OPTIMIZATION OF THE CHOICE OF AGRICULTURAL MACHINES

Jacek Skwarcz
Chair of Technology Basis, Agricultural University in Lublin, Poland

ABSTRACT

The paper presents a new method of optimization of the choice of agricultural machines, which consists in determining the conditions that should be fulfilled in order that the purchase of a machine will be profitable for a farm. The method means making use of functional relations describing the dependence of unit costs of exploitation of an aggregate for organic fertilization with liquid fertilizers on the efficiency and the yearly time of the use of an aggregate. The results were analyzed in three aspects. The first referred to the profitability of the purchase of a machine for one’s individual use. The second concerned the profitability of rendering the services, while the third – determining the conditions in which it will be profitable to use the purchased machine or device.

Key words: method, choice, ascenization fertilizers, optimization.

INTRODUCTION

Competition on the market of agricultural producers and the resulting necessity of using modern technologies of agricultural production require using highly efficient machines and devices in agricultural farms. Machines of high efficiency are expensive and require the proper use throughout the period of utilization hence in the financial year. A farmer individually is often unable to buy such a machine. Then two most frequently used possibilities are left. The first is to use outside services, while the other is common use of the machine purchased by a few or more farmers. The problems connected with the profitability of the purchase of a machine by a farm and the use of services are presented in papers [1, 2, 4, 5]. At this point the conditions that should be fulfilled in order that the use of a machine will be more profitable than the above mentioned forms of the performance of a production act will be discussed. In such a view this is a new look at the problems of optimization of the choice of agricultural machines. The factors making up the costs, such as the time of using a machine, should determine the choice of a solution in a greater degree apart from technical and exploitative parameters of a machine. So far these problems have been neglected in most papers, which was the result of broken up area of agricultural farms in Poland. Attention was mainly focused on minimizing the energetic expenditures, the labour or exploitation costs, but the fact was overlooked that such a machine would be used in a farm only in a few or several percents of its potential. The discussion here will be presented on the example of ascenization fertilizers.

PURPOSE OF THE PAPER

The problem of choosing the best sets of tractors, machines and devices for the realization of technological treatments has been so far in most publications viewed from the point of view of an individual agricultural farm. Economic reasons and the growing competition on the agricultural market caused that such a treatment of the issue turned out to be insufficient. The amount of work to do in one farm is too small, which brings about a rapid increase of the exploitation costs of aggregates in relation to a scheme in which this set would operate fully utilized. This gave rise to an attempt to work out a method supporting the future users of machines in undertaking the decisions concerning the number and efficiency of aggregates for common use.

The purpose of the paper is to present a new method of supporting the user in undertaking decisions referring to the performance of a definite technological treatment in the process of cereal production.

Methodology of simulation studies

The data base prepared at the Chair of Agricultural Machines and Devices of the Agricultural University in Lublin contains information on 31 types of ascenization carts and 17 agricultural tractors with the power ranging from 18.5 to 211 kW. The output of particular aggregates was 3.2, 4.5 and 10.8 ha/h and they included the whole range of ascenization carts available on the market. 7 types of aggregates for fertilization were selected with liquid fertilizers (tractor + ascenization cart, according to the criterion of minimizing the exploitation costs of an aggregate) and 5 different area complexes, where the treatment of organic fertilization would be performed. Those farms had the following areas requiring fertilization: 56 ha – 6 farms, 400 ha – 4 farms, 900 ha – 2 farms, 1,300 ha – 2 farms, 1,986 ha – 1 farm. Such a number and structure of the farms resulted from the range of analyses that will be presented in the further part of the paper. The results will be analyzed in three different aspects.

1. When is it profitable for the user of machines to purchase a device for their own use?

2. What conditions must be fulfilled for the services to be profitable to the attendant of services?

3. How many participants must there be and what should the minimum area of the cultivations be for the common use of the purchased machine or device to be profitable?

On the basis of so assumed data the equations of index-exponential regression were determined, which described the relation between the unit exploitation costs and organic fertilization with liquid fertilizers. The form of the function resulted from the irregular change of the value of unit costs for different values of the yearly time of using the aggregate, which is seen on an exemplary draft (fig. 1) [6].

Calculation of costs was performed according to the methodology given by Muzalewski [3]; besides, a 15-year-long period of amortization of ascenization carts and a 20-year-long period of tractor amortization were adopted. All the coefficients of determination were more than 0.99. The following relations (1-7) were obtained, where y means a unit cost of exploiting the aggregate (PLZ/h), while x – annual utilization of the aggregate [h].

For an aggregate with the output of 3.2 ha/h

(1)

For an aggregate with the output of 3.6 ha/h

(2)

For an aggregate with the output of 4.5 ha/h

(3)

For an aggregate with the output of 5.4 ha/h

(4)

For an aggregate with the output of 6.8 ha/h

(5)

For an aggregate with the output of 8.1 ha/h

(6)

For an aggregate with the output of 10.8 ha/h

(7)

Unit costs of performing the treatment of organic fertilization with liquid fertilizers decrease with the increase of the annual use of the aggregate (strictly connected with the area of the cultivation) and its output.

The general form of a dimensional function describing the unit costs of exploiting the aggregates in relation to its annual utilization and the output was described [6] with function (8), the draft of which is presented in figure 2.

(8)

where:

z – unit costs of exploiting the aggregate for organic fertilization with liquid fertilizers, PLZ/h,
x – the aggregate output, ha/h,
y – annual utilization of the aggregate, h.

METHOD VERIFICATION

Table 1 includes the results of simulation calculation of the costs of performing the treatment of organic fertilization with liquid fertilizers for 15 farms situated in the area of the operation of a hypothetical company offering services of organic fertilization with liquid fertilizers. With the aim of presenting particular variants of analyses, four characteristic sets of aggregates, differing with the output, were chosen. The costs of performing the treatment were calculated for each of the chosen aggregates and the labour costs were established at 10 PLZ/h. Direct calculations of unit costs of exploitation were performed using the equations (1, 3, 5, 7), describing the relation of these costs to the annual utilization of the aggregate. The annual utilization of the aggregate in a farm was calculated on the basis of the cultivated area and the output of particular aggregates. It ranged from 5.2 to 620.6 [h].

Results presented in tables 1 and 2 will be analyzed in three aspects, according to the assumptions in the methodological part of the paper.

The first concerns answering the question when it is profitable for the farm’s owner to purchase a device in order to perform a definite treatment on their own.

For the studied farms with the cultivated areas meant for organic fertilization with liquid fertilizers from 56 to 1,986 ha, it is profitable only for the owner of a farm with the area of 1,986 ha to buy an aggregate tractor Pronar 2048A with the power of 33 kW with ascenization cart Wukom PA 35A with the output of 3.2 ha/h. This aggregate will be used in the farm throughout the year for 620.6 h, and the cost of performing the treatment will be 38,738.2 PLZ. In the case of other analyzed sets of machines in this farm and for all the other farms with a smaller area the value of the annual utilization of the aggregate is too low and it decreases with the increase of the output of the aggregate, hence the cost of the purchase and exploitation of the aggregate becomes unprofitable. The analysis does not consider the possibilities of using the aggregate to transport the sewage produced in the farm.

The second aspect of the analyses concerns the situation when the performance of the treatment is ordered outside the farm, and it refers to two subjects: on the one hand, the owner of the farm, and on the other, the service attendant. The solution must take into consideration such a level of service costs that is acceptable for both sides.

In this case it is not the annual time of using the aggregate for fertilization but also the number of contractors that is important. The comparison can be made considering the multiplicity of costs borne by the customers.

The analysis of the data from table 1 points out that the highest profits can be achieved by the service attendant using an aggregate made of an ascenization cart Meprozet PN 120 with the output of 10.8 ha/h and a tractor Zetor Z 9641 with the power of 93 kW. Assuming that the farm owners would possess aggregates consisting of an ascenization cart Wukom PA 35A with the output of 3.2 ha/a and a tractor Pronar 2048A with the power of 33kW, their total costs of performing the treatment would be 421,199.5, while the service attendant’s own costs would be 133,147.8 PLZ with the annual use of aggregate Meprozet PN120 with the output of 10.8 ha/ha and a tractor Zetor Z 9641 with the power of 93 kW equal to 770.6 h. The service attendant, however, has some possibilities to further search for the farms where they could use the remaining processing capacity.

Table 2 includes the values of differences in the costs of performing the treatment in the farms and by the service attendants for selected aggregates and for various coefficients increasing the service costs. The following values of these coefficients were adopted for the analysis: 1.0, 1.5 and 2.0. The values of these coefficients present an increased cost of the service in such a way that the service attendant can cover all the costs connected with the functioning of their company and achieve the intended goal. When the coefficient increasing the service cost is fixed at the value 1, the cost of the service is acceptable for all the farm owners with an exception of a farm with the area of 1,986 ha. The service attendant can perform these jobs using all the aggregates taken for analysis. In the case of coefficient 1.5, the price of the service for aggregates with the output of 3.2, 4.5 and 6.8 ha/h can be accepted by the owners of farms with the areas ranging from 56 to 400 ha, while being unacceptable fro the farms with the areas from 900 to 1,986. For an aggregate with the output of 10.8 ha/h and a farm with the area of 1,986 ha the price of the service is not attractive for the farm owner. With the value of the cost coefficient equal to 2.0, the price for the performance of the service is possible to be accepted by the owners of farms with the areas ranging from 56 to 400 ha. It can be profitable for the service attendant to perform these treatments using the aggregates with the output of 3.2, 4.5, 6.8 and 10.8. For the other areas the level of the service process will not be acceptable and it is recommended to do these jobs with one’s own aggregates.

The third aspect of the analyses concerns determining the number of participants with definite needs for jobs linked to the realization of a technological treatment in such a way that the minimum area of cultivations can be settled in order that common use of a purchased machine or device should be profitable.

An important argument for common use of an aggregate can be the fact that the service can be realized with one efficient aggregate, while individual owners would have to buy as many as 15 aggregates. Using an aggregate Meprozet PN 100 with the output of 6.8 ha/h and a tractor Zetor Z 9641, the annual utilization of the aggregate reaches the value of 1,223.9 h. Using an aggregate of higher output, e.g. Meprozet PN 120 with the output of 10.8 ha/h, with the same number of participants in the common use of the aggregate, the annual utilization of the aggregate drops to the value of 770.6 h. Hence, a possibility arises to widen the circle of participants in the common use of the machine. If aggregates of lower output are chosen, the annual utilization increases to the values to 2,600.6 h for the output of 3.2 ha/h and 1,849.3 for the output of 4.5 ha/h, respectively. Such an increase of the yearly use would have to cause the purchase of two machines or a necessity of charging the jobs with an outside service attendant so that the jobs can be done within the recommended agricultural periods.

CONCLUSIONS

The paper presents a new method of optimizing the choice of agricultural machines consisting in determining the conditions that should be fulfilled for the purchase of a machine to be profitable. The method means using the functional relations describing the dependence between the unit costs of aggregate exploitation for organic fertilization with liquid fertilizers and the output and the yearly time of using the aggregate. Alternative manners of performing the treatment are indicated. These include the following:

1. Having this job done in the form of a service rendered by a specialist firm,

2. common use of machines by a group of farm holders who have to perform similar cultivation treatments.

Points 2 and 3 would also require the creation of possibilities to make full analyses concerning the establishment of such a price of the service or the treatment in case of common use of the machine that it would be acceptable for all the parties interested.

The following conclusions were formulated on the basis of simulation studies:

1. For the farms with the cultivated areas meant for organic fertilization with liquid fertilizers ranging from 56 to 1,986 ha, it is profitable only for the owner of a farm with the area of 1986 ha to purchase tractor Pronar 2048A with the power of 33 kW with an ascenization cart Wukom PA 35A with the output of 3.2 ha/h. This aggregate will be used in the farm for 620.6 h in a year, and the costs of the treatment will be 38,738.4 PLZ.

2. With the assumption that farm owners would possess aggregates consisting of an ascenization cart Wukom PA 35A with the output of 3.2 ha/h and tractor Pronar 2048A with the power of 33 kW: the highest profits can be achieved by the service attendant using an aggregate consisting of an ascenization cart Meprozet ON 120 with the output of 10.8 ha/h and tractor Zetor Z 9641 with the power of 93 kW.

3. With the value of the coefficient increasing the service costs fixed at 1, the price of the service settled by the service attendant is acceptable for all the farm owners with the exception of farms with the area of 1986 ha. The service attendant can do these jobs using all the aggregates taken for analysis.

4. With the value of the cost coefficient equal to 2.0, the price of the service is acceptable for the owners of farms with the area from 56 to 400 ha. These treatments can be profitable for the service attendant using all the aggregates taken for analysis. For the other areas the level of the service prices will not be acceptable and it is recommended to perform the treatments with private aggregates.

5. An important argument for common use of an aggregate can be the fact that the service can be realized with one efficient aggregate, while individual owners would have to buy as many as 15 aggregates. Using an aggregate with a higher output, e.g. Meprozet PN 120 with the output of 10.8 ha/h, with the same number of participants in the common use of the aggregate, the annual utilization of the aggregate decreases to the value of 770.6 h. Therefore, a possibility appears of widening the circle of participants in the common use of the machine.

REFERENCES

1. Muzalewski A., 2001. Wybrane zagadnienia optymalizacji i oceny doboru sprzętu oraz usług do gospodarstw rolniczych [Chosen problems of selection of farm machines and services optimization and evaluation]. Pr. Nauk. 2(4). IBMER-ZP, 59-88. Warszawa [in Polish].

2. Muzalewski A., 2003. Zakup czy usługa – opłacalnosc zakupu i użytkowania maszyn rolniczych na przykładzie kombajnu zbożowego (Purchase or service – the profitability of purchase and use of agricultural machines on the example of a grain combine). Tech. Rol. 4, 8-11. Warszawa [in Polish].

3. Muzalewski A., 2005. Koszty eksploatacji maszyn [Operating costs of machines]. Wyd. IBMER, 20. Warszawa [in Polish].

4. Skwarcz J., 2006a. Wpływ wykorzystania agregatu do nawożenia mineralnego na jednostkowe koszty eksploatacji. Poster na XIII Ogólnopolskiej Konferencji Naukowej “Postęp naukowo-techniczny i organizacyjny w rolnictwie” [The influence of the use of a unit for mineral fertilization on the unitary operating costs. A poster for XIII National Scientific Conference “Scientific, Technological and Organizational Development in Agriculture”], Zakopane. (Praca złożona w Inżynierii Rolniczej do recenzji – The paper sent to Inżynieria Rolnicza for review) [in Polish].

5. Skwarcz J., 2006b. Metoda oceny opłacalnosci wykonania usług nawożenia mineralnego upraw zbożowych Puszczykowo [The method of evaluation of crop mineral fertilization service profitability Puszczykowo 2006]. (Praca złożona w Inżynierii Rolniczej – The paper sent to Inżynieria Rolnicza for review) [in Polish].

6. Statistica 6.0, 2001. StatSoft, Inc. 2300 East 14th Street, Tulsa, OK 74104, USA.

Accepted for print: 07.09.2006

Responses to this article, comments are invited and should be submitted within three months of the publication of the article. If accepted for publication, they will be published in the chapter headed 'Discussions' and hyperlinked to the article.