leung 1986 aquacultural-engineering

7/28/2019 Leung 1986 Aquacultural-Engineering

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Aq uacu l tural Engineer ing 5 (1986) 171-182

A pplications of System s M odeling in A quaculture*

P i n g S u n L e u n gDepartment o f Agricultural and Resource Econ om ics, Universityof Haw aii,Honolulu, Hawaii 96822, USA

A B S T R A C TT h i s p a p e r d e a l s w i th t h e a p p l i c a t io n s o f s y s te m s m o d e l i n g i n a q u a -c u l tu r e . D i f fe r e n t t y p e s o f b i o l o g i c a l m o d e l s a n d t e c h n i q u e s o fe c o n o m i c a n a l y s i s s u c h a s o p t i m i z a t i o n a n d s i m u l a t i o n a r e d i s c u s s e di n th e c o n t e x t o f a q u a c u l t u r e p r o d u c t i o n . E m p h a s i s i s o n t h e a p p l i c-a b i l it y o f su c h m o d e l i n g t e c h n i q u e s f o r p r o d u c t i o n s y s te m d e s ig n a n do p e r a t i o n m a n a g e m e n t . P a s t m o d e l i n g e ff o rt s f o r s e v e r a l a q u a t i cs p e c i e s a re r e v i e w e d a n d s ur e'e ye d w i t h a s p e c i a l d i s c u s s i o n o n a n o n -g o i n g m o d e l i n g e ff or t o f p ra w n p r o d u c t i o n i n H a w a i i.

I N T R O D U C T I O NT h i s p a p e r d e a l s w i th t h e a p p l i c a ti o n s o f s y st e m s m o d e l i n g in a q u a -c u l t u re . I t s ta r ts b y d e f i n i n g t h e t e r m ' m o d e l ' a n d t h e p u r p o s e o fm o d e l i n g . D i f f e r e n t t y p e s o f b i o l o g i c a l m o d e l s p e r t i n e n t t o a q u a -c u l t u re p r o d u c t i o n a r e i d e n t if ie d . D i s c u s s i o n o n t h e t e c h n i q u e s o fe c o n o m i c a n al y si s s u c h a s o p t i m i z a t i o n a n d s i m u l a t i o n in t h e c o n t e x to f a q u a c u l t u r e p r o d u c t i o n t h e n f o l l o w s . E m p h a s i s i s o n t h e a p p l i c -a b il it y o f s u c h m o d e l i n g te c h n i q u e s fo r p r o d u c t i o n s y s t e m d e s i g n a n do p e r a t i o n m a n a g e m e n t . P as t m o d e l i n g ef fo r ts f o r se v e r a l aq u a t ics p e c i e s a r e s u r v e y e d . I n p a r t i c u l a r , t h e p r o g r e s s o f o n g o i n g r e s e a r c ha i m e d a t d e v e l o p i n g a c o m p u t e r - o p e r a t i o n a l b i o e c o n o m i c m o d e l f o ra s se s si ng t h e e c o n o m i c s o f a lt e rn a t iv e p o n d m a n a g e m e n t a n d m a r k e t -i ng st ra t e g ie s f o r a f r e s h w a t e r p r a w n p r o d u c t i o n s y s t e m i n H a w a i i isb r i e fl y d i s c u s s e d .*Journal Se ries No. 3 03 0, Haw aii Institute of Tropical Agriculture and Hum anResources. 171Aquacu lmra l Engb leer ing 0144 -8609 /86/S03 .50- Elsev ier App l ied Sc iencePublishers Ltd, Eng land, 198 6. Printed in Great Britain


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172 R LeungMODELS AND MODELING

A model is a s i m p l i f i e d representation of reality for the purpose ofexperimenting with alternative strategies. Note the emphasis on theword simplified. Almost without exception, models are simpler thanthe systems they are designed to represent. Models incorporate somebut not all of the elements of their real world counterparts. The art ofmodeling is to choose the dominant elements that explain most but notall of a system's behavior.Models can be classified into three major types: iconic, analogueand symbolic (Ackoff and Sasieni, 1968). Iconic models possess someof the physical properties of the things they represent. They areusually made on a different scale. Examples are model airplanes andautomobiles. Pilot plant in aquaculture production is another goodexample. Analogue models use one set of properties to representanother set of properties. A hydraulic system can be used as ananalogue of electrical, traffic, economic and aquaculture productionsystems. Symbolic models employ letters, numbers and other kinds ofsymbols to describe real situations. The relationships betweensymbols are expressed mathematically. Hence, they are also referredto as mathematical models. One of the major advantages of mathe-matical models is that they are adaptable to manipulations by digitalcomputers. This is the type that we will be referring to as models here-after.A model is used in lieu of the real thing because of economy, avail-ability and information (Machol and Miles, 1973). It may cost less toderive knowledge from the model than the real world counterpart.The model may represent a system which does not yet exist or cannotbe manipulated. In addition, the model may provide a convenientmedium to collect and/or transmit information. These are the threemajor factors in the design and analysis of large, complex and dynamicsystems.The modeling and decision process can be summarized as follows(adapted from Shore, 1978). The need for a model arises because adecision problem must be resolved. The first step is to isolate thesystem within which this problem exists and gain familiarity with theelements which comprise this system. Then it must be determinedwhich of these elements are to be included and excluded from themodel. Next, the model is formulated by establishing the relationship


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Applications of systems modeling in aquaculture 17 3among the included elements. The model is then verified to ensurethat it is a reasonable representation of the system of interest. Afterthese steps have been completed, the model can be used to generateinformation for the decision process. The decision maker takes thisinformation together with information generated from other sourcesand reaches a decision. The last step is, of course, to implement theresults of the decision.

AQUACULTURE MODELSModels in aquaculture try to provide answers to the questions ofeconomic feasibility, optimal system design, optimal methods ofoperations and research direction.The ways in which biological and physical elements of a functioningaquaculture facility are related to the economics of production areshown schematically in Fig. 1. The biological component describes theresponse of the cultured organism to the environment. Food andoxygen are consumed, resulting in growth of the cultured organism.Waste products are excreted which affect the culture environment.The influence of the external environment can be regulated bycontrols within the physical system. Economic considerations andattributes, such as maximizing profits or minimizing production costs,are criteria for evaluating culture systems.B i o l o g i c a l s u b - m o d e l sConstruction of the biological sub-model is usually the most difficultpart of the modeling process, because of the complexity of the bio-logical organism and its interactions with the environment. It isimportant since it forms the hub of the total model, in that it definesthe requirements of the other sub-models. Bernard (1983) categorizedthe biological sub-model into three general classes. They are: empiri-cal, stock and mechanistic. Empirical models set out principally todescribe situations in which the ecosystem is treated as a 'black box"with only inputs and outputs. Stock models generally separate thestock or population dynamics into growth, mortality, reproductionand recruitments of stock members. Stock models are somewhere inbetween empirical models and mechanistic models. Mechanistic


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174 P L e u n g

C O S T S

C A P I T A L

E C O N O M I C S$

ENERGY$R E T U R N S

O P E R A T I O N S

dP H Y S I C A L S Y S T E M

Fig. 1.

-J lPUMP NG HE AT SP ACE FEED f l

REMOVAL

BIOLOGICAL

G R O W T H A N D REPRODUCTION

OXYGEN & FOOD HETABOLITES

CULTUR ENVIRONMENT

B a sic c o m p o n e n t s o f a n a q u a c u l t u r e p r o d u c t i o n s y s te m ( a d a p t e d f r o m A l l e ne ta l . , 1984).

m o d e l s a t t e m p t t o g iv e a d e s c r i p t i o n w i th u n d e r s t a n d i n g o f th e b i o -l og ic al a n d e n v i r o n m e n t a l p r o c e s s e s o f t h e e c o s y s t e m o n a f i n er s c al et h a n d o s t o c k m o d e l s . T h e y a r e c o m p l e x s y n t h e se s o f w h a t i s k n o w no f t h e e c o s y s t e m , a n d h e n c e a r e v e r y d i f fi c u lt t o b u i l d a n d u s e . B o t hs t o c k a n d m e c h a n i s t i c m o d e l s m u s t e v e n tu a l l y r e s t o n e m p i r i c is m .

It is a lw a y s p o s s i b l e t o f i n d a n e m p i r i c a l m o d e l t h a t g i v e s a b e t t e r f itt o a g i v e n s e t o f d a t a t h a n a s t o c k o r m e c h a n i s t i c m o d e l . T h i s a r is e sb e c a u s e t h e e m p i r i c a l m o d e l h a s f e w e r c o n s t r a in t s , w h e r e a s a s to c k o rm e c h a n i s t i c m o d e l c a n b e v e r y c o n s t r a i n e d b y i t s a s s u m p t i o n s , e v e nw h e n i t c o n t a i n s m o r e a d j u s t a b l e p a r a m e t e r s .

E m p i r i c a l a n d , t o a c e r t a i n e x te n t , s t o c k m o d e l s c a n b e a d a p t e d f o rm a n a g e m e n t . M e c h a n i s t ic m o d e l s o n t h e o t h e r h a n d a r e n o t v er y w el l


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Applications of systems modeling in aquaculture 17 5suited for management purposes as they are rather difficult to buildand use. However, they can provide insight to the precision in theempirical or stock models, and direct future experiments to improvethat precision.T ech n iq u es o f e con o m ic an a lys isThe choice of appropriate techniques of economic analysis shouldproceed in parallel with the choice of the biological sub-modelsbecause their joint effectiveness depends upon their compatibility.Techniques should be selected that are most appropriate to the natureof the system and the problems to be solved. The most common tech-niques are optimization and simulation. Optimization is the process ofdetermining the values of variables in a system that provides the bestvalue of a function of these variables, while satisfying a set of givenconstraints. An example could be determining the harvesting andstocking policies of a prawn farm in order to maximize profit, subjectto the constraints of biological growth and survival.A wide variety of optimization techniques are available. The mostcommon one is the use of differential calculus when there is no con-straint, or the use of Lagrangian multipliers when the constraints areequalities. In the event that these equations cannot be solved analyti-cally, one has to resort to numerical search techniques. By far the mostwidely used optimization technique is linear programing, because ofits computational advantage. Linear programing is the process ofdetermining the values of variables which optimize the objective func-tion which is linear and satisfy a set of linear constraints. When it isdesired to optimize over time, optimal control theory and dynamicprograming can be used. This is particularly suitable for aquacultureproduction as decisions are usually time-dependent.Optimization techniques require tractable functional forms and therealism of the model is often sacrificed. Simulation can be used whenit is not possible to express the interrelations in a convenient mathe-matical form because the system is too complex or because responsesare subject to random variations. It merely describes the outputbehavior of different combinations of inputs, control variables andparameter values. It is in general non-optimizing and usually requiresa large amount of computing time.


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176 P LeungI n s u m m a r y , o p t i m i z a t i o n m o d e l s r e q u i r e t r a c t a b l e f u n c t i o n s b u ty i e l d t h e b e s t s o l u t io n , w h i le s i m u l a t i o n c a n u s e m o r e r e a li s ti c m o d e l s

b u t m a y n o t f i n d t h e b e s t s o l u t io n a n d m a y b e v e r y e x p e n s i v e i n t e r m so f c o m p u t i n g t i m e . A h y b r i d o f t h e s e t w o c l a s s e s o f m o d e l s c a n b ehe lp fu l in som e cases.

S U R V E Y O F S O M E P AS T M O D E L SJ o h n s o n ( 1 9 7 4 ) u s e d l i n e a r p r o g r a m i n g t o o p t im i z e b o t h t h e sc h e d u leo f r e le a s e d a t e s f o r e a c h l o t o f s a l m o n a n d t h e c h o i c e o f s t o c k s fo r u s ein the ha tchery fac i l i ty . Ga tes e t a L ( 1 9 8 0 a , b ) u s e d a m u l t i- p e r i o dl i n e a r p r o g r a m i n g m o d e l t o d e t e r m i n e t h e o p t i m a l m e t h o d s o f o p e r a -t i o n o f fu l l t e r m s a l m o n c u l t u r e f a c i li ty . L i p s c h u l t z a n d K r a n t z ( 1 9 8 0 )u s e d l i n e a r p r o g r a m i n g t o m a k e p r o d u c t i o n d e c i si o n s fo r o y s t er p r o -d u c t i o n . B a r b i e r i a n d C u z o n ( 1 9 8 0 ) u s e d l i n e a r p r o g r a m i n g to d e te r -m i n e t h e o p t i m a l n u t r i t i o n a l l ev e l s o f P e n a e u s j a p o n i c u s .

O p t i m a l c o n t r o l t h e o r y w a s u s e d t o d e t e r m i n e t h e o p t i m a l o p e r a t -i n g m e t h o d s f o r l o b s t e r c u l t u r e s y s t e m b y B o t s f o r d e t a L ( 1 9 7 4 , 1 9 7 5 )a n d S c h u u r e t a L ( 1 9 7 4 ) . T h e y u s e d t h e m o d e l t o d e t e r m i n e t h e o p t i -m a l t e m p e r a t u r e , r e c i r c u l a t i n g r a t e , c o n t a i n e r s i z e , f e e d i n g r a t e a n df o o d t yp e . E m a n u e l a n d M u l h o l l a n d ( 1 9 7 5 ) u s e d o p t i m a l c o n t r o lt h e o r y t o m a x i m i z e t h e s t a n d i n g c r o p o f l a r g e m o u t h b a s s .

Ki tche l l e t a l . ( 1 9 7 7 ) a n d S p a r r e ( 1 9 7 6 ) u s e d d y n a m i c p r o g r a m i n gto d e t e r m i n e t h e o p t i m a l m e t h o d s o f o p e r a t i o n s o f y e ll o w p e r c h a n dr a i n b o w t r o u t c u l t u r e s r e s p e c t i v e l y . M c N o w n a n d S e i r e g ( 1 9 8 3 ) u s e dd y n a m i c p r o g r a m i n g t o d e t e r m i n e t h e o p t i m a l s y s t e m d e s i g n f o r t h es a m e t w o c u l tu r e s .E x a m p l e s o f s i m u l a t i o n a p p l ic a t i o n s a r e m a n y . T h e s im p l e s t f o r mo f s i m u l a t i o n i s b u d g e t i n g s u c h a s t h e T e x a s A & M A q u a c u l t u r eB u d g e t G e n e r a t o r ( G r i f f i n e t a L , 1 9 8 4 ) . T h e r e a r e n u m e r o u s o t h e re x a m p l e s o f b u d g e t i n g i n t h e l i t e r a t u r e . A l l e n a n d J o h n s t o n ( 1 9 7 6 )a n d B o t s f o r d e t a L ( 1 9 7 7 ) b r o u g h t m o r e r e a l i s m t o t h e e a r l i e r l o b s t e rm o d e l b y u s i n g s i m u l a t i o n t e c h n i q u e . T h e T e x a s A & M g r o u p h a sd e v e l o p e d a ra t h e r e x t e n s i v e s h r i m p s i m u l a t i o n m o d e l f o r th e p u r p o s eo f p r o v i d i n g y e a r t o y e a r f i n a n c i a l s i t u a t i o n s o f p r o p o s e d f a c i l i t y( A d a m s e t a l . , 198 0a , b ; Gr i f f in e t a l . , 1981 ).H u a n g e t a l . ( 1 9 7 6 ) a n d P o l o v in a a n d B r o w n ( 1 9 7 8 ) d e v e l o p e dm o d e l s t o s im u l a t e t h e g r o w t h o f p r a w n s b y s iz e c la s s. E c o n o m i c e le -


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App lications o f systerns m odeling in aq uaculture 177m e n t s a r e n o t i n c l u d e d in th e m o d e l s . T h e y a r e p u r e l y b i o l o N c a l s t o c km o d e l s . G i b s o n a n d W a n g ( 1 9 7 7 ) d e v e l o p e d a d e te r m i n i s ti c p o p u l a -t io n m o d e l u s i n g e m p i r i c a l g r o w t h a n d h a r v e s t in g f u n c t io n s , th e p a r a -m e t e r s o f w h i c h w e r e d e t e r m i n e d b y li n e a r r e g re s s io n . A z i z a n ( 1 9 8 3 ) ,u s in g th e s a m e d a t a a s P o l o v in a a n d B r o w n , d e v e l o p e d a s i m u l a t i o nm o d e l w h o s e p u r p o s e w a s to d e t e r m i n e th e e c o n o m i c a l ly o p t im a l( b a tc h ) h a r v e s t p e r i o d .R e v i e w s o f m o s t o f t h e m o d e l s m e n t i o n e d a b o v e c a n b e f o u n d i nt h e e x c e l le n t a q u a c u l t u r e m o d e l i n g t e x t b y A l l e n e t a l . ( 1 9 8 4 ) . M o d e l so f a q u a c u l t u r e s y s t e m s a r e f e w i n c o m p a r i s o n w i th a g r ic u l tu r e s y s t e mm o d e l s . H o w e v e r , t h e y a r e i n c r e a s i n g i n n u m b e r r e c e n t l y . W i t h t h ea d v e n t o f l o w - c o s t m i c r o c o m p u t e r s a n d p o w e r f u l s o f t w a r e l i k e t h ee l e c t r o n i c s p r e a d s h e e t , t h e d e v e l o p m e n t o f m o d e l s , p a rt ic u l a rl ys i m u l a t i o n m o d e l s , m a y b e e v e n f as te r.

A P R A W N P R O D U C T I O N M A N A G E M E N T M O D E LT h i s s e c t i o n p r e s e n t s t h e p r o g r e s s o f a n o n g o i n g r e s e a r c h p r o j e c t a tt h e U n i v e r s i ty o f H a w a i i. T h e o b j e c t i v e is to d e v e l o p a c o m p u t e r -o p e r a t i o n a l b i o e c o n o m i c m o d e l f o r a ss e ss in g t h e e c o n o m i c s o f a lt er -n a t iv e p o n d m a n a g e m e n t a n d m a r k e t i n g st ra t e g ie s fo r a f r e s h w a t e rp r a w n p r o d u c t i o n s y s t e m i n H a w a i i.T h e m o d e l c o n si st s o f t w o p a r t s - a s to c h a st ic p o p u l a t i o n s u b-m o d e l a n d a n e c o n o m i c o p t i m i z a t i o n s u b - m o d e l . T h e s t o c h a s t i cp o p u l a t i o n s u b - m o d e l f ol lo w s a M a r k o v p r oc e ss . T h e e c o n o m i c s u b-m o d e l is fo r m u l a t e d a s a d y n a m i c p r o g r a m i n g p r o b l e m i n c o r p o r a ti n gt h e M a r k o v p r o c e s s a s d e f i n e d in th e p o p u l a t i o n s u b - m o d e l .

T h e p u r p o s e o f t h e p o p u l a t i o n s u b - m o d e l i s t o s i m u l a t e t h e s i z ed i s t ri b u t i o n o f p r a w n s i n a g r o w - o u t p o n d o v e r t im e . W e d i v i d e t h ep r a w n p o p u l a t i o n i n t o 1 6 l e n g t h s i ze c la s s e s ( o r st a te s ) o f i c m i n c r e -men t . T ha t i s , l eng t h c l a s s 1 cons i s t s o f p r aw ns w i t h o r b i t t o t a i ll e n g t h s f r o m 0 t o 1 c m , l e n g t h c la s s 2 c o n t a i n s p r a w n s w i t h l e n g t h sf r o m 1 t o 2 c m , a n d s o o n . T h e m o v e m e n t s o f a n i m a l s b e t w e e n l en g thc l a s s e s i n a s p e c i f i e d t i m e i n c r e m e n t c a n b e r e p r e s e n t e d b y as t och as t i c ma trL x T as s h ow n i n F i g . 2 . t 0 is t he p r ob ab i l i t y t ha t t h ep r a w n s w i ll g r o w f r o m l e n g t h c l as s i to l e n g t h c l as s j i n o n e t i m e i n c r e -m e n t . If w e a s s u m e t h e t i m e p e r i o d t o b e s u f f i c ie n t l y s h o r t , th e p r a w n sw i l l e i t he r s t ay i n t he s ame c l a s s , g r ow t o t he nex t l a r ge r c l a s s , o r d i e .


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1 7 8 P . L e u n g

From

State1234

t516d

1 2 3 4t~ l t t : 0 00 t2: t ,3 00 0

0 00 0

.0 0F i g . 2 .

T o15 16 d

0 t l , d0 tz . d

/ 1 5 . 1 5 / [ 5 . 1 6 t l S . d0 tl6.~ 6 t~6.a0 0 I

Th e on e-step transition matrix T.

W e h a v e c h o s e n a p e r i o d o f t w o w e e k s . T h e s t r u c t u r e o f t hi s m a t r i xi m p li c i tl y a s s u m e s t ha t th e r a n d o m b e h a v i o r o f th e p r a w n g r o w - o u tp r o c e s s is M a r k o v i a n .

S u c c e s s i v e s a m p l i n g s o f t h e p o p u l a t i o n d i s t r i b u t i o n in t w o w e e ki n t e r v a ls a n d e s t i m a t i o n o f m o r t a l i t y r a t e w i ll a l l o w u s to e s t i m a t e t hi sm a tr ix . T h e c o m p u t a t i o n a l d e ta i ls a re d o c u m e n t e d in L e u n g e t a l .( 1 9 8 4 ) .

D e c i s i o n sD 1 h a r v e s t ( 0 . 1 )D2 s t ock (0 , 1 )

Yt ~I tage Y t . l = G ( Y t , D 1 . D 2 , z )

Fig . 3 .R e w a r dR = R ( Y , D 1 , D 2 )

A g e n e r a l i z e d s t a g e o f a p r a w n g r o w - o u t p r o c e s s


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Applications of systems modeling in aquacul;ure 17 9I N T E R E S T R A T E * 0 .1 2H A R V E S T E F F I C I E N C Y = 0 .5 0 0H A R V E S T S I Z E = 1 0P R I C E F O R 2 6 T H . P E R I O D = 2 .2 5M A X I M U M B I O M A S S = 1 50 0M I N I M U M S T O C K R A T E = 0S T A R T I N G R A T E = 2 0 00S T O C K I N G R A T E = 5 0 0 0T { 1 . 1 6 , 1 6 ) = 0.965

PERIOD STOCK H A R V E S T R E V E N U E H A R V E S T ST O CK NET BIOMASSD E C I S I O N D E C I S I O N C O S T C O S T R E T U R N

1 l 1 1927 80 60 1787 10282 I 1 I 1 4 8 8 0 6 0 1 0 0 9 7 0 93 1 1 7 9 2 7 9 5 9 6 5 3 5 5 64 I 1 5 6 9 7 9 5 9 4 3 1 4 8 25 I 0 0 0 59 -59 4626 1 I 6 4 4 7 8 5 9 5 0 8 5 9 27 1 0 0 0 58 -58 5838 1 0 0 0 58 -58 7469 l 1 1 0 9 9 7 7 5 8 9 6 4 9 3 7

10 I 0 0 0 58 -58 87411 1 0 0 0 57 -57 109512 I 1 1789 76 57 1656 134313 I 0 0 0 57 -57 115614 0 0 0 0 0 0 141615 I I 245 2 75 56 2321 167816 0 0 0 0 0 0 13421 7 I I 2 3 1 0 7 4 5 6 2 1 8 0 1 5 8818 I 0 0 0 55 -55 12651 9 1 I 2 2 0 3 7 4 5 5 2 0 7 4 1 5 1820 I 0 0 0 55 -55 120621 I 1 205 8 73 55 1930 144722 I 0 0 0 54 -54 116023 0 0 0 0 0 0 13972 4 1 I 2 3 9 3 7 2 5 4 2 2 6 7 1 6 3325 0 0 0 0 0 0 12612 6 0 1 5 0 6 0 7 1 0 4 9 8 8 1 4 7 9

Fig. 4.24 ,-143 988 1200 222 55

A sam ple output from the program.

T h e e c o n o m i c s u b - m o d e l is a s e q u e n ti a l d e c i s i o n m o d e l f o r m u l a te da s a d y n a m i c p r og r a m . T h e m o d e l a s s u m e s a 2 6 b i -w e e k l y p e r io d ( o n ey e a r ) t i m e h o r i z o n . A t e a c h p e r i o d t h e r e a r e f o u r d i s t i n c t a c t i o n s o rd e c i s i o n s t h a t c a n b e t a k e n ( s e e F i g . 3 ) . T h e y a r e : 1 , h a r v e s t o n l y ; 2 ,s t o c k o n l y ; 3 , d o n o t h i n g ; a n d 4 , p e r f o r m b o t h 1 a n d 2 . T h e s t a te v a ri -a b l e (y ,) o f a p r a w n g r o w - o u t p r o c e s s is a v e c t o r r e p r e s e n t i n g t h ep r a w n p o p u l a t i o n b y s i z e c l a s s a t a n y i n s t a n c e o f t i m e . T h e v a l u e s o ft h is v a r i a b l e te ll us al l w e n e e d t o k n o w a b o u t t h e p r a w n p o n d s y s t e mf o r t h e p u r p o s e o f m a k i n g d e c i s io n s a b o u t it. T h e d e c i s i o n s c a n b et h o u g h t o f a s t h e o p p o r t u n i t y t o c h a n g e t h e s t at e v a r ia b l e i n o r d e r t or e a l i z e a p r o f i t .


10/12

180 P LeungH o w e v e r , t h e r e i s n o s i m p l e s o l u t i o n t o s u c h a d y n a m i c p r o g r a m .

W i t h f o u r p o s s i b l e d e c i s i o n s i n e a c h p e r i o d , a b r u t e - f o r c e a p p r o a c hw o u l d r e q u i r e e v a l u a t i o n s o f 426 o r 4 . 5 10 t5 p o s s i b l e p a t h s . T h i sw o u l d r e q u ir e a t r e m e n d o u s a m o u n t o f c o m p u t i n g t im e e v e n o n a v e r yf a s t s p e e d c o m p u t e r . S o w e r e s o r t e d t o a h e u r i s t i c s o l u t i o n a p p r o a c h .A s e t o f h e u r i s ti c d e c i si o n r u l e s is d e r i v e d a n d is d o c u m e n t e d inL e u n g e t a l . ( 1 9 8 5 ) .

T h e h e u r i s t i c d e c i s i o n r u l e s w e r e p r o g r a m e d o n a n I B M p e r s o n a lc o m p u t e r . T h e b a s i c i n p u t s t o t h i s p r o g r a m a r e t h e t r a n s i t i o n m a t r i x ,t h e b e g i n n i n g s t o c k , h a r v e s t i n g e f f i c ie n c y , t h e s t o c k i n g d i s t r i b u t i o n ,t h e m a ~ m u m b i o m a s s , i n te r e s t r a te , s to c k i n g c o s t, h a r v e s t in g c o st a n dp r a w n p r ic e . T h e p r o g r a m p r o d u c e s t h e o p t i m a l h a r v e st in g a n d s t oc k -i n g s t r at e g i e s f o r e a c h o f t h e 2 6 b i - w e e k l y p e r i o d s . I t a l so p r i n t s o u tt h e t o t a l n e t r e v e n u e s a n d b i o m a s s f o r e a c h t i m e p e r i o d . A s a m p l eo u t p u t is s h o w n i n F ig . 4 .

W e h a v e j u s t c o m p l e t e d t h e d e b u g g i n g p r o c e s s o f t h e p r o g r a m .H e n c e , w e w i l l b e t h o r o u g h l y t e s t i n g t h e p r o g r a m i n t h e c o m i n gm o n t h s t o e n s u r e v a li d it y o f t h e m o d e l a n d t h e a s s o c ia t e d d e c i s i o nr u l e s . R uns w i l l a l s o be m a de t o t e s t t he s e ns i t i v i t y o f t he ha r ve s t i nga n d s t o c k i n g d e c i s i o n s t o d i f f e r e n t p r i c e a n d c o s t s i t u a t i o n s . T h e p r o -g r a m w i ll a l so b e m o d i f i e d s o a s t o f a c i li ta t e e a s e o f in p u t s a n de n h a n c e t h e r e a d a b i l it y o f o u t p u t s . I t is h o p e d t h a t th e m o d e l c a n b ea d a p t e d a n d u s e d b y p r a w n p r o d u c e r s t o a s s i s t t h e m i n b e t t e r m a n a g -i n g t h e i r p r a w n f a r m s f o r m o r e p r o f i ts .

R E F E R E N C E SAckoff, R. L. & Sasieni M. W. (1968). Fundam entals o f Operations Research,Joh n W i ley & Sons , New Y ork .Adams, C. M., Griff in, W. L., Nichols, J . P. & Bricks, R. W. (1980a). Bio-enginee r ing-econom ic m ode l fo r shr im p m ar i cu l tu re sys tem. TA MU - SG -80-203, Texas A& M Univers i ty , 118 pp.A dam s, C. M ., Griff in, W. L., Nichols, J. P. & Bricks, R. W. (198 0b). A ppl ica-t ions o f a b ioeco nom ic eng inee r ing mod e l fo r shr imp mar i cu l t u re systems.Southern J. Aqr. Econ., 12 , 135 - 41 .Al len, K. R . & Johnston, W. E. (1976) . Research di rec t ion and economic

feasibi l i ty: an example of system analysis for lobster cul ture . Aquaculture,9 , 155-80 .Allen, P. G., Botsford, L. W., Schuur, A.M. & Johnston, W. E. (1984). Bio-economics o f Aquacu lture, Elsevier Sc ience Publ i shers , N ew York.


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App lications o f systems mo deling in aquactdture 181A zi zan , Z . ( 1 9 8 3 ) . U s i n g s i mu l a t i o n me t h o d s t o d e t e rmi n e t h e o p t i ma lh a r v e s t i n g p e r i o d f o r t h e c u l t u r e d M a l a y s i a n f r e s h w a t e r p r a w n s , M a cr o -

brachium rosenbergii . M asters T hes i s , Un ivers i ty o f Il lino is , 196 pp .Ba rb i e r i , M. A . & Cu zo n , G . (1 9 8 0 ) . Imp ro v ed n u t r i en t s p ec i f i ca t i o n fo rl in e a r p r o g r a m m i n g o f p e n a e i d r a ti o ns . A q u a cu l t u r e , 1 9 , 3 1 3 - 2 3 .Be rn a rd , D . R . ( 1 9 8 3 ) . A s u rv ey o f t h e m a t h em a t i ca l mo d e l s p e r t i n en t t o f is hp r o d u c t i o n a n d t r o p i c a l p o n d a q u a c u l t u r e . I n : Principles and Practices ofP on d AquaculttLre, e d s J. E . L a n n a n , R . O . S m i t h e r m a n a n d G . T c h o b a n o -g l o us , O reg o n S t a t e U n i v e r si ty . p p . 2 2 5 -3 5 .Bo t s fo rd , L . W . , Rau ch , H . E . & Sh l e s e r . R . A . (1 9 7 4 ) . O p t i ma l t emp era t u recon t ro l o f a lobs te r p lan t. IE E E Trans. Au tom at ic Control , A C - 1 9 , 5 4 1 - 3 .Bot s fo rd , L . W. , Rauch , H . E . , Schuur , A . M. & Sch leser , R . A . (1975) . Ane c o n o m i c a l l y o p t i m u m a q u a c u l t u r e f ac ilit y. Proc. World Maric. Soc., 6.4 0 7 - 2 0 .Bo ts fo rd , L . W., van O ls t, J. C . , Ca r lberg , J . M. & Go ssar d , T .W. (1977) . T heu s e o f ma t h ema t i ca l mo d e l i n g an d s i mu l a t i o n t o ev a l u a t e aq u acu l t u r e a s ab en e f i c ia l u s e o f t h e rma l e f f l u en t. P ro c. 1 9 7 7 S u m m e r C o m p u t e r S i m u l a t io nConference, C h i c a g o , 1 8 - 2 0 J u l y l 9 7 7 , p p . 4 0 5 - 1 0 .E m an u e l , W . R . & M u l h o l l an d , R . J . ( 1 9 7 5 ) . E n e rg y b as ed d y n am i c m o d e l fo rL ag o Po n d , G a . IEEE Trans . Au tomat ic Contro l , A C - 2 0 , 9 8 - 1 0 1 .Gates , J . M. , MacDonald , C. R. & Po l l a rd , B. J . (1980a) . Sa lmon cu l tu re inw a t e r r eu s e s y s t em: an eco n o mi c an a l y s i s . University o f R ho de LslatzdMarine Technical Report , 78 , 52 pp .Gates , J . M. , MacDonald , C. R. & Po l l a rd , B. J . (1980b) . A dynamic l inearp ro g rammi n g mo d e l o f f i s h cu l t u r e i n w a t e r r eu s e s y s t ems . R h o d e I s l a n dAgrictdtural Experimept t S tat ion Co ntr ibut ion No. 1892, 20 pp.G i b s o n , R . T . & W an g, J. K . ( 1 9 7 7 ) . A n a l t e rn a t iv e p r aw n p ro d u c t i o n s y s t emsdes ign in Haw ai i. U N IH I -S G -TR - 7 7-05 , U n i v e r s i ty o f H aw a i i, 3 6 p p .Gri ff in , W. L. , Hanson, J . S. , Brick, R. W. & Johns , M. A. (1981). Bio-eco n o mi c mo d e l i n g w i t h s t o ch as t i c e l emen t s i n s h r i mp cu l t u r e . J. WorldMaric. Sot., 1 2 , 9 4 -1 0 3 .Gr i f f in , W. L . , Adams , C. M. & Jensen , L . A . (1984) . A genera l i zed budgets i mu l a t i o n mo d e l fo r aq u acu l t u r e . T A M U - S G - 8 3 - 2 0 2 , T e x a s A & MUnive rs i ty , 131 pp .Huang , W. Y. , Wang , J . K . & Fu j imura , T . (1976) . A model fo r es t imat ingp raw n p o p u l a t i o n s i n p o n d s . Aqttactdture, 8 , 5 7 - 7 0 ,J o h n s o n , E C . ( 1 9 74 ) . H a t c h - - a m o d e l f o r f is h h a t c h e r y a n al ys is . R ep o r tNBSIR 74-521 , U S N a t i o n a l Bu reau o f S t an d a rd s , W as h i n g t o n D C , 5 1 p p .Ki tche l l , D . F . , S tewar t , D . J . & Wein inger , D . (1977) . Appl i ca t ions o f a b io -e n e r g e t i c s m o d e l t o y e l l o w p e r c h (Perca f lavesceus) an d w a l l ey e (Stizo-s tedion vi treum v). 3".Fish. Res . Board Canada, 3 4 , 1 9 2 2 - 3 5 .Leung , P . S . , Fa l lon , L . A . & Shang , Y . C. (1984) . Bioeconomic model ing o ff r e s h w a t e r p r a w n p r o d u c t i o n : th e H a w a i ia n e x p e r i e n c e . J. Int. Soc. Eco-logical Modeling, 6, 12.Leu ng , P . S ., Fa l lon , L . A . & Shang , Y . C. (1985) . M ode l ing p ra w n p rod uc t ionm a n a g e m e n t sy s te m : a M a r k o v d e c i s i o n a p p r o a c h . P r e s e n t e d a t 16th Ann .M eet ing W orm Maric. Soc. , O r l a n d o , F l o r id a .


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1S 2 P. Le ungLip sch u l t z , E & Kran tz , G . E . ( 1 9 8 0 ). P ro d u c t io n o p t im iza t io n an d ec o n o m icanalys is o f an oyste r (Crassostrea virginica) h a tch e ry , o n th e Ch esap eak e

Bay, M ary lan d , USA . Proc. WorldMaric. Soc., 1 1 , 5 8 0 - 9 1 .M achol , R. E . & M iles , R. F . J r. (1973) . T he eng ineer ing o f la rge-sca lesystems. In : Systems Concepts, ed . R. E Miles J r., Joh n W iley & So ns , NewYork .M c N o w n , W . & S e i r e g , A . ( 1 9 8 3 ) . C o m p u t e r a i d e d d e s i g n a n d c o n t r o l o fs t ag ed aq u acu l tu r e sy s t em . Proc . ~ br ld Maric. Soc., 1 4, 4 1 7 - 3 3 .Po lo v in a , J . & Bro wn , H . ( 1 9 7 8 ) . A p o p u la t io n d y n am ics m o d e l f o r p r awnaq u acu l tu r e . Proc. Worm Maric. Soc., 8 , 3 9 3 - 4 0 4 .Sho re, B. ( 1978 ) . Quan titative M etho ds fo r Business Decisions, McGraw-Hi l l ,N e w Y o r k.Shuur , A. M. , Al len , R G. & Botsford , L . W. (1974) . An ana lys is o f th reef ac i l i t i e s f o r t h e co m m erc ia l p ro d u c t io n o f Ho ma rus americanus. W i n t e rMee t in g , A m . Soc. A g r. Eng., Paper No. 74-5517, Ch icag o . 1 0 -1 3D ecem b er 1 9 7 4 , 1 9 p p .Sp a r r e , E (1 9 7 6 ) . A M ark o v ian d ec i s io n p ro cess ap p l i ed to o p t im iza t io n o fp ro d u c t io n p lan n in g in fi sh f a rm in g . Meddeklser f ra Danmarks Fisker i -OgHavundersogelser N.S., 7 , 1 1 1 -9 7 .

leung 1986 aquacultural-engineering

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