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Mathematical Research Systems Analysis and Simulation 1988 II edited by A.Sydow • S.G.Tzafestas R. Vichnevetsky

Band 47 A K A D E M I E - V E R L A G BERLIN

In this series original contributions of mathematical research in all fields are contained, such as — research monographs — collections of papers to a single topic — reports on congresses of exceptional interest for mathematical research. This series is aimed at promoting quick information and communication between mathematicians of the various special branches.

In diese Reihe werden Originalbeiträge zu allen Gebieten der mathematischen Forschung aufgenommen wie — Forschungsmonographien — Sammlungen von Arbeiten zu einem speziellen Thema — Berichte von Tagungen, die für die mathematische Forschung besonders aktuell sind. Die Reihe soll die schnelle Information und gute Kommunikation zwischen den Mathematikern der verschiedenen Fachgebiete fördern.

Manuscripts in English and German comprising at least 100 pages and not more than 500 pages can be admitted to this series. With respect to a quick publication the manuscripts are reproduced photomechanically. Authors who are interested in this series please turn directly to the 'Akademie-Verlag'. Here you will get more detailed information about the form of the manuscripts and the modalities of publication.

Manuskripte in englischer und deutscher Sprache, die mindestens 100 Seiten und nicht mehr als 500 Seiten umfassen, können in diese Reihe aufgenommen werden. Im Interesse einer schnellen Publikation werden die Manuskripte auf fotomechanischem Weg reproduziert. Autoren, die an der Veröffentlichung entsprechender Arbeiten in dieser Reihe interessiert sind, wenden sich bitte direkt an den Akademie-Verlag. Sie erhalten dort genauere Informationen über die Gestaltung der Manuskripte und die Modalitäten der Veröffentlichung.

Systems Analysis and Simulation 1988 II

Mathematical Research Wissenschaftliche Beiträge herausgegeben von der Akademie der Wissenschaften der DDR Karl-Weierstraß-Institut für Mathematik

Band 47 Systems Analysis a n d Simulation 1988 II

Mathematische Forschung

Systems Analysis and Simulation 1988 II: Applications Proceedings of the International Symposium held in Berlin (GDR), September 12-16,1988

edited by Achim Sydow Spyros G. Tzafestas Robert Vichnevetsky

Akademie-Verlag Berlin 1988

Herausgeber : Prof. Dr. Achim Sydow, Zentralinstitut prozesse

der Akademie

der Wissenschaften

Prof. Dr. Spyros G. Tzafestas,

Computer

University

Athens

Technical

of Athens,

Prof. Dr. Robert Vichnevetsky, University,

New

Schriftenreihe

3-05-500655-0

ISSN

0138-3019

Erschienen

im Akademie-Verlag

(c) Akademie-Verlag Lizenznummer:

Berlin

Division,

Science,

National

Rutgers

vom Originalmanuskript

der

Berlin, DDR-1086

Berlin,Leipziger

Str.3-4

1988

202-. 100/501/88 VEB Kongreß-

Republic und Werbedruck,

1095

Bestellnummer: 05600

werden

in the German Democratic

Gesamtherstellung: LSV

Engineering

Dept. of Computer

Informations-

Berlin

reproduziert.

ISBN

Printed

der DDR,

Brunswick

Die Titel dieser Autoren

für Kybernetik und

763 960 2

(2182/47)

9273

Oberlungwitz

PREFACE The

present volume contains the papers which were accepted for

tation

at

the

3rd International Symposium for

Systems

presen-

Analysis

and

Simulation held in Berlin (GDR), September 12-16, 1988. It

is

already a tradition to meet a broad international in systems analysis,

experts sium.

community

modelling and simulation at this

of

sympo-

This fact shows the requirements for a forum of presentation

and

discussion of new developments and applications of modelling and simulation in systems analysis. To

the great interest in this field one has to take into

con-

sideration the developed role of computer simulation as a powerful

realize

tool

of problem solving. been

More and more areas in sciences and production have

investigated by mathematical models and computer simulation.

Bio-

logical sciences and social sciences are even by now influenced by

this

trend. The

model

use on the computer has been very much improved in

decision

support systems.

Parallel simulation will provide drastic shortening of

computing

Parallel simulation and model based

time.

decision

support

systems are brought in the focus of international activities. Numerical mathematics," algorithms or

systems theory and control sciences provide with

supporting the modelling process itself based on

analytic

modelling

methods.

simulation

Such simulation systems equipped with tools

and graphics for representing results are real model

for

support

systems. A

new important impact comes from artificial intelligence by

processing.

knowledge

Expert systems may help decision making in case of

mathematical models.

missing

Expert systems may also support teaching and using

simulation systems. New teria

application areas are investigated. control

problems

of

qualitative

Applications sciences

Complex systems with multicri-

problems are in the scope of the symposium analysis of small

in engineering sciences,

scale

as

nonlinear

economy and management,

well

as

systems. natural

and social sciences are examined but also mixed problems

from

different areas. The

state

efficient

of

computer technique and programming

conditions for simulations.

environment

set

Personal computer are even

up used

for simulation more and more. The

symposium

reflects

the state of the art

and

trends

in

systems

analysis, modelling and simulation.

5

The 3rd International Symposium is organized by 'the Central Institute of Cybernetics and Information Processes of the Academy of Sciences of the GDR (ZKI) with cosponsorship of the -International Association for Mathematics and Computers in Simulation (IMACS), -International Federation of Automatic Control (IFAC), -International Institute for Applied Systems Analysis Laxenburg (IIASA), -Scientific Society of Measurement and Automation (WGMA) in the Chamber of Technology (KdT) of the GDR, -Mathematical Society (MG) of the GDR. The papers included in these proceedings were not formally refereed. The authors themselves are fully responsible. The international Program Committee consisted of: W. Ameling (FRG), P. Borne (France), L. Dekker (The Netherlands), S. Deng (PRC), A. A. Dorodnicyn (USSR), K. H. Fasol (FRG), W. Findeisen (Poland), 0. I. Franksen (Denmark), V. Hamata (Czechoslovakia), C. Hu (PRC), A. Javor (Hungary), K. Kabes (Czechoslovakia), V. V. Kalashnikov (USSR), V. Kempe (GDR), E. J. H. Kerckhoffs (The Netherlands), R. KlGtzler (GDR), R. Kulikovski (Poland), A. Kurzhansky (Austria, USSR), N. Levan (USA), A. H. Levis (USA), T. I. Oren (Canada), M. Peschel (GDR), P. D. Dieu (Vietnam), F. Pichler (Austria), K. Reinisch (GDR), W. Schirmer (GDR), B. Schmidt (FRG), V. V. Solodovnikov (USSR), F. Stanciulescu (Romania), J. M. Svirezhev (USSR), M. Thoma (FRG), I. Troch (Austria), S. G. Tzafestas (Greece), .G. C. Vansteenkiste (Belgium), R. Vichnevetsky (USA) , A. Sydow (GDR). Many thanks should be given to the members of this committee for the very helpful cooperation. Special thanks are said to Prof. Dr. V. Kempe, Director of the ZKI, for his great support in preparing and performing the symposium. Furthermore, great gratitude is to express to Prof. Dr. R. Vichnevetsky (USA), IMACS-President, Prof. Dr. B. Tamm (USSR), IFAC-President, Prof. Dr. R. H. Pry (USA), IIASA-Director, Prof. Dr. W. Richter (GDR), Chairman of WGMA, Prof. Dr. R. KlStzler (GDR), Chairman of MG for help and encouragement. A lot of the hard preparation work was done by the Department for Systems Analysis and Simulation of the Central Institute of Cybernetics and Information Processes. The editor expresses his thanks to all col-

6

leagues and friends who were very much engaged in the research work and in the preparation. First of all I would like to name Dr. P. Rudolph and Dr. A. Wittmüß who helped to prepare the proceedings. Furthermore I thank these colleagues and Dr. K.Bellmann, Dr. W.Jansen, Dr. E.Matthäus, Dr. E. Straubel and all the other colleagues for engaged cooperation for years in developing this research area. Mrs. Ch. Fröhlich and Mrs. J. Obretenov should be named for speedy service in preparing the manuscript. Mrs. S. Böttcher made an excellent job as organizer. Last not least I would give my thanks to the publishers, especially Mrs. R. Helle and Mrs. 6. Reiher, for their assistance and cooperation. Finally I would like to express my expectation also on behalf of the coeditors Prof. Dr. S. G. Tzafestas and Prof. Dr. R. Vichnevetsky that also the third symposium will be a contribution to the further development in systems analysis, modelling and simulation as well as a place for cooperation and communication like the first both.

April 1988

Achim Sydow On behalf of the editors

7

TABLE OF

CONTENTS

1. Complex Systems Analysis for Environmental 1.1. B a s i c P r o b l e m s Page,B. /INVITED PAPER/: Environmental Protection

Problems

R e v i e w of A p p l i e d I n f o r m a t i c s

Dorrer.G.A.; Ovezgeldyev,0.G.; Dmitriev,M.G.; Application of O p t i m a l Control M e t h o d s to N a t u r e P r o c e s s e s in A r i d Z o n e Puta.H.; Gerecke,D.: A Repetitive Algorithm Using Actual Climate Data

M a n s i m o v , M.R. : Simulation of

Working

Irrigation

17

21 24

K o r b i c z , J . ; P a r m a s t e , I . L . ; G a w l o w i c z , P . : S i m u l a t i o n of U r b a n Air Pollutant Processes and Monitoring Stations Location Problem

29

Carl,P.; S t e n c h i k o v , G . L . : S t r u c t u r a l A n a l y s i s of t h e tic Response to a Nuclear War

33

1.2. A c i d

1.3.

in

Clima-

Rain

Sydow,A.; Bellmann,K.; Straubel.R.; Imming,I.; Kaschenz.H.; Damrath,U.; Hofmann.G.; Anders,S.: PEMU - An Impact Model Based Environment Protection Decision Support System

37

Lasch,P.; Model,N.; Bellmann,K.: The PEMU/Air Pollutant transport M o d e l B a s e d on Emittent-Receptor-Point-Transmission Calculation

42

Forestry Bellmann,K.; Lasch,P.; Hofmann.G.; Anders,S.; Schulz,H.: PEMU F o r e s t - I m p a c t - M o d e l FORSTK. A Pine Stand Decline Wood Supply Model «

1.4. W a t e r

The and

45

Systems

Richter,J. /INVITED Agro-Ecosystems

PAPER/:

.

Water and Matter Dynamics

G r a e b e r , P . - W . : A u t o m a t i c a l C o n t r o l S t r a t e g y of S y s t e m s in t h e G r o u n d w a t e r Zone

in

Non-Technical

Popescu,Th.D.; Demetriu,S.; Marinescu,V.: Modelling F o r e c a s t i n g of R i v e r F l o w s U s i n g S t o c h a s t i c M o d e l s

and

51 61 65

Bereziriski, M. ; Petryczek,G.: Application of Trajectory D e c o m p o s i t i o n M e t h o d of t h e W a t e r Q u a l i t y C o n t r o l P r o b l e m

69

Braun,P.; Rudolph,P.; A l b r e c h t , K.-F. : C o m p u t e r A i d e d s i o n for W a t e r Q u a l i t y M a n a g e m e n t

75

Deci-

Gnauck,A.; Rathke,P.; Straubel.R.; Wittmuess,A.: ParetoOptimal Cost Division for t h e D e s i g n of Sewage Water T r e a t m e n t P l a n t s b y m e a n s of t h e D S S R E H 2. C o m p l e x S y s t e m s A n a l y s i s for I n d u s t r i a l 2.1. B a s i c P r o b l e m s

79

Automation

Gutenbaum,J. /INVITED PAPER/: Two-Level Heuristic for P a r a l l e l M a c h i n e s S c h e d u l i n g Zhou Shichang; Cao Xinming; Yao Guiyou: The State D i a g r a m of a H y d r a u l i c C o n t r o l S y s t e m

Algorithm 84 Variable

90

Valdes Pardo,V.G.: Decision-Making Simulations with the Micro-CED Programming System

94

G e s c h k e , S. ; Kempe.N.; Schlawatzky,H.: Application of H i e r a r c h i c a l C o m p u t e r S y s t e m for P i c o s e c o n d T e c h n o l o g y Wrycza,St.: Some C o m m e n t s on C o n s t i t u e n t s of Information Systems Development Methodologies Singer,D.: Systems

Model

Based

Default

a

Contemporary

Data Generation

for

Net

98 102 107

W i n n i c k i . A . ; P l o s z a j s k i , G . : O p t i m i s a t i o n P r o b l e m for B y - P a s s Routes Creation in t h e C a s e of a Teletransmission Line Break-Down 121 Hydro,K.: S u b s t i t u t i o n a l R o u t i n g for T r u n k L i n e in t h e T e l e t r a n s m i s s i o n N e t w o r k

Break-Down

Holena.M. : Object System Structure and Behaviour Analysis Database Design

in

125 131

Schiele,K.; Koch.M.; Nachbar,M.: Computer-Aided Elaboration of R e s e a r c h S t r a t e g i e s - The E x p e r t S y s t e m P H A R M E X 136 2.2. M a n u f a c t u r i n g

S y s t e m s and

CIM-Structures

Bobeanu.C.; Neagu.G.; Filip.F.: A Simulation O p t i m i z a t i o n A l g o r i t h m for O p e r a t i o n s C o n t r o l in F M S Lorenz,P.; Tolujev.J.: S i m u l a t i o n of M a n u f a c t u r i n g Goals, Methods, Tools and Problems

Based Systems.

Krug,W.; Blume,F.; Erfurth.F.: Modeling and Simulation Automated Welding Manufacturing System Voigt,G.: On the Application Simulation Processes for the Manufacturing Systems

2.3.

of

of Advisory Systems Planning and Control

and of

Yashkov,S.F.: T h e N o n - S t a t i o n a r y D i s t r i b u t i o n of N u m b e r C a l l s in t h e M / G / l P r o c e s s o r - S h a r i n g Q u e u e

of

140 144 150

154 158

Robotics Tenreiro Machado.J.A.; Martins de Carvalho,J.L.: pulator Systems : Analysis and Control Tenreiro Machado,J.A.; Costa,A.M.C.; Matos,J.S.: Robot Manipulators

Martins Dedicated

de Carvalho,J.L. Computer System for

Miernik,J.W.; Zaremba,M.B.: Performance Robotic Systems Using Rendezvous Networks 2.4. A u t o m a t i o n of C o n t i n u o u s

Industrial

Robot Mani-

Approximation

of

163

167 171

Systems

Matsevity,Yu.M.; Moultanovsky,A.V.: Solution of P a r a m e t e r Optimization and C o n t r o l P r o b l e m s in T h e r m a l Systems by m e a n s of a Local A d a p t i v e F i l t e r 175 Vajta.M.; Rijnsdorp,J.E.; van der Meulen,S.F.; Verberne,J.F.C: O p t i m i z a t i o n of H e a t D e l i v e r y t o B u i l d i n g s U s i n g an I m p r o v e d B u i l d i n g M o d e l

Apartment

179

Zhou Shichang; Cao Xinming; Gao Chengrui; Yang Yanyong: Performance Measurement and Mathematical Model Identification of t h e H y d r a u l i c S e r v o C o n t r o l S y s t e m of a Vacuum Electric-Arc Furnace 183 10

Zhou Shichang; Cao Xinming; Gao Chenrui; Yang Yanyong: Identification of the Mathematical Model of a Servo Valve by means of a Square Wave Signal 190 Piiaciriski, J.: Analog Simulation of Transient Behavior of Converters with the Application of Dynamic Thyristor Models 194 Hvala,N.; Strmcnik,S.; £erneti,i*)on elementary area element which is constrained by j)',^'*and Jid . Here («^j 5 ) are variables of curvilinear coordinated system, U) - initial direction of magistral ( 0 £ idi.H5T) and J> - relative distance from a centre - water source ). The pressure u*, for which normal phytomass volume S equals zero, is called the crytical pressure. If u u * , we have 3 > 0 - it is possible the stable management and by u » u * we have the desertification. For our model we have also S-*0, in origin neighborhood, where u .

Siberian Technological Institute, Krasnoyarsk, 660049, USSR ^FTI AN TS3R, Ashkhabad, 744000, USSR ^Turkmengydromet,Ashkhabad,744000,USSR

21

This fact corresponds the physics sence and observations i n the areas of watering-place the plant cover is destroyed, as a rule. 2.

Parameters identification of spreading processes

in.

There are often appeared the inverse problems under the models parameters estimation on the base of remote sensing side by side w i t h the problems of direct m o d e l l i n g of natural

processes.

ihs wave fronts transfer speeds are represented the greatest i n terest from the dynamical parameters. In our study the two approaches for this problem solution are proposed.

2.1

Parameters estimation of wave front speeds

indicatrix.

Let consider some dynamical set contours o n the earth surface are fixed in sequential time moments, i.e. we have the spreading processes

3oundary

w h i c h we approximate the points sequence,

is the two-dimontional vectors set 'dJCp&l . At first we identify the contours sequence i n topographic m a p s . Then changed sets dJCcfa 1 are used for normal speeds set construction. Further w i t h the help of s t a tistical analysis methods we find the formules parameters for describing of the normal speeds set.

2.2

Optimal guaranted estimates of spreading

processes.

/ere we use the results [ 2 ] by control systems

attainability

sets estimates on the base of the ellipsoids. Let us consider the spreading process parameters estimate p r o b lem by observed fronts positions

(A front is characterized by the c i r -

cumscribed ellipse). Let have the ellipse

E(t) = £[ci({)>

1

^{xeR :

sequence

(x-a)7HU~

a)< i j

, a - the

ellipse centre, II is the matrix defining the ellipse amounts and orien tation. Our problem - find the C, f, K , where x = C x + K u + f-, x e

22

P r o m £ 2 J it is known, that X € i * 5 f M d r ^ i =

+A

= L

J=

fit*

l ( o c - x ! ) T (T(-t^)(jc-X J i

).

arbitrary function,

Further we propose the next algorithm: I.

J-calculated ellipsoid estimate JC

estimate

E(iz)

approximates to o b s e r v e d

,i.e.

' « W - H W c X l e . t x(it)= QUz).

T h e n constructed

functions

t and get the forecasting ellipsoidal

exprapolate

by

estimates.

Numerical experiments, w h i c h were fulfilled for the dynamics

pre-

dictions of the eolian land forms n e a r the Sarykamysh lake on the basis of two set forth approaches have s h o w n the satisfactory c o n f o r m i t y

bet-

w e e n calculations and observations.

Literature i l l Dorrer, G.A.: Dynamical systems parameters estimate by their a t t a i n ability sets. Avtomatika and Telemechanica. (1986) I, 39-46 (In R u s s i a n ) [2] Konstantinov, G.N., G.V. Sidorenko : O u t e r estimates of the control systems attainability sets. Izv. AN 333R. T e c h n . k y b e r n e t i c s . (I98S) 3, 28-34 ( In Russian)

23

A REPETITIVE WORKING IRRIGATION ALGORITHM USING ACTUAL CLIMATE DATA Puta, H.

1)

and Gerecke, D.

2)

1. INTRODUCTION For

a long -time biologists and scientists in agriculture are engaged

develope growth models (see e.g. 1980).

Descriptive

detail.

van KEULEN,

1986;

AUGUSTIN,

models have the benefit to be as true as possible in

Control models represent as correct as possible the input-output

behavior and contain the control parameters explicitely. is

to

SCHMIDT,

The latter

one

suitable for design of control strategies but it is more difficult to

build

it

original been

directly.

For this end a deskriptive model can be

substitute.

In this paper a control model for sugar beets

available (HOFFMANN,

1977),

1980) and also a soil water model

with respect to the water amount which comes from

irrigation.

Both

models have been developed by the

as has

(KOITZSCH,

which enables to ascertain the water supply of the plant

waterstress) and/or

useful

(called rainfall

Academy

of

Agriculture of the GDR. Using these two models it is possible to give the farmer a computer aided help

for

irrigation

decisions taking into account the

present

growth

state and climate data from the past.

2. MODEL DISCUSSION The

growth

model of HOFFMANN (1980) can be at least

described

by

thev

following nonlinear differential equations:

where body

B(t)=f x *f 2 *f 3

(1)

Z(t)=f 1 *f 2

(2)

W(t)=Z(t)-B(t)

(3)

Z is the total dry matter or nettophotosynthesis rate of both W and the leaves B.

The anabolite distribution between leaves

the and

the total dry matter describes f^. The f^ are as following: f =0.01*f(R,t)*B(t),

(4)

f ^ K ^ / E ^ K ^ R *B 2 / 3 +K *WS+K *(ST-2)+K *(ST-2)2 +K,*WS*(ST-2)+K„*ln(TFZ)+Ka*WS*ln(TFZ)) /

2)

24

0

7

Institute of Technology, Ilmenau, GDR Institute for Cybernetics and Information Processes, Berlin, GDR

(5)

f 3=a0-a1#B-a2*-t+a.5#ST1' 2-a4*WS-a5*T+afi*ln< TFZ)-a? *t*ln(TFZ)

(6)

The coefficients K^ are linear interpolated within the four growth intervals: 45...63, 64...87, 88...129, 130...180th day. Waterstress WS and nitrogen content ST can be treated as the control variables, because they are directly conneted with the effects of irrigation and fertilization on the growing behaviour of the plant. Positive values of WS means water demand. Uncontrollable inputs are the radiation R and the outside temperature T. The soil quality is given by the parameter TFZ. The K^ and the constants a^ has been ascertained by regression. The function f(R,T) gives a proper weight every day on the nettoassimilation rate in dependence of the actual courses for global radiation and temperature. Analytical models are available for R(t) and T(t) but it is also possible to use measured data. The waterstress WS represents the state of the water supply of the plant. The soil water model of KOITZSCH (1977) can be used to elaborate the actual WS in dependence of the water supply in the past and the actual growth state of the plant. To get reference courses for WS(t) we applied a dynamic optimization procedure (ARNOLD, PUTA, 1986) with the goal to maximize the yield of dry matter of the body at harvest time. In agreement with the definition of HOFFMANN (1980) the course for waterstress results in about WS(t) - 0 without a short period between 9 0 t h and 110 t h day. During this period the waterstress could be a bit positiv (water demand) for better qualification of the roots. Up to the availability of a proper nitrogen soil model, nitrogen courses ST(t) from the practical experience have to be used. For given values or courses, resp., of the discussed control variables it is possible to use the growth model, eqs. (1) to (5), to predict the yield of dry matter of the body and dry matter of the leaves for any day during the growing season of about 135 days (from 165 t h to 300 t h day of the year).

3. THE IRRIGATION ALGORITHM For application it is desirable to make control decisions (here for irrigation) with respect to the annual climate situation and adapted to the actual growth state of the plant. For this task are available the growth model and the soil water model. The latter one allows the computation of waterstress in dependence of climate date as inputs and using the growth model. The inversion of the soil water model would be desirable to compute the necessary irrigation for required values of waterstress. But this is because of the algorithmic structure of this model impossible. Therefore another strategie will be proposed.

25

At

a

given

actual time t g during the growing period we know

the

real

climate

from t„ (initial time) up to t . With this information we 0 % simulate this time interval and compute the actual growth state of

plant using both of the models. With predicted climate data

for

can the

the in-

terval from t a to t. I(t„I is the estimated harvest time) it is now possible to give a irrigation proposal (fig. 1). The prediction results may be applied as long as there are not too deviations fall.

If

between estimated this

not hold,

and real climate including

large

expected rain-

a new prediction is needed at a new time

Therefore the algorithm should have repetitive character.

A fragment

the repetitive irrigation algorithm is shown in figure 2.

Fig. 1

Choosing t

between t•o n and t. 'f

-- input WS r e f, tig., t a , tf - - compute WS at g r o w t h model

ta

P {OAIS - W S r e f > > 0

using

soil

water

and

?>

n g i v e one i r r i g a t i o n u n i t i e . g . 1mm)

n

P -(sum of p r o p o s e d i r r i g a t i o n > - 3 0 m m ?)•

store WS

- - input : t a

prediction results

--



of

i r r i g a t i o n : amount & d a t e

climate

P -C t e s t o f WS d e s i r e d

n

Fig. 2 26

The repetitive irrigation algorithm

?>

and

expected

yield

t . a

of

4. SIMULATION RESULTS The dialogoriented algorithm (GERECKE, 1988) allows the prediction of five variants of expected climate on the screen of the 8 Bit PC 1715. The program needs about 50 kByte of memory and is written in TURBO-PASCAL. The protocol is shown in figure 3.

Ergebnisprotokoll 1.Variante 2.Variante 3.Variante

4.Variante 5.Variante

Blattmasse 90 dt/'ha 79 dt/ha 83 dt/ha 72 dt/ha 41 dt/ha Ruebenmasse 227 dt/ha 201 dt/ha 203 dt/ha 177 dt/ha 94 dt/ha Zuckerertrag 134 dt/ha 114 dt/ha 117 dt/ha 97 dt/ha 45 dt/ha Gesamterloes 8936.-M/ha 8947.-M/ha 7846.-M/ha 10023.-M/ha 4234.-M/ha Transportkosten 1555.-M/ha 1538.-M/ha 1392.-M/ha 1705.-M/ha 958.-M/ha Beregnungskosten 225.-M/ha 338.-M/ha 338.-M/ha 225.-M/ha 0.-M/ha >> Gewinn