- Email: [email protected]
Simulation modelling for orchard management
AgriculturalSystems7 (1981)21-36
SIMULATION MODELLING FOR ORCHARD MANAGEMENTt
J. DAVIS~ & G. F. THIELE
Lincoln College, University College of Agriculture, Canterbury, New Zealand
SUMMARY
A simulation modelispresentedfor a typical Australianpomefruit orchard. The main routine calculates annual after-tax profit and sub routines generate optimum replacement age and stochastic variability due to hail and drought. The principal dependent variables such as prices, yields and costs can be changed as required to add flexibility for various practical circumstances. Two replacement policies are used, self replacement (270 trees/ha) and semi-intensive (715 trees~ha). Under mean price and yield conditions, converting the orchard to semi-intensive production gives an average annual improvement in profit of $13 000 over a 100 year simulation period. Results emphasised the need for earlier replacement of trees than is usual practice. Existing trees were replaced at 31 years of age and thereafter recycled at 46 year intervals. Application of regression analysis to produce iso-performance curves revealed important interactions between price, cost, yield and orchard profitability with price being the most sensitive parameter.
INTRODUCTION
The production of long term perennial crops, such as fruit trees, requires a careful consideration of the economics of establishment and production when the orchard is being planted. Once the rootstock, variety, planting pattern and training system have been determined the physical components of the orchard are set for 40 or 50 years. In practice, the orchard may remain static in structure for the natural life of t Based on a Master's thesis by J. Davis submitted in the Department of Horticulture, Lincoln College, University College of Agriculture, New Zealand. $ Orange Agricultural College, Orange, NSW, Australia.
21 AgriculturalSystemsO308-521X/81/O007-O021/$02.50 © Applied Science Publishers Ltd, England, 1981 Printed in Great Britain
22
J. DAVIS, G. F. THIELE
the tree or until such time as production costs exceed returns. Often the pattern of profitability follows the life of the orchardist so that profitability declines as the grower nears retirement and the new owner is faced with a period of poor returns until the orchard can be renewed. Many orchards are in a poor cash flow position because trees have not been replaced early enough. In these situations substantial borrowing is necessary to upgrade the orchard. In a long-term business, technological change must be considered in order to maximise average, net return, even if it means replacing trees which are economically viable but which are contributing less to profitability than would be obtained by using new varieties, rootstocks, training methods and planting systems. An orchard is a complex system of biological, economic and technical elements, all interrelated and influenced by the uncertainties of the environment and market conditions. Without simulating the possible outcomes of these varying conditions the producer of perennial horticultural crops is in no position to make decisions on change. As a result he tends to maintain the s t a t u s quo until declining profitability forces a change rather than maximising profitability over the long term. Anderson (1974) has reviewed the application of simulation in a wide range of farming activities but horticultural examples are lacking. The authors constructed a simulation model of an apple orchard, applying basic biological constants and essential husbandry practices, to establish guidelines for tree replacement which would stabilise average annual net income while maintaining orchard value at a maximum. The model is not fully stochastic for all parameters but provides a basis for further development by incorporation of probabilities for the occurrence of hail and drought. The sensitivity of orchard profit and replacement age to independent changes in variety price, yield, husbandry costs and harvesting-marketing-fixed costs was tested by inserting values about an arbitrarily determined mean for each of these parameters. In addition, the model was used to compare the projected financial outcomes of management systems such as the standard, vase-shaped tree with the semi-intensive, central leader system, with and without irrigation. Some criticism may be directed at the selection of a 100 year simulation period from the point of view of biological, economic and technical changes which could be expected over such a long period. In the absence of reliable probability data to forecast future trends for all of the variables, the question must be asked 'on what basis can a simulation period be selected?'. The decision was made on the basis of replacement patterns to ensure that all trees would go through a minimum of two replacement cycles. The case study orchard used, in the Orange district of NSW, contained some young trees which would not be replaced for 40-50 years. To allow the replaced trees to reach the age of replacement needed a further 40-50 years. Hence the arbitrary 100 year simulation period. The use of a particular property allows personal realism to be incorporated, in that the model can be tested under the decision policies and management goals specified by the orchardist. The case study orchard comprises 20.6 ha of apples and is run as a company. Although the skeleton
SIMULATION MODELLING FOR ORCHARD MANAGEMENT
23
structure and operation of the model may appear over-simplified it provided the basis for relatively cheap substitution of data from other individual orchards of a similar nature. THE MODEL
The major components known to influence alternative management and tree replacement policies are climate, orchard structure, age-yield, and age-cost relationships, and fruit production and prices. Climate
Hail and drought are the main considerations (Table 1). Estimates of pl:obability and extent of crop loss were made from meteorological data for the district and an objective assessment from growers' records. Hail results in crop loss and/or marked fruit. For example, one year in every 20, 40 ~ of the crop is a total loss, 40 ~ is suitable for the fresh market and 20 ~ is suitable for processing. Drought reduces fruit size, lowers prices and increases harvesting and packing costs. Late summer drought results in fruit of poor keeping quality requiring early sales with lower average prices. Irrigation is simulated in the model to eliminate the drought influence. Orchard structure
The factors which influence the structure and tree characteristics at any time are age, varietal mix, rootstock and production system. Costs and yields per tree are influenced by age. Varietal mix provides a range of seasonal maturity times influencing environmental risk and facilitating labour organisation. Rootstock selection determines size and spacing of trees and influences the age at which trees commence bearing. TABLE 1 STOCHASTIC SPECIFICATIONSFOR THE ORCHARD MODEL
Probability
Influence Crop loss (%)
Marketable fruit (%)
Salvage fruit (%)
40 30 20 0
40 50 60 80
20 20 20 20
Hail 0-05 0.05 0.05 0-10
Drought 0.15
1 0 ~ increase in harvesting and marketing cost; 30 ~ decrease in average price.
24
J. DAVIS, G. F. THIELE
tt ?.~ •
°
n o
DO
0
P < or'~
.~.,p
~ c
<
~ c
"0
<
;s ©
~ c ~ c
u~e-
~e
t¢.5~
=
~ c
~.c..
me.r t~t¢-
~± II II
.o .o o
©
SIMULATIONMODELLINGFOR ORCHARD MANAGEMENT
25
The particular combination of rootstock, training system, and density is referred to as a production system. The model was developed to test the following production systems and numbered as such subsequently. (I)
(2)
Standard: Vigorous: Vase. Trees are planted at 250-350 per hectare on vigorous rootstocks (M 12, Northern Spy or seedling) and trained as open centred 'vases'. Semi-Intensive: Semi-Dwarf: Central Leader. Trees are planted at 550-750 per hectare on semi-dwarfing rootstock (MM 106) and trained as central leaders.
Intensive, 1700-7000 trees per hectare, and Ultra-Intensive systems, 30 000-100 000 trees per hectare were developed also but not reported in this paper. Density, in the model, determines the yield per tree and influences size of trees and costs per tree. The orchard structure is expressed as a matrix of tree numbers, age, variety, and production systems and is updated annually in the operation of the model.
Age:cost relationships Where adequate husbandry operations are practised costs are considered constant for trees of a given variety, age and production system. A relative system is used to express costs with a mature 20 year old Delicious vase tree, on vigorous rootstock in a standard planting of 270 trees per hectare considered to have the highest husbandry cost with a factor of 1.00. An 8 year old semi-intensive tree on semi-dwarfing r o o t s t o c k and central leader trained has a husbandry cost factor of 0-5, meaning that these trees incur 50 ~ of the husbandry cost of mature vase trees (Table 2). Cost factors are considered constant for any orchard but varietal costs may change from orchard to orchard and district to district. The orchard costs for the case study business are detailed in Table 3. TABLE 3 ESTIMATED ORCHARD COSTS
Establishment cost Husbandry costs variety: Red Delicious Golden Delicious Jonathan Granny Smith Bonza Rome Beauty Harvesting costs Marketing costs Fixed cost
$2.53 per tree $4.21 per mature tree $4-00 per mature tree $3.47 per mature tree $3.82 per mature tree $4-21 per mature tree $3-47 per mature tree $21.00 per tonne $79.80 per tonne $34,000.00 per annum
26
J. DAVIS, G. F. THIELE TABLE 4 YIELD FACTOR~ AGE~ PRODUCTION
Year 1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
Production system 1 2 --
-----0.10 0.15 0.30 0-50 0-60 0.70 0.75 0-78 0.80 0.82 0.84 0.86 0.88 0.90 0.90 0.89 0.89 0.88 0.88 0.88 0.87 0.87 0.86 0.86 0.85 0.84 0.83 0.82 0.81
---0-10 0-20 0.30 0.40 0.45 0.50 0.55 0.60 0.65 0.68 0.70 0.70 0.70 0-70 0-70 0.70 0.70 0.69 0.69 0.69 0.68 0.68 0.68 0.67 0-67 0.66 0-66 0-65 0-65 0.64 0.63 0-63
SYSTEM RELATIONSHIP
Year 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70
Production system 1 2 0.80 0.78 0.77 0.76 0.74 0.72 0.70 0.68 0.66 0.64 0.60 0-56 0-54 0-52 0.50 0.48 0.46 0.44 0.42 0.40 0-38 0.36 0.34 0.32 0.30 0.28 0.27 0-26 0-25 0-24 0-23 0-22 0.21 0.20 0.19
0.62 0.61 0.60 0.58 0.56 0.52 0.50 0.48 0-46 0-44 0-42 0-40 0.38 0.36 0.34 0.32 0.30 0.28 0.26 0-24 0.22 0.21 0-20 0.19 0.18 0-17 0.16 0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.08
A g e : y i e l d relationships Yield factors have been established for age and production system on the same b a s i s as t h e c o s t f a c t o r s , w i t h a 20 y e a r o l d s t a n d a r d , c e n t r a l l e a d e r t r e e h a v i n g t h e h i g h e s t yield, a n d a f a c t o r o f 1 "0. A l l o t h e r y i e l d s w i t h i n e a c h p r o d u c t i o n s y s t e m a r e r e l a t e d t o t h i s t r e e so t h a t m a x i m u m y i e l d o f t h e s e m i - i n t e n s i v e , c e n t r a l l e a d e r t r e e is a t t a i n e d in y e a r s 1 4 - 2 0 a t a f a c t o r o f 0.7 a n d f o r t h e s t a n d a r d , v a s e - s h a p e d t r e e i n y e a r s 20 a n d 21 ( T a b l e 4). T h e y i e l d f a c t o r s f o r a s t a n d a r d , c e n t r a l l e a d e r t r e e h a v e not been presented to allow simple comparison between two production systems only. Y i e l d s a l s o v a r y w i t h v a r i e t y so t h a t y i e l d p e r t r e e is d e t e r m i n e d b y a p p l y i n g t h e a p p r o p r i a t e y i e l d f a c t o r t o a v a r i e t a l yield. A s a n o r c h a r d a g e s a n u m b e r o f t r e e s will
SIMULATION MODELLING FOR ORCHARD MANAGEMENT
27
die or be reduced in production by disease or other causes. An annual percentage loss for each group has been calculated and'incorporated in the model. Trees over 70 are considered unproductive. Total orchard production is expressed in tonnes. Unit costs per tonne for harvesting and marketing and an annual average cost for storage are included in the input data. Total orchard costs are a summation o f the establishment, husbandry, harvesting and marketing costs for each production system. Fruit production and prices
Table 5 details average variety production and prices for the case study orchard. Price is one of the critical factors in the model and the effects of hail, drought and TABLE 5 AVERAGE VARIETY YIELDS AND PRICES
Variety Red Delicious and Bonza Golden Delicious Jonathan Granny Smith Rome Beauty
YieM (tonnes/tree)
Price ($/tonne)
0-114 0.152 0.137 0.114 0-173
275 275 225 205 160
industry production variables have been carefully considered. Information on yields and prices is not well documented in Australia and much reliance has been placed on the work of McKenzie (1965, 1969, 1970a, 1970b, 1971) and on subjective information from extension officers and orchardists. The relationship between the various orchard factors considered in the model is expressed in Fig. 1. R e p l a c e m e n t policy
Apart from natural losses, trees are removed and replaced when marginal net revenue from the present trees is equal to the highest amortised present value of anticipated net revenue from the following trees (Faris, 1960; Faris & Reed, 1962). Net present value is influenced by the cost, yield and price structure of the orchard. Faris expresses the net revenue in any year as N R , = Y, - a , _ l i - b, - c,
where Yn is the gross revenue, a,_ ai is the interest o n the unpaid balance of the establishment cost at the beginning of the year, b, is the annual cost and e, is the planting cost.
28
J. DAVIS, G. F. THIELE
Yesr
I
l"°~sndry O~ra"onsl
+ ORCHARD ~[ ReplacementPe,cyI STRUCTURE [[ = I + Tree Losses'J+ Yield PerTree II
l Weatier [ Rainfall
Tree NumbersI
Cost PerTree
Husbandry Costs]
I
I
•
EstablishmentCosts =
[Orchard Production]
Unit Cost Per Tonne] t
Price
]
1
Marketing Costs] + Storage CostsI
J
OrchardMargin}
I
[Fixed Costs]
•
+
I
ORCHARD]
I PROFITI Fig. ]. Mode] of an apple orchard system. The amortised present value in year n can be expressed as fl
ANR=[~Yk--ak_li--bk--Ck~rr ( l + r ) " (1 + r-)~
1
J L ( i + r)-" ~ 1
k=O
where a k_ 1 = O. The rate of tree replacement will be controlled by the availability of funds to meet establishment costs to break-even point and the personal income needs of the orchardist. With all decisions his objective is to maximise his average net revenue over time. A subjective judgement must be made by the orchardist on the replacement system, namely self-replacement using the same variety and production system or new technology using a semi-intensive system for instance and/or new varieties.
SIMULATION MODELLING FOR ORCHARD MANAGEMENT
29
In order to take full advantage of the simulation technique, and to ensure practical reality, the incorporation of stochastic elements is essential (Anderson, 1974). Results are presented of random variation of the hail and drought factors. All other factors in this model were subjectively varied about the mean.
OPERATION OF THE MODEL
The simulation year commences in July, coinciding with the production cycle, taxation year and tree planting. The model may be run over any number of years but 100 years was chosen in this instance to demonstrate the effect of the calculated optimum replacement policy. The flow diagram is shown in Fig. 2, incorporating the following sub-routines and loops. A procedure which applies the cost and yield factors to calculate the annual orchard income, costs and profit for any one production system. A sub-routine which uses the Faris model to determine the optimum tree replacement ages for a change in production system (standard to semi-intensive). A sub-routine which calculates the optimum replacement age for self-replacement within the present system. A random number generator to incorporate the stochastic effects of hail and drought. A treatment loop which tests the various replacement policies. An annual loop which updates the orchard structure according to the replacement age patterns determined by each sub-routine. A treatment loop for input prices. For each simulation run, one card each of the following is introduced as input data: variety yields, husbandry costs, harvesting-marketing-fixed costs, irrigation indicator and up to seven price parameter cards. The model output provides replacement age pattern, current orchard structure, annual costs, returns, and tree planting numbers, annual orchard profit before and after tree replacement, and cumulative profit before and after tax. Taxation is applied at the company rate of 42.5 ~ with losses carried forward into profitable years to reduce taxable income in these years. One development still required is to provide for investment of profits a n d t o relate this investment to replacement policy. Another modification needed is to incorporate the effects of stochastic factors on annual net revenue before calculating replacement ages. Faris (1960) in his work with cling peaches pointed out that the cost of establishing trees can be paid for in most instances before the trees are replaced. This means that interest would be compounded only on the unpaid balance of the establishment costs. Should the stochastic factors affect net revenue to such an extent that interest payments were increased/decreased then there would be a slight increase/decrease in replacement age. However, any regular increase or
J. DAVIS, G. F. THIELE
30
J Read and printinputdata J t I Select a price assumption J t ] Select a replacement policy I t I Determine optimum repl.a~e pattern I t [ Print o p t i m ~ pattern I yes '
yes
.,,,"~ I reola~rnent~,,, ~ pol[cesbeen j
I Adiust yield and )rice
no '
I no
yes J Ajust costs and ~rice J Adjust orchard structure Calculate no; trees to be planted and update orchard structure
L
Ca Iculate total COSTS,returns, net profit ,cumulated after tax profit
i
Print costs, returns~ profit
I yes
no
rag yes |
IO
C-~ ~p-) Fig. 2.
Flow diagram of the orchard simulation model.
SIMULATION MODELLING FOR ORCHARD MANAGEMENT
31
decrease in costs does not alter replacement age. Although in the short term stochastic effects could not be considered regular, the distribution over the long term of this orchard model would tend to even out the effect on average net revenues and fit into Faris' concept. Furthermore, in considering replacement, Faris considers that fixed costs in most instances need not be taken into account. Nevertheless, in spite of these arguments, the fact that the stochastic influence is based on a proportion of the net revenues indicates that the effect will be greater after, rather than before, replacement and should be taken into account in determining replacement age.
SOME RESULTS OF T H E M O D E L O P E R A T I O N
Interaction of variables To facilitate analysis of the vast amount of output data from the large number of simulation runs, iso-performance curves were calculated (Candler & Cartwright, 1969). Two sets of iso-performance curves were constructed to demonstrate the interaction of price and yield on the cumulative after tax profit. One set concerns the self-replacement policy and the other, replacement with the semi-intensive system (Fig. 3). The regression procedure used has been simply a tool to obtain an equation so that iso-performance curves could be plotted. The relative influence of pairs of variables may not have great significance in an orchard management, decisionmaking context but it is useful to determine what factors have greatest effect on the model. The unbroken lines in Fig. 3 represent the range of values used in the analysis from which the function was derived. For example the price parameters ranged from 0-7-1.3 about the mean price o f 1.0. The slope of the performance surfaces demonstrates the high degree of sensitivity of profit to price and the low level of sensitivity of the profit to yield relationship. By comparing points (a), (b) and (c), in Fig. 3a, it can be seen that a 40 ~o increase in yield is needed to bring about the same increase in cumulative after tax profit (CATP) as a 10 ~o increase in price would achieve, namely $750 000. Point (a) in Fig. 3b, at co-ordinates P = 0.82, Y = 1.0 indicates the~break-even'.position. Annual after tax profit is improved by $20 000 with the introduction of the semi-intensive production system (compare point (a) in Fig. 3a with point (d) in Fig. 3b). The standard method of orchard management requires a 15 ~ increase in price to achieve the same break-even point as that for the semiintensive production system. Replacement age Optimum replacement age suggested by the simulation programme is considerably lower than generally accepted by orchardists. Table 6 indicates
32
J. DAVIS~ G. F. THIELE
a
~
~ ~ ~;4m
1.3
1"2'
1.1
(
1-0
"''"
c
~
~~
"-{~)1
(b] - -
0.9
8 II
0.8'
t~
0.7
0:8
1-0
1;2
1"4
1.6
Yield index (base =1-0)
1.3'
1-2
1.1
1.0
0.9 II .~
0,8 •
"~
0.7,
"~
(al
o ~
n 0:8
1.0
1?2
1;4
Yield index ( base = 1 •O) Fig. 3.
Iso-performance curves for price and yield showing cumulative after tax profit; a = self replacement, b = semi-intensive replacement.
SIMULATION MODELLING FOR ORCHARD MANAGEMENT
33
TABLE 6 OPTIMUM REPLACEMENT AGE (YEARS) FOR TREES UNDER SELF REPLACEMENT AND CHANGING REPLACEMENT POLICIES
Variety
Red Delicious Golden Delicious Jonathan Granny Smith Bonza Rome Beauty
Self replacement policy
Changing replacement policy
Standard
Semi-intensive
Standard to semi-intensive
55 56 54 54 55 53
46 47 46 46 46 46
31 28 32 34 31 38
replacement ages varying from 28 to 56 years depending on the replacement production system and variety, using the mean cost:price:yield structure for the calculation. As would be expected a change to a more profitable production system requires removal of the standard system trees at a much younger age. The more profitable the variety in making a change to the semi-intensive system the earlier should the standard trees be removed (compare Golden Delicious 28 years and R o m e Beauty 38 years). Conversely, if the standard system is retained the profitable varieties are left longer before replacement (compare Golden Delicious 56 years and R o m e Beauty 53 years). These results emphasise the importance of making a change to a new profitable production system or to new, more profitable varieties much sooner than has been the case in p o m e fruit areas. One of the limiting factors in practice is the availability of working capital at a reasonable rate of interest. Using a discount rate of 5 ~ compared with 10 ~ , the model demonstrated that replacement age would be up to eight years earlier at the lower rate, other factors being equal. Where semi-intensive plantings are to be replaced with semi-intensive plantings the replacement age is about the 46 year level with little variation between varieties. Again, this is much earlier than would be considered by the practical orchardist.
Stochastic influence An example of annual and cumulative after tax profits over a 100 year period is given in Table 7. The influence of the stochastic variables of hail and drought arelwell demonstrated with drought having the greatest influence on profitability. The table represents the simulated outcome for one computer run under mean cost:price:yield conditions, with semi-intensive replacement and no irrigation. Details on tree replacement numbers and timing are provided in the printout but not presented here. The average annual after tax profit in this instance is approximately $25 000. Under a self replacement policy and no irrigation the average return on capital was calculated at 2.8 ~o. For semi-intensive replacement with irrigation installed the return on capital increases to 14 ~ . This indicates the importance of a simulation
34
J. DAVIS, G. F. THIELE TABLE 7 ANNUAL AND CUMULATIVE AFTER TAX PROFITS FOR SELECTED FIVE YEARLY INTERVALS IN 1 0 0 YEARS OF SIMULATED ORCHARD PRODUCTION UNDER SEMIINTENSIVE REPLACEMENT
Year
Stochastic influence
Annual orchard profit ($)
Cumulative after tax profit (~)~
0 4 9 14 19 24 29 34 39 44 49 54 59 64 69 74 79 84 89 94 99
Nil Nil Hail Hail Drought and hail Drought Nil Drought Nil Nil Nil Nil Nil Drought Nil Nil Drought Nil Nil Hail Drought
-1331 33467 34604 10066 - 15261 -6866 90803 -20574 75892 73833 65068 78079 101821 - 5635 97535 96639 - 17093 73318 71740 -6433 -16464
-1331 - 12089 19932 206213 267561 396092 428286 602032 745007 958348 1013209 1140074 1373788 1564648 1714806 1865619 2088856 2183252 2347304 2488557 2512123
p r o g r a m m e of this n a t u r e in p r o v i d i n g the basis for n e g o t i a t i o n with financiers. In reality, the case study orchardist used the results to b o r r o w finance from his b a n k to install irrigation a n d replace some of his older trees immediately. Before being confident of the result it was necessary to allow the r a n d o m n u m b e r generator to operate over a n u m b e r of 100-year periods with variables other t h a n hail a n d d r o u g h t held c o n s t a n t . F o r 20 runs the c u m u l a t i v e after tax profit for self replacement, for the 100-year period varied between $1108 930 to $1 853164 with a m e a n of $1 580258 a n d a s t a n d a r d deviation of $0.191 m. W i t h semi-intensive replacement the C A T P range was $2 447 883 to $3 225 536 with a m e a n of $2 816 587 a n d a s t a n d a r d deviation of $0.200 m. I n the case of self replacement the 95 confidence limits are _+$0-374m f r o m the m e a n a n d with semi-intensive r e p l a c e m e n t the 95 ~o confidence limits are at _+$0-392 m from the m e a n . The m e a n increase for semi-intensive r e p l a c e m e n t c o m p a r e d with self replacement is 52 ~o. The d i s t r i b u t i o n s of the net c u m u l a t e d after tax profit for b o t h self a n d semiintensive replacement are shown in Fig. 4 as p r o b a b i l i t y densities. T h e chi-squared values of 1.37 a n d 5-95 for self a n d semi-intensive replacement respectively were well below the chi-squared value of 7-43 required for a 99.5 ~o confidence level that the curves exhibit a n o r m a l d i s t r i b u t i o n .
SIMULATION MODELLING FOR ORCHARD MANAGEMENT
z.o.
.0~ >,
0.
A
self
f-~
35
semi-intensive
1"0'
1"0
2"0
3"0
Net cumulative after tax profit ($ m)
Fig. 4.
Probability density of the net cumulative after tax profit for self and semi-intensivereplacement with hail and drought varied stochastically.
CONCLUSIONS
The model has demonstrated a marked increase in profitability with the adoption of the semi-intensive production system and irrigation. It further demonstrated that optimum replacement age is considerably lower than that generally accepted by the community (compare 46 years with approximately 60 years). Optimum replacement age is affected by changes in price and yield, but changes in the level of cost factors have little influence on tree replacement timing. The simulation approach used, has taken into account the inherent variability of the environment and, as such, satisfied the common compb/int of lack of realism in forward planning models. It would be very difficult to use multi-period and risk programming to plan orchard development and redevelopment, when the lack of biological and climatic data is considered. The model output volume needs to be kept in mind when designing experiments. The simplicity and flexibility of such a model can lead the user into the trap of producing large volumes of output, creating methodological problems of sample size and analysis of results. Significant improvements could be made to the orchard model given more reliable stochastic information. Although this may affect profitability it would have little, if any, influence on optimum replacement age. Any refinement of this broad model should be orientated towards sub-model development for such factors as, tree growth:age: yield relationships, production systems and irrigation responses. The model needs to be tested now on other properties, in other districts and other industries. Refinements should be introduced to deal with personal taxation, investment of cash surpluses and alternative marketing strategies. Given appropriate data to establish basic assumptions, relationships and systems logic, the
36
J. DAVIS, G. F. THIELE
m o d e l c o u l d be e x p a n d e d to suit t h e f i n a n c i a l a n d requirements of other orchard and perennial crops.
redevelopment planning
REFERENCES ANDERSON,J. R. (1974). Simulation: methodology and application in agricultural economics, Rev. Mktg. Agric. Econ., 42, 3-55. CANDLER, W. & CARTWRIGHT,W. (1969). Estimation of performance functions for budgeting and simulation studies, Am. J. Agric. Econ., 51, 159-69. FARlS, E. J. (1960). Analytical techniques used in determining the optimum replacement pattern, J. Fro. Econ., 42, 755-66. FARIS, E. J. & REED, A. D. (1962). When to replace cling peach trees, Calif. Ag. Expt. Stn. Extension Service Circular, 512, 29 pp. McKENzIE, D. W. (1965). Further suggestions on semi-intensive apple plantings, Orchard, N.Z., 38, 234-7. McKENzlE, D. W. (1969). Planning a new orchard, Mimeograph, Havelock North Research Orchard, Plant Diseases Division, DSIR, NZ, 81 pp. MCKENzm, D. W. (1970a). The value of an established orchard, Mimeograph, Havelock North Research Orchard, Plant Diseases Division, DSIR, NZ, 88 pp. MCKENZIE,D. W. (1970b). An assessment of the economic efficiency of semi-intensive apple orchards in Hawkes Bay, Orchard, NZ, 43, 92-4. McKENzm, D. W. (1971). Intensive orchards in NZ, Orchard, NZ, 43, 175-81.
SIMULATION MODELLING FOR ORCHARD MANAGEMENTt
J. DAVIS~ & G. F. THIELE
Lincoln College, University College of Agriculture, Canterbury, New Zealand
SUMMARY
A simulation modelispresentedfor a typical Australianpomefruit orchard. The main routine calculates annual after-tax profit and sub routines generate optimum replacement age and stochastic variability due to hail and drought. The principal dependent variables such as prices, yields and costs can be changed as required to add flexibility for various practical circumstances. Two replacement policies are used, self replacement (270 trees/ha) and semi-intensive (715 trees~ha). Under mean price and yield conditions, converting the orchard to semi-intensive production gives an average annual improvement in profit of $13 000 over a 100 year simulation period. Results emphasised the need for earlier replacement of trees than is usual practice. Existing trees were replaced at 31 years of age and thereafter recycled at 46 year intervals. Application of regression analysis to produce iso-performance curves revealed important interactions between price, cost, yield and orchard profitability with price being the most sensitive parameter.
INTRODUCTION
The production of long term perennial crops, such as fruit trees, requires a careful consideration of the economics of establishment and production when the orchard is being planted. Once the rootstock, variety, planting pattern and training system have been determined the physical components of the orchard are set for 40 or 50 years. In practice, the orchard may remain static in structure for the natural life of t Based on a Master's thesis by J. Davis submitted in the Department of Horticulture, Lincoln College, University College of Agriculture, New Zealand. $ Orange Agricultural College, Orange, NSW, Australia.
21 AgriculturalSystemsO308-521X/81/O007-O021/$02.50 © Applied Science Publishers Ltd, England, 1981 Printed in Great Britain
22
J. DAVIS, G. F. THIELE
the tree or until such time as production costs exceed returns. Often the pattern of profitability follows the life of the orchardist so that profitability declines as the grower nears retirement and the new owner is faced with a period of poor returns until the orchard can be renewed. Many orchards are in a poor cash flow position because trees have not been replaced early enough. In these situations substantial borrowing is necessary to upgrade the orchard. In a long-term business, technological change must be considered in order to maximise average, net return, even if it means replacing trees which are economically viable but which are contributing less to profitability than would be obtained by using new varieties, rootstocks, training methods and planting systems. An orchard is a complex system of biological, economic and technical elements, all interrelated and influenced by the uncertainties of the environment and market conditions. Without simulating the possible outcomes of these varying conditions the producer of perennial horticultural crops is in no position to make decisions on change. As a result he tends to maintain the s t a t u s quo until declining profitability forces a change rather than maximising profitability over the long term. Anderson (1974) has reviewed the application of simulation in a wide range of farming activities but horticultural examples are lacking. The authors constructed a simulation model of an apple orchard, applying basic biological constants and essential husbandry practices, to establish guidelines for tree replacement which would stabilise average annual net income while maintaining orchard value at a maximum. The model is not fully stochastic for all parameters but provides a basis for further development by incorporation of probabilities for the occurrence of hail and drought. The sensitivity of orchard profit and replacement age to independent changes in variety price, yield, husbandry costs and harvesting-marketing-fixed costs was tested by inserting values about an arbitrarily determined mean for each of these parameters. In addition, the model was used to compare the projected financial outcomes of management systems such as the standard, vase-shaped tree with the semi-intensive, central leader system, with and without irrigation. Some criticism may be directed at the selection of a 100 year simulation period from the point of view of biological, economic and technical changes which could be expected over such a long period. In the absence of reliable probability data to forecast future trends for all of the variables, the question must be asked 'on what basis can a simulation period be selected?'. The decision was made on the basis of replacement patterns to ensure that all trees would go through a minimum of two replacement cycles. The case study orchard used, in the Orange district of NSW, contained some young trees which would not be replaced for 40-50 years. To allow the replaced trees to reach the age of replacement needed a further 40-50 years. Hence the arbitrary 100 year simulation period. The use of a particular property allows personal realism to be incorporated, in that the model can be tested under the decision policies and management goals specified by the orchardist. The case study orchard comprises 20.6 ha of apples and is run as a company. Although the skeleton
SIMULATION MODELLING FOR ORCHARD MANAGEMENT
23
structure and operation of the model may appear over-simplified it provided the basis for relatively cheap substitution of data from other individual orchards of a similar nature. THE MODEL
The major components known to influence alternative management and tree replacement policies are climate, orchard structure, age-yield, and age-cost relationships, and fruit production and prices. Climate
Hail and drought are the main considerations (Table 1). Estimates of pl:obability and extent of crop loss were made from meteorological data for the district and an objective assessment from growers' records. Hail results in crop loss and/or marked fruit. For example, one year in every 20, 40 ~ of the crop is a total loss, 40 ~ is suitable for the fresh market and 20 ~ is suitable for processing. Drought reduces fruit size, lowers prices and increases harvesting and packing costs. Late summer drought results in fruit of poor keeping quality requiring early sales with lower average prices. Irrigation is simulated in the model to eliminate the drought influence. Orchard structure
The factors which influence the structure and tree characteristics at any time are age, varietal mix, rootstock and production system. Costs and yields per tree are influenced by age. Varietal mix provides a range of seasonal maturity times influencing environmental risk and facilitating labour organisation. Rootstock selection determines size and spacing of trees and influences the age at which trees commence bearing. TABLE 1 STOCHASTIC SPECIFICATIONSFOR THE ORCHARD MODEL
Probability
Influence Crop loss (%)
Marketable fruit (%)
Salvage fruit (%)
40 30 20 0
40 50 60 80
20 20 20 20
Hail 0-05 0.05 0.05 0-10
Drought 0.15
1 0 ~ increase in harvesting and marketing cost; 30 ~ decrease in average price.
24
J. DAVIS, G. F. THIELE
tt ?.~ •
°
n o
DO
0
P < or'~
.~.,p
~ c
<
~ c
"0
<
;s ©
~ c ~ c
u~e-
~e
t¢.5~
=
~ c
~.c..
me.r t~t¢-
~± II II
.o .o o
©
SIMULATIONMODELLINGFOR ORCHARD MANAGEMENT
25
The particular combination of rootstock, training system, and density is referred to as a production system. The model was developed to test the following production systems and numbered as such subsequently. (I)
(2)
Standard: Vigorous: Vase. Trees are planted at 250-350 per hectare on vigorous rootstocks (M 12, Northern Spy or seedling) and trained as open centred 'vases'. Semi-Intensive: Semi-Dwarf: Central Leader. Trees are planted at 550-750 per hectare on semi-dwarfing rootstock (MM 106) and trained as central leaders.
Intensive, 1700-7000 trees per hectare, and Ultra-Intensive systems, 30 000-100 000 trees per hectare were developed also but not reported in this paper. Density, in the model, determines the yield per tree and influences size of trees and costs per tree. The orchard structure is expressed as a matrix of tree numbers, age, variety, and production systems and is updated annually in the operation of the model.
Age:cost relationships Where adequate husbandry operations are practised costs are considered constant for trees of a given variety, age and production system. A relative system is used to express costs with a mature 20 year old Delicious vase tree, on vigorous rootstock in a standard planting of 270 trees per hectare considered to have the highest husbandry cost with a factor of 1.00. An 8 year old semi-intensive tree on semi-dwarfing r o o t s t o c k and central leader trained has a husbandry cost factor of 0-5, meaning that these trees incur 50 ~ of the husbandry cost of mature vase trees (Table 2). Cost factors are considered constant for any orchard but varietal costs may change from orchard to orchard and district to district. The orchard costs for the case study business are detailed in Table 3. TABLE 3 ESTIMATED ORCHARD COSTS
Establishment cost Husbandry costs variety: Red Delicious Golden Delicious Jonathan Granny Smith Bonza Rome Beauty Harvesting costs Marketing costs Fixed cost
$2.53 per tree $4.21 per mature tree $4-00 per mature tree $3.47 per mature tree $3.82 per mature tree $4-21 per mature tree $3-47 per mature tree $21.00 per tonne $79.80 per tonne $34,000.00 per annum
26
J. DAVIS, G. F. THIELE TABLE 4 YIELD FACTOR~ AGE~ PRODUCTION
Year 1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
Production system 1 2 --
-----0.10 0.15 0.30 0-50 0-60 0.70 0.75 0-78 0.80 0.82 0.84 0.86 0.88 0.90 0.90 0.89 0.89 0.88 0.88 0.88 0.87 0.87 0.86 0.86 0.85 0.84 0.83 0.82 0.81
---0-10 0-20 0.30 0.40 0.45 0.50 0.55 0.60 0.65 0.68 0.70 0.70 0.70 0-70 0-70 0.70 0.70 0.69 0.69 0.69 0.68 0.68 0.68 0.67 0-67 0.66 0-66 0-65 0-65 0.64 0.63 0-63
SYSTEM RELATIONSHIP
Year 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70
Production system 1 2 0.80 0.78 0.77 0.76 0.74 0.72 0.70 0.68 0.66 0.64 0.60 0-56 0-54 0-52 0.50 0.48 0.46 0.44 0.42 0.40 0-38 0.36 0.34 0.32 0.30 0.28 0.27 0-26 0-25 0-24 0-23 0-22 0.21 0.20 0.19
0.62 0.61 0.60 0.58 0.56 0.52 0.50 0.48 0-46 0-44 0-42 0-40 0.38 0.36 0.34 0.32 0.30 0.28 0.26 0-24 0.22 0.21 0-20 0.19 0.18 0-17 0.16 0.15 0.14 0.13 0.12 0.11 0.10 0.09 0.08
A g e : y i e l d relationships Yield factors have been established for age and production system on the same b a s i s as t h e c o s t f a c t o r s , w i t h a 20 y e a r o l d s t a n d a r d , c e n t r a l l e a d e r t r e e h a v i n g t h e h i g h e s t yield, a n d a f a c t o r o f 1 "0. A l l o t h e r y i e l d s w i t h i n e a c h p r o d u c t i o n s y s t e m a r e r e l a t e d t o t h i s t r e e so t h a t m a x i m u m y i e l d o f t h e s e m i - i n t e n s i v e , c e n t r a l l e a d e r t r e e is a t t a i n e d in y e a r s 1 4 - 2 0 a t a f a c t o r o f 0.7 a n d f o r t h e s t a n d a r d , v a s e - s h a p e d t r e e i n y e a r s 20 a n d 21 ( T a b l e 4). T h e y i e l d f a c t o r s f o r a s t a n d a r d , c e n t r a l l e a d e r t r e e h a v e not been presented to allow simple comparison between two production systems only. Y i e l d s a l s o v a r y w i t h v a r i e t y so t h a t y i e l d p e r t r e e is d e t e r m i n e d b y a p p l y i n g t h e a p p r o p r i a t e y i e l d f a c t o r t o a v a r i e t a l yield. A s a n o r c h a r d a g e s a n u m b e r o f t r e e s will
SIMULATION MODELLING FOR ORCHARD MANAGEMENT
27
die or be reduced in production by disease or other causes. An annual percentage loss for each group has been calculated and'incorporated in the model. Trees over 70 are considered unproductive. Total orchard production is expressed in tonnes. Unit costs per tonne for harvesting and marketing and an annual average cost for storage are included in the input data. Total orchard costs are a summation o f the establishment, husbandry, harvesting and marketing costs for each production system. Fruit production and prices
Table 5 details average variety production and prices for the case study orchard. Price is one of the critical factors in the model and the effects of hail, drought and TABLE 5 AVERAGE VARIETY YIELDS AND PRICES
Variety Red Delicious and Bonza Golden Delicious Jonathan Granny Smith Rome Beauty
YieM (tonnes/tree)
Price ($/tonne)
0-114 0.152 0.137 0.114 0-173
275 275 225 205 160
industry production variables have been carefully considered. Information on yields and prices is not well documented in Australia and much reliance has been placed on the work of McKenzie (1965, 1969, 1970a, 1970b, 1971) and on subjective information from extension officers and orchardists. The relationship between the various orchard factors considered in the model is expressed in Fig. 1. R e p l a c e m e n t policy
Apart from natural losses, trees are removed and replaced when marginal net revenue from the present trees is equal to the highest amortised present value of anticipated net revenue from the following trees (Faris, 1960; Faris & Reed, 1962). Net present value is influenced by the cost, yield and price structure of the orchard. Faris expresses the net revenue in any year as N R , = Y, - a , _ l i - b, - c,
where Yn is the gross revenue, a,_ ai is the interest o n the unpaid balance of the establishment cost at the beginning of the year, b, is the annual cost and e, is the planting cost.
28
J. DAVIS, G. F. THIELE
Yesr
I
l"°~sndry O~ra"onsl
+ ORCHARD ~[ ReplacementPe,cyI STRUCTURE [[ = I + Tree Losses'J+ Yield PerTree II
l Weatier [ Rainfall
Tree NumbersI
Cost PerTree
Husbandry Costs]
I
I
•
EstablishmentCosts =
[Orchard Production]
Unit Cost Per Tonne] t
Price
]
1
Marketing Costs] + Storage CostsI
J
OrchardMargin}
I
[Fixed Costs]
•
+
I
ORCHARD]
I PROFITI Fig. ]. Mode] of an apple orchard system. The amortised present value in year n can be expressed as fl
ANR=[~Yk--ak_li--bk--Ck~rr ( l + r ) " (1 + r-)~
1
J L ( i + r)-" ~ 1
k=O
where a k_ 1 = O. The rate of tree replacement will be controlled by the availability of funds to meet establishment costs to break-even point and the personal income needs of the orchardist. With all decisions his objective is to maximise his average net revenue over time. A subjective judgement must be made by the orchardist on the replacement system, namely self-replacement using the same variety and production system or new technology using a semi-intensive system for instance and/or new varieties.
SIMULATION MODELLING FOR ORCHARD MANAGEMENT
29
In order to take full advantage of the simulation technique, and to ensure practical reality, the incorporation of stochastic elements is essential (Anderson, 1974). Results are presented of random variation of the hail and drought factors. All other factors in this model were subjectively varied about the mean.
OPERATION OF THE MODEL
The simulation year commences in July, coinciding with the production cycle, taxation year and tree planting. The model may be run over any number of years but 100 years was chosen in this instance to demonstrate the effect of the calculated optimum replacement policy. The flow diagram is shown in Fig. 2, incorporating the following sub-routines and loops. A procedure which applies the cost and yield factors to calculate the annual orchard income, costs and profit for any one production system. A sub-routine which uses the Faris model to determine the optimum tree replacement ages for a change in production system (standard to semi-intensive). A sub-routine which calculates the optimum replacement age for self-replacement within the present system. A random number generator to incorporate the stochastic effects of hail and drought. A treatment loop which tests the various replacement policies. An annual loop which updates the orchard structure according to the replacement age patterns determined by each sub-routine. A treatment loop for input prices. For each simulation run, one card each of the following is introduced as input data: variety yields, husbandry costs, harvesting-marketing-fixed costs, irrigation indicator and up to seven price parameter cards. The model output provides replacement age pattern, current orchard structure, annual costs, returns, and tree planting numbers, annual orchard profit before and after tree replacement, and cumulative profit before and after tax. Taxation is applied at the company rate of 42.5 ~ with losses carried forward into profitable years to reduce taxable income in these years. One development still required is to provide for investment of profits a n d t o relate this investment to replacement policy. Another modification needed is to incorporate the effects of stochastic factors on annual net revenue before calculating replacement ages. Faris (1960) in his work with cling peaches pointed out that the cost of establishing trees can be paid for in most instances before the trees are replaced. This means that interest would be compounded only on the unpaid balance of the establishment costs. Should the stochastic factors affect net revenue to such an extent that interest payments were increased/decreased then there would be a slight increase/decrease in replacement age. However, any regular increase or
J. DAVIS, G. F. THIELE
30
J Read and printinputdata J t I Select a price assumption J t ] Select a replacement policy I t I Determine optimum repl.a~e pattern I t [ Print o p t i m ~ pattern I yes '
yes
.,,,"~ I reola~rnent~,,, ~ pol[cesbeen j
I Adiust yield and )rice
no '
I no
yes J Ajust costs and ~rice J Adjust orchard structure Calculate no; trees to be planted and update orchard structure
L
Ca Iculate total COSTS,returns, net profit ,cumulated after tax profit
i
Print costs, returns~ profit
I yes
no
rag yes |
IO
C-~ ~p-) Fig. 2.
Flow diagram of the orchard simulation model.
SIMULATION MODELLING FOR ORCHARD MANAGEMENT
31
decrease in costs does not alter replacement age. Although in the short term stochastic effects could not be considered regular, the distribution over the long term of this orchard model would tend to even out the effect on average net revenues and fit into Faris' concept. Furthermore, in considering replacement, Faris considers that fixed costs in most instances need not be taken into account. Nevertheless, in spite of these arguments, the fact that the stochastic influence is based on a proportion of the net revenues indicates that the effect will be greater after, rather than before, replacement and should be taken into account in determining replacement age.
SOME RESULTS OF T H E M O D E L O P E R A T I O N
Interaction of variables To facilitate analysis of the vast amount of output data from the large number of simulation runs, iso-performance curves were calculated (Candler & Cartwright, 1969). Two sets of iso-performance curves were constructed to demonstrate the interaction of price and yield on the cumulative after tax profit. One set concerns the self-replacement policy and the other, replacement with the semi-intensive system (Fig. 3). The regression procedure used has been simply a tool to obtain an equation so that iso-performance curves could be plotted. The relative influence of pairs of variables may not have great significance in an orchard management, decisionmaking context but it is useful to determine what factors have greatest effect on the model. The unbroken lines in Fig. 3 represent the range of values used in the analysis from which the function was derived. For example the price parameters ranged from 0-7-1.3 about the mean price o f 1.0. The slope of the performance surfaces demonstrates the high degree of sensitivity of profit to price and the low level of sensitivity of the profit to yield relationship. By comparing points (a), (b) and (c), in Fig. 3a, it can be seen that a 40 ~o increase in yield is needed to bring about the same increase in cumulative after tax profit (CATP) as a 10 ~o increase in price would achieve, namely $750 000. Point (a) in Fig. 3b, at co-ordinates P = 0.82, Y = 1.0 indicates the~break-even'.position. Annual after tax profit is improved by $20 000 with the introduction of the semi-intensive production system (compare point (a) in Fig. 3a with point (d) in Fig. 3b). The standard method of orchard management requires a 15 ~ increase in price to achieve the same break-even point as that for the semiintensive production system. Replacement age Optimum replacement age suggested by the simulation programme is considerably lower than generally accepted by orchardists. Table 6 indicates
32
J. DAVIS~ G. F. THIELE
a
~
~ ~ ~;4m
1.3
1"2'
1.1
(
1-0
"''"
c
~
~~
"-{~)1
(b] - -
0.9
8 II
0.8'
t~
0.7
0:8
1-0
1;2
1"4
1.6
Yield index (base =1-0)
1.3'
1-2
1.1
1.0
0.9 II .~
0,8 •
"~
0.7,
"~
(al
o ~
n 0:8
1.0
1?2
1;4
Yield index ( base = 1 •O) Fig. 3.
Iso-performance curves for price and yield showing cumulative after tax profit; a = self replacement, b = semi-intensive replacement.
SIMULATION MODELLING FOR ORCHARD MANAGEMENT
33
TABLE 6 OPTIMUM REPLACEMENT AGE (YEARS) FOR TREES UNDER SELF REPLACEMENT AND CHANGING REPLACEMENT POLICIES
Variety
Red Delicious Golden Delicious Jonathan Granny Smith Bonza Rome Beauty
Self replacement policy
Changing replacement policy
Standard
Semi-intensive
Standard to semi-intensive
55 56 54 54 55 53
46 47 46 46 46 46
31 28 32 34 31 38
replacement ages varying from 28 to 56 years depending on the replacement production system and variety, using the mean cost:price:yield structure for the calculation. As would be expected a change to a more profitable production system requires removal of the standard system trees at a much younger age. The more profitable the variety in making a change to the semi-intensive system the earlier should the standard trees be removed (compare Golden Delicious 28 years and R o m e Beauty 38 years). Conversely, if the standard system is retained the profitable varieties are left longer before replacement (compare Golden Delicious 56 years and R o m e Beauty 53 years). These results emphasise the importance of making a change to a new profitable production system or to new, more profitable varieties much sooner than has been the case in p o m e fruit areas. One of the limiting factors in practice is the availability of working capital at a reasonable rate of interest. Using a discount rate of 5 ~ compared with 10 ~ , the model demonstrated that replacement age would be up to eight years earlier at the lower rate, other factors being equal. Where semi-intensive plantings are to be replaced with semi-intensive plantings the replacement age is about the 46 year level with little variation between varieties. Again, this is much earlier than would be considered by the practical orchardist.
Stochastic influence An example of annual and cumulative after tax profits over a 100 year period is given in Table 7. The influence of the stochastic variables of hail and drought arelwell demonstrated with drought having the greatest influence on profitability. The table represents the simulated outcome for one computer run under mean cost:price:yield conditions, with semi-intensive replacement and no irrigation. Details on tree replacement numbers and timing are provided in the printout but not presented here. The average annual after tax profit in this instance is approximately $25 000. Under a self replacement policy and no irrigation the average return on capital was calculated at 2.8 ~o. For semi-intensive replacement with irrigation installed the return on capital increases to 14 ~ . This indicates the importance of a simulation
34
J. DAVIS, G. F. THIELE TABLE 7 ANNUAL AND CUMULATIVE AFTER TAX PROFITS FOR SELECTED FIVE YEARLY INTERVALS IN 1 0 0 YEARS OF SIMULATED ORCHARD PRODUCTION UNDER SEMIINTENSIVE REPLACEMENT
Year
Stochastic influence
Annual orchard profit ($)
Cumulative after tax profit (~)~
0 4 9 14 19 24 29 34 39 44 49 54 59 64 69 74 79 84 89 94 99
Nil Nil Hail Hail Drought and hail Drought Nil Drought Nil Nil Nil Nil Nil Drought Nil Nil Drought Nil Nil Hail Drought
-1331 33467 34604 10066 - 15261 -6866 90803 -20574 75892 73833 65068 78079 101821 - 5635 97535 96639 - 17093 73318 71740 -6433 -16464
-1331 - 12089 19932 206213 267561 396092 428286 602032 745007 958348 1013209 1140074 1373788 1564648 1714806 1865619 2088856 2183252 2347304 2488557 2512123
p r o g r a m m e of this n a t u r e in p r o v i d i n g the basis for n e g o t i a t i o n with financiers. In reality, the case study orchardist used the results to b o r r o w finance from his b a n k to install irrigation a n d replace some of his older trees immediately. Before being confident of the result it was necessary to allow the r a n d o m n u m b e r generator to operate over a n u m b e r of 100-year periods with variables other t h a n hail a n d d r o u g h t held c o n s t a n t . F o r 20 runs the c u m u l a t i v e after tax profit for self replacement, for the 100-year period varied between $1108 930 to $1 853164 with a m e a n of $1 580258 a n d a s t a n d a r d deviation of $0.191 m. W i t h semi-intensive replacement the C A T P range was $2 447 883 to $3 225 536 with a m e a n of $2 816 587 a n d a s t a n d a r d deviation of $0.200 m. I n the case of self replacement the 95 confidence limits are _+$0-374m f r o m the m e a n a n d with semi-intensive r e p l a c e m e n t the 95 ~o confidence limits are at _+$0-392 m from the m e a n . The m e a n increase for semi-intensive r e p l a c e m e n t c o m p a r e d with self replacement is 52 ~o. The d i s t r i b u t i o n s of the net c u m u l a t e d after tax profit for b o t h self a n d semiintensive replacement are shown in Fig. 4 as p r o b a b i l i t y densities. T h e chi-squared values of 1.37 a n d 5-95 for self a n d semi-intensive replacement respectively were well below the chi-squared value of 7-43 required for a 99.5 ~o confidence level that the curves exhibit a n o r m a l d i s t r i b u t i o n .
SIMULATION MODELLING FOR ORCHARD MANAGEMENT
z.o.
.0~ >,
0.
A
self
f-~
35
semi-intensive
1"0'
1"0
2"0
3"0
Net cumulative after tax profit ($ m)
Fig. 4.
Probability density of the net cumulative after tax profit for self and semi-intensivereplacement with hail and drought varied stochastically.
CONCLUSIONS
The model has demonstrated a marked increase in profitability with the adoption of the semi-intensive production system and irrigation. It further demonstrated that optimum replacement age is considerably lower than that generally accepted by the community (compare 46 years with approximately 60 years). Optimum replacement age is affected by changes in price and yield, but changes in the level of cost factors have little influence on tree replacement timing. The simulation approach used, has taken into account the inherent variability of the environment and, as such, satisfied the common compb/int of lack of realism in forward planning models. It would be very difficult to use multi-period and risk programming to plan orchard development and redevelopment, when the lack of biological and climatic data is considered. The model output volume needs to be kept in mind when designing experiments. The simplicity and flexibility of such a model can lead the user into the trap of producing large volumes of output, creating methodological problems of sample size and analysis of results. Significant improvements could be made to the orchard model given more reliable stochastic information. Although this may affect profitability it would have little, if any, influence on optimum replacement age. Any refinement of this broad model should be orientated towards sub-model development for such factors as, tree growth:age: yield relationships, production systems and irrigation responses. The model needs to be tested now on other properties, in other districts and other industries. Refinements should be introduced to deal with personal taxation, investment of cash surpluses and alternative marketing strategies. Given appropriate data to establish basic assumptions, relationships and systems logic, the
36
J. DAVIS, G. F. THIELE
m o d e l c o u l d be e x p a n d e d to suit t h e f i n a n c i a l a n d requirements of other orchard and perennial crops.
redevelopment planning
REFERENCES ANDERSON,J. R. (1974). Simulation: methodology and application in agricultural economics, Rev. Mktg. Agric. Econ., 42, 3-55. CANDLER, W. & CARTWRIGHT,W. (1969). Estimation of performance functions for budgeting and simulation studies, Am. J. Agric. Econ., 51, 159-69. FARlS, E. J. (1960). Analytical techniques used in determining the optimum replacement pattern, J. Fro. Econ., 42, 755-66. FARIS, E. J. & REED, A. D. (1962). When to replace cling peach trees, Calif. Ag. Expt. Stn. Extension Service Circular, 512, 29 pp. McKENzIE, D. W. (1965). Further suggestions on semi-intensive apple plantings, Orchard, N.Z., 38, 234-7. McKENzlE, D. W. (1969). Planning a new orchard, Mimeograph, Havelock North Research Orchard, Plant Diseases Division, DSIR, NZ, 81 pp. MCKENzm, D. W. (1970a). The value of an established orchard, Mimeograph, Havelock North Research Orchard, Plant Diseases Division, DSIR, NZ, 88 pp. MCKENZIE,D. W. (1970b). An assessment of the economic efficiency of semi-intensive apple orchards in Hawkes Bay, Orchard, NZ, 43, 92-4. McKENzm, D. W. (1971). Intensive orchards in NZ, Orchard, NZ, 43, 175-81.