. Abreak-even point–price and return on investment (ROI) are calculated using cage-holding density andvolume, mean fish weight at harvest, feed conversion ratio (FCR), survival rate of seed, costs of feed, seedand cages, the interest rate on borrowed funds and the fish price. All model components are integratedseamlessly into a user-friendly interface implemented in Java� called CADS_TOOL (Cage AquacultureDecision Support Tool). The program with a user’s guide is freely available.

� 2008 Elsevier Ltd. All rights reserved.

1. Introduction

Cage aquaculture is expanding worldwide, with the cage cultureof high value finfish the fastest growing sector (Tacon and Halwart,2007). Delgado et al. (2003) predict that fish consumption indeveloping countries will increase by 57%, from 62.7 million metrictons in 1997 to 98.6 million in 2020, and cage aquaculture isexpected to play a major role in meeting this demand (Tacon andHalwart, 2007). In Asia, over 95% of marine finfish aquaculture is incages, and production has steadily increased in the region, to reach1.7 million tons in 2004 (De Silva and Phillips, 2007). With suchrapid increase in sea cage aquaculture, there is an urgent need todevelop planning tools that can be applied to the predominatelytropical environments of Asia, so that the high level of productioncan be managed in an environmentally sustainable manner.

There are many forms of impact resulting from cage aquaculturethat could threaten its sustainability. For instance, the settling of

nuddin University, Jl. Perintistan, Indonesia. Tel.: þ62 411

[email protected] (A. Stigebrandt),.gov.au (A.D. McKinnon).

All rights reserved.

wastes of high organic content from uneaten feed and faecesfavours the growth of bacteria on the seabed underneath the cages.Decomposition of this organic material by bacteria consumesoxygen and can cause hypoxia in bottom waters and sediment(Aure and Stigebrandt, 1990; Nilsson and Rosenberg, 2000; Grayet al., 2002; Holmer et al., 2003). In addition, accumulation ofsulphides in the sediment pore water affects benthic organisms,which in turn, may cause the loss of fauna and seagrasses (Cancemiet al., 2003; Greve et al., 2003; Bongiorni et al., 2005; P-Martiniet al., 2006). Discharge of phosphorous and nitrogen compoundsfrom the farms might also change the nutrient ratio nearbyfavouring local algal blooms and eutrophication (Aure and Stige-brandt, 1990; Maldonado et al., 2005; Buschmann et al., 2006;Mente et al., 2006; Pitta et al., 2006; Sara, 2007). In the tropics,eutrophication originating from fish farms can threaten coralsurvival (Loya et al., 2004; Villanueva et al., 2006).

A broad range of aquaculture decision support systems are inexistence. Some of them have taken environmental impacts intoaccount, such as those for selecting and licensing aquaculturesites (Silvert, 1994a,b; Ervik et al., 1997; Stagnitti, 1997; Stagnittiand Austin, 1998; Hargrave, 2002; Stigebrandt et al., 2004;Moccia and Reid, 2007) and for planning nutrient removal(Vezzulli et al., 2006). Others are used for designing aquaculturefacilities (Ernst et al., 2000), managing hatchery production

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H. Halide et al. / Environmental Modelling & Software 24 (2009) 694–702 695

(Schulstad, 1997), forecasting aquaculture products (Xiaoshuanet al., 2005), facilitating aquaculture research and management(Bourke et al., 1993), and evaluating economic impact (Bolteet al., 2000).

In this study we develop a decision support tool for cageaquaculture. It covers various activities starting from classifyinga site, selecting the best site from several site alternatives, calcu-lating a sustainable holding density from a chosen site, and finallyperforming an economic appraisal of a site. Each activity is formedinto a specific module and all modules are integrated into a Javaprogram called CADS_TOOL (Cage Aquaculture Decision SupportTool).

2. Decision support modules

The decision support tool developed here is divided into fourmodules. The modules are (i) site classification; (ii) site selection;(iii) holding density; and (iv) economic appraisal. Each module isdescribed below.

2.1. Site classification

This module has the purpose of classifying a site into poor,medium and good suitability classes. Each class is determined bya set of criteria and sub-criteria adopted from the literature(NACA, 1989; Nilsson and Rosenberg, 1997; UNESCO, 2000;APEC/SEAFDEC, 2001; Håkanson and Boulion, 2001; Wildishet al., 2001; Frankic, 2003). The relative importance (RI) ofcriteria and sub-criteria can be preset. A questionnaire describedin Appendix A collects the necessary information from experts.In the example described in Table 1, ‘hydrometeorology’ is themost highly rated criterion, followed by ‘water quality’,‘substrate quality’, and ‘socioeconomic’ criteria. Similarly,amongst sub-criteria under ‘hydrometeorology’, ‘current’ is thehighest followed by ‘water depth’, and ‘significant wave height’sub-criteria.

The result of this module is shown in Fig. 1. The user types invalues measured from a site and the classification score for the siteis calculated. For this example, the site is mostly suitable (‘Good’)except for few parameters: secchi disk, wave height and proximityto market.

Table 1Criteria and sub-criteria values used to determine the suitability class of a site.

No Criteria and sub-criteria Classification RI

Good Medium Poor

1 Water quality 301.1 NH4 [mg/L] <0.5 0.5–1.0 >1.0 401.2 Dissolved oxygen (DO) [mg/L] 4–7 <4 351.3 Secchi depth [m] >4 2–4 <2 25

2 Substrate quality 202.1 Textures Sand Mud 302.2 Redox potential [mV] >(�200) <(�200) 452.3 Organic matter [%] 3–8 >8 25

3 Hydrometeorology 403.1 Current [cm/s] 5–20 <1; >50 503.2 Significant Wave height [m] <0.5 0.5–1.0 >1.0 103.3 Water depth [m] 10–30 <10; >30 40

4 Socioeconomic 104.1 Market Close Far 454.2 Infrastructure Available None 354.3 Regulations Available None 20

The relative importance RI (in percent) of criteria and sub-criteria is also presentedat the last column.

2.2. Site selection

The objective of this module is to determine a suitability scorefor each potential site. The scores are ‘good’, ‘medium’, and ‘poor’.The score is determined by applying a multi-criterion decisionanalysis tool called AHP (analytical hierarchy process) developed bySaaty (1980). This method has been previously applied to envi-ronmental studies (Karatzas et al., 2003; Thirumalaivasan et al.,2003; Uddameri, 2003; Moffett et al., 2005; Yatsalo et al., 2007;Ying et al., 2007; Bruggemann et al., 2008), engineering educationand designs (Drake, 1998; Wong and Li, 2008), project management(Al-Harbi, 2001), fisheries management (Mardle and Pascoe, 2004),aquaculture site selection (Salam et al., 2005), bridge construction(Salem and Miller, 2006), and contaminated sediment studies(Yatsalo et al., 2007). The AHP inputs RI scores given in Table 1 forcriteria and sub-criteria and outputs the weights of criteria/sub-criteria and the consistency ratio. This ratio fulfils the so calledtransitivity property, i.e. if criterion A is better than criterion B, andcriterion B is better than criterion C, then criterion A should bebetter than criterion C (Mardle and Pascoe, 2004). Saaty (1980)invented a heuristic rule to check this property (Saaty, 1980), i.e. theratio should not exceed 0.1. If it does, the value of the relativeimportance in Table 1 should be changed. The AHP procedures arefully described in Appendix B.

The AHP procedure is first performed to obtain a pair-wisematrix of the four criteria: water quality, substrate quality, hydro-meteorology and socioeconomic data. The results are shown inTable 2, and confirm the result that ‘hydrometeorology’ is the mostimportant criterion, i.e. it has the highest weight. The relativeimportance does not need to be changed since the consistency ratiois below 0.1.

The AHP procedure is also performed for all sub-criteria undereach criterion to obtain their sub-criteria weights. Total weight foreach sub-criterion is obtained by multiplying each of these sub-criteria weights by the weight of their respective criteria. Per-forming an AHP analysis for sub-criteria under the ‘water quality’criterion is taken as an example. Here the sub-criteria are NH4, DO,and secchi depth. The analysis obtains weights of 0.4934, 0.3108,and 0.1958, respectively. In this case, the consistency ratio is foundto be 0.0516. By multiplying these weights with that of waterquality of 0.2683 as in Table 2, the final weights for these sub-criteria are found to be 0.1413, 0.0890, and 0.0561, respectively.Final weights of all sub-criteria are presented in Table 3. The totalweight is found to be 1, and the first three important variables arecurrent, water depth and NH4.

Now, we are in a position to determine the score of eachpotential site. The total score for each site is calculated by multi-plying the final weight and suitability class for each sub-criterionand adding the results. The suitability class for the site is auto-matically entered from the Site Classification tab. Fig. 2 shows theoverall result, with the site scored as of ‘medium’ suitability.

2.3. Holding density

The goal of this module is to calculate the maximum permissiblefish biomass in a cage. Given a set of environmental conditions,feeding regimes, and sea cage arrangements, what monthlymaximum production of fish can be sustained? A solution to thisquestion is provided by the MOM (Modelling-On growing-Moni-toring) method developed by Ervik et al. (1997), Hansen et al.(2001), and Stigebrandt et al. (2004). The original version of theMOM model needs 28 inputs. We ran 100 simulations in which wevaried each of these inputs as depicted in Table 4 to calculateholding density, i.e. holding capacity divided by cage volume. Astepwise multivariate regression was then performed to select themost pertinent variables. The chosen input variable(s) are based on

Fig. 1. Site suitability classification diagram showing scores from a site.

Table 2Pair-wise matrix, weight for the criteria and a consistency ratio generated from thefour criteria.

Waterquality

Substratequality

Hydro-meteorology

Socio-economic

Weight

Water quality 1 2 1/2 3 0.2863Substrate quality 1/2 1 1/2 2 0.1820Hydrometeorology 2 2 1 4 0.4348Socioeconomic 1/3 1/2 1/4 1 0.0969

Consistency ratio 0.0172

Table 3Weight for all the sub-criteria.

Sub-criteria Weight

NH4 0.1413Dissolved oxygen 0.0890Secchi disk 0.0561Textures 0.0566Redox potential 0.0898Organic matter 0.0356Current 0.2476Significant wave height 0.0423Water depth 0.1448Market 0.0523Infrastructure 0.0288Regulations 0.0158

H. Halide et al. / Environmental Modelling & Software 24 (2009) 694–702696

a significant level of 0.95 (Draper and Smith, 1981). The resultingstepwise regression model, called SMOM (simplified MOM), forcalculating holding density (in kg/m3) is

HD ¼ 0:002X1� 0:018X2þ 0:004X3� 0:012X4� 0:081X5

þ 0:075X6� 0:008X7þ 0:008X8� 0:004X9þ 0:096

(1)

where:

X1¼water flow at the surface (b1¼0.487);X2¼ critical oxygen concentration in the cage (b2¼�0.375);X3¼ flow variance (b3¼ 0.34);X4¼ number of cage rows (b4¼�0.258);X5¼ ammonium concentration in the cage (b5¼�0.234);X6¼ critical ammonium concentrations in the cage (b6¼ 0.173);X7¼ food conversion ratio (b7¼�0.166);X8¼ critical oxygen concentration at the seabed (b8¼ 0.155);andX9¼ cage length (b9¼�0.151).

Standardized coefficients b’s measuring relative importance foreach selected variable in (1) is also given as above. The SMOMmodel has an adjusted R2 and standard error of estimate of 0.59 anda holding density of 20 kg/m3. Fig. 3 gives result of implementingSMOM in CADS_TOOL. Note that we added another variable called‘‘percentage dry matter’’ to account for the type of fed given. Pelletsand trash fish are assigned a dry matter content of 90% and 25%,respectively (Boyd et al., 2007), but this can be adjusted for directmeasurements of dry matter content where they are available. Thevariable X4 applies when cages are arranged as a group or array. Inthe case of a farm with isolated (rather than connected) cages (e.g.‘‘polar circle’’ designs), each cage should be treated as an isolated

Fig. 2. Site selection tab.

Table 4Input parameters used in 100 simulations for computing maximum holding capacityfor tropical fish species (grouper, rabbit fish and barramundi).

No. Input parameters Range

1. Temperature (�C) 28–322. Water depth (m) 21–1003. Sigma (cm/s) 2–204. Salinity (ppt) 29–335. Bottom oxygen (mg/l) 1–66. Ammonium* (mg/l) 0.01–0.387. Surface current (cm/s) 1–308. Bottom current (cm/s) 1–299. Number of cage rows 1–310. Cage area (m2) 36–10011. Cage length (m) 6–1012. Cage depth (m) 1–2013. Distance between cage rows (m) 0–214. Reduction factor 0.7–0.815. Critical oxygen in cage (mg/l) 3–516. Critical ammonium in cage (mg/l) 0.12–0.5017. Critical oxygen at the bottom (mg/l) 1–318. FCR (food conversion ratio) 1–319. Protein content of feed (%) 43–8020. Fat content of feed (%) 15–5321. Carbohydrate content of feed (%) 2–1022. Ash content of feed (%) 10–1523. Sinking velocity of feed (cm/s) 5.68–13.8824. Fish initial weight (g) 30–4025. Fish final weight (g) 122–39826. Protein content of fish carcass (%) 10–2027. Fat content of fish carcass (%) 5–1028. Sinking velocity of fish faeces (cm/s) 1–9.07

Six parameters, denoted by asterisks, are selected by a stepwise discriminantanalysis in classifying production into low, medium and high holding density.


cage, since it has its own flow and waste dispersal regimes, and thenumber of row should be set to 1.

Note that CADS_TOOL includes other models for calculatingcarrying capacity: two oxygen budget models for marine cages(Tookwinas et al., 2004; Hanafi et al., 2006), and a phosphorusbudget model for fresh water cages (Pulatsu, 2003).

2.4. Economic appraisal

The last module is an economic appraisal of an aquaculturepractice at the chosen site. Given a holding density, cage volume,survival rate of fish seed, mean fish weight at harvest, FCR, cost ofseed, feed, and cage (for construction and operation), interest rateon borrowed funds, and fish price at harvest, the break-even price(BEP) and the return on investment (ROI in percent) are calculated.The formulae for both measures are derived in Appendix C.

An example is presented in Fig. 4. Here we use Indonesiancurrency, the Rupiah (Rp.). Based on data provided by a user, thefish has to be sold at the price of Rp. 12,025.71 to achieve the break-even point. Accordingly, if the fish is sold at Rp. 70,000, the farmerwill obtain a return about 4 times the original investment.

3. Discussion and conclusion

A decision support tool for aquaculture called CADS_TOOL hasbeen developed for application to the rapidly growing sea cageaquaculture industry in SE Asia and is available free of charge fromthe Australian Institute of Marine Science website (http://www.aims.gov.au). Tools for site classification, site selection,

http://www.aims.gov.au

http://www.aims.gov.au

Fig. 3. Holding/carrying capacity of a sea cage determined by the simplified MOM model.


determination of holding density and economic appraisal areassembled into modules integrated into a Java program that can berun on any computer supporting the Java Runtime Environment.The modular form has the advantage that modifications can beeasily made. We have endeavoured to make CADS_TOOL easilyavailable and easy to implement, but users should interpret modeloutput considering the behaviour and validation of the model withregard to suitability classification and the estimation of holdingcapacity, as discussed below.

3.1. Suitability classification

There is a circumstance when CADS_TOOL classifies a site asunsuitable only by considering a single parameter, i.e. water flow offew meters per second. We can implement such a case by per-forming a check on whether or not an input value for a parameter isstill within its class range. If the value does not belong to any of theclass, the site is classified as an unsuitable site for aquaculture.

There are also potential modifications in the classificationscheme. For instance, changes in the suitability classificationcriteria and sub-criteria could include other factors such as benthicdiversity, habitat quality and abundance (Nilsson and Rosenberg,1997; UNESCO, 2000), sediment quality (Wildish et al., 2001;Viaroli et al., 2004), water retention times (Viaroli et al., 2004),water quality (Bricker et al., 2003), biophysical criteria (Nath et al.,2003), and nutrient thresholds (Devlin et al., 2007).

3.2. Holding density

Formula 1 of SMOM shows that holding density increases underthe following conditions: (i) in strong water flows (X1 and X3) thatimprove waste removal: (ii) when critical ammonium concentra-tions are higher, i.e. higher tolerance by cultured fish (X6); and (iii)when critical oxygen concentration at the seabed are higher (X8).Having stronger flows and higher critical ammonium concentra-tions to obtain higher holding density is in agreement with MOMformulations, i.e. formulae 13 and 14 of MOM (Stigebrandt et al.,2004). Higher critical bottom oxygen, however, should result inlower holding density according to the MOM formulae, i.e. Eq. (8) ofStigebrandt et al., (2004). In this case, X8 is spurious.

On the other hand, holding density is negatively correlated withthe other five factors: (i) critical oxygen in a cage, i.e. the minimumoxygen concentration allowable for cultured fish to grow (X2); (ii)ammonium concentration (X5); (iii) FCR (X7); (iv) larger farm size(X4 and X9). Farm size is determined by the number of cage rows(X4) and the cage length (X9), and is negatively correlated withholding density because more wastes are being released into theenvironment.

3.2.1. How to calibrate SMOM against the original MOM?We performed a curve fitting exercise to calibrate SMOM against

MOM holding densities. In this case both linear and quadraticfunctions were used (Fig. 5). The linear fit results in a few spuriouspoints, i.e. holding density is less than 0 and an error estimate of

Fig. 4. Economic appraisal of an aquaculture site.

Fig. 5. Linear and quadratic fitting of holding density between MOM and SMOMmodels.


21.4 kg/m3 while those of the quadratic fit has less error, i.e. 20 kg/m3. As a consequence, the uncorrected holding density HD(formulae 1) should be corrected as:

HD corrected ¼ 11:0822HD2 þ 0:3312HDþ 0:0009: (2)

3.2.2. How does SMOM compare to other models?Two other carrying capacity models for sea cages are imple-

mented in CADS_TOOL, i.e. the cage-scale model of Tookwinas et al.(2004) and the bay-scale model of Hanafi et al., (2006). A directcomparison of results is only possible using the former.

The Tookwinas et al., (2004) model calculates fish biomassthat can be grown in a cage array, and needs oxygen inflow andoutflow around cages, oxygen consumptions by cultured fish,sediment and water column, water flow, cage area and cagedepth. Let us calculate carrying capacity based on the followinginformation taken from Tookwinas et al. (2004): oxygen inflowand outflow around cages (in mg/l) are 5.24 and 3.4, respectively;oxygen consumptions by cultured fish, sediment and watercolumn are 0.25 g oxygen/kg fish/h, 211 mg oxygen/m2/h, and0.15 mg oxygen/l/h, respectively; water flow of 90 cm/s; cage areaand depth of 16 m2 and 2.7 m, respectively. In this case theTookwinas model estimates a holding density (cultured fish, i.e.grouper biomass divided by cage volume) of 40.11 kg/m3. SMOMalso produces a holding density of 40.4 kg/m3 under thefollowing conditions: surface current and current variation of 10and 5 cm/s, respectively; critical oxygen in cage and at seabed of3 and 2 mg/l, respectively; ammonium in cage and its criticalvalue of 0.2 and 0.3 mg/l, respectively; FCR of 3, cage length andcage row of 4 m and 1, respectively. Changing the surface currentto 90 cm/s while keeping all other parameters the same, however,results in a much higher holding density of 200.4 kg/m3.

3.2.3. How do SMOM estimates compare the observed holdingdensity at the farms?

During our program for disseminating CADS_TOOL from July toAugust 2008 in Indonesia, we visited and managed to collect farmdata from Lampung, Aceh and Batam provinces of Indonesia. Theparameters (either measured or estimated) and observed holdingdensity from three cage farmers CF1, CF2 and CF3 with their nameretained, are described in Table 5. Estimates resulting from SMOMcalculations based on these input parameters are also presented inTable 5.

Beside the models already implemented in CADS_TOOL, thereare other carrying capacity models that could also be included in

Table 5Observed and estimated holding density.

Parameter CF1 CF2 CF3

Surface current [cm/s] 30 35 35Current standard deviation [cm/s]* 5 5 5Critical oxygen in cage [mg/l]* 6 5 5Critical bottom oxygen [mg/l]* 4 3 3Ammonium in cage [mg/l]* 0.2 0.2 0.2Critical ammonium in cage [mg/l]* 0.4 0.4 0.4% Dry matter of feed 25 25 10Food conversion ratio (FCR) 8 6.9 10Farm length [m] 15 15 15Cage rows 1 3 2Observed holding density [kg/m3] 25 25 45SMOM calculated holding density [kg/m3] 30.22 26.67 53.2

Parameters marked with an asterisk ‘*’ are estimated.


future versions. They are the environmental capacity models formarine cages (Sumagaysay-Chavoso et al., 2004; Yokoyama et al.,2007) and fresh water cages (Abery et al., 2005).

Acknowledgement

The development of the simplified MOM model and its applicationto the aquaculture of tropical finfish is part of the ACIAR project FIS/2003/027 Planning tools for environmentally sustainable finfish cageculture in Indonesia and northern Australia. We thank H. Stigebrandtfor helping us to run MOM through the Internet from the ANCYLUSwebsite. Halmar Halide would also like to express his gratitude to theAustralian Government for the ACIAR post-doctoral fellowship.

Appendix A. Survey: cage suitability criteria (adopted fromSalem and Miller, 2006)

Purpose: determining weight for each criterion and sub-crite-rion using analytical hierarchy process.

A.1. What is the relative importance that should be given to thefollowing criteria for a sustainable aquaculture cage project?

Criterion Weight [%]

Water quality
Substrate quality (sediment below cages) Hydrometeorology Socioeconomic
Total
100
A.2. The following sub-criteria have been identified for each of theabove criteria. Please rate the relative importance of each sub-criterion

A.2.1. Water quality

Sub-criterion Weight [%]

Dissolved oxygen (DO)
Ammonium (NH4) Water depth
Total
100
A.2.2. Substrate quality


Textures
Redox potential Organic matter
Total
100
A.2.3. Hydrometeorology


Current
Significant wave height Water depth
Total
100
A.2.4. Socioeconomics


Market
Infrastructure Regulations
Total
100
Appendix B. AHP procedures

B.1. Converting the relative importance RI into pair-wise matrixelements M

Suppose we have two relative importance values of c1 and c2.We then take the ratio of these values. There are two conditions tobe considered.

B.1.1. c1> c2

ratio1 ¼ c1=c2 (B.1.1)

if ratio1¼1 then m¼ 1if 1< ratio1�2 then m¼ 2if 2< ratio1�3 then m¼ 3if 3< ratio1�4 then m¼ 4otherwise m¼ 5.

B.1.2. c1< c2

ratio2 ¼ c1=c2 (B.1.2)

if ratio2¼1 then m¼ 1if 1< ratio2� 2 then m¼ 1/2if 2< ratio2� 3 then m¼ 1/3if 3< ratio2� 4 then m¼ 1/4otherwise m¼ 1/5.

B.2. Interpreting the pair-wise matrix elements M in terms ofSaaty’s intensity of importance measures (Al-Harbi, 2001)

M Meaning

1
Equally preferred 2 Equally to moderately preferred 3 Moderately preferred 4 Moderately to strongly preferred 5 Strongly preferred
B.3. Calculating eigen value and consistency ratio

Let the pair-wise matrix is represented by a matrix M of order n.

M ¼�mij�: (B.3.1)

This matrix is also a reciprocal matrix, i.e.


mij ¼ mji: (B.3.2)

The eigen value problem is able to derived from this matrix(Saaty, 1980; Chandran et al., 2005) and has the form:

ðM � lIÞ ¼ 0; (B.3.3)

where I is the unity matrix.The eigen vectors, i.e. the weights, and the maximum eigen

value lmax is obtained through a MATLAB subroutine called ‘EIG’(Scott, 2007).

Consistency index CI ¼ ðlmax � nÞðn� 1Þ: (B.3.4)

Random index Rdi ¼ 0:5ðfor n ¼ 3Þand ¼ 0:9ðfor n ¼ 4Þ:

Consistency ratio ¼ CI=Rdi: (B.3.5)

Appendix C. Economic appraisal formulae

Given a holding density (HD in kg/m3), cage volume (CV in m3),survival rate of fish seed (SR in percent), mean fish weight atharvest (FW in kg), FCR (food conversion ratio), seed cost (SC), feedcost (FC), cage cost (CC) for construction and operation, interest ratefor borrowed funds to cover the cost (IR in percent), and fish priceat harvest (FP), we seek to determine the break-even price (BEP)and the return on investment (ROI in percent). The followingformulae are used.

Suppose that at harvest, the total weight of fish WH and the totalfish biomass BH are

WH ¼ HD� CV (C1)

BH ¼ WH=FW: (C2)

The total number of seed NS and fed needed to produce biomassat harvest FN are:

NS ¼ BH=SR (C3)

FN ¼ FCR � HW: (C4)

The total costs for seed TSC and fed TFC are

TSC ¼ SC� NS (C5)

TFC ¼ FC� FN: (C6)

The total cost TC is

TC ¼ ðTSCþ TFCþ CCÞð1þ IRÞ: (C7)

The break-even price is calculated as:

BEP ¼ TC=WH: (C8)

Now, if the fish is sold at a price of FP, the revenue REV and profitPRO obtained is

REV ¼ FP�WH (C9)

PRO ¼ REV� TC: (C10)

Return on investment ROI (in percent) is found as:

ROI ¼ 100� ðPRO=TCÞ: (C11)

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Developing a decision support system for sustainable cage aquaculture