Application of the boundary line analysis method for the optimisation of the number of tractors used in an agricultural company

Transcription

1 Agric. Eco. Czech, 6, 2 (): 8 Origial Paer Alicatio of the boudary lie aalysis method for the otimisatio of the umber of tractors used i a agricultural comay Miroslav MIMRA, Miroslav KAVKA, Karel OMŠÍK 2, Mariá SRUHÁR Deartmet of Machiery Utilisatio, Czech Uiversity of Life Scieces Prague, Prague, Czech Reublic 2 Deartmet of Ecoomics, Czech Uiversity of Life Scieces Prague, Prague, Czech Reublic Abstract: he boudary lie aalysis method calculates the miimal total aual oeratioal costs used for the otimisatio of umber of tractors owed by agricultural comaies. his calculatio reflects the actual eed of tractors used i the selected time eriods durig a year. he above method is based o data gaied durig five day eriods (so-called etads) i t he lat roductio Farm Estate Láy which belogs to the Czech Uiversity of Life Scieces Prague. Based o the aual use of tractors i the comay, oeratioal costs ivolve tractors owed ad hired. he calculated curve chages i relatio to the total aual costs for the owed tractors. he ecoomically otimal umber of the owed tractors would be reached at the miimum oit where the total aual costs curve is low whilst all workig oeratios i the comay have bee doe. Due to the use of tractors durig the etads, it is recommeded to ow exactly the umber of tractor-machie sets give by the calculated miimum. For all the other works, it is advisable to use hired tractors, oeratioally leased tractors or outsourced services. Key words: costs otimisatio, tractors deloymet, tractor umber otimisatio he curret ecoomic situatio requires that agricultural comaies otimise their costs to be able to achieve the roductio rofitability. he otimisatio ca be doe i may ways. Regardig tractors, it ca be solved by determiig their otimal umber i the comay, decreasig of oeratioal cost, chagig the roductio structure ad techological methods or usig more efficiet ad larger tractors categories. Pulley ad Chali (28) develoed a comuter alicatio called the Commo Agricultural ractor Selectio System (CASS). It uses mathematical models for may asects of techological oeratios i order to select the cost-effective ad roer tye of tractor ad to determie the techological oeratio of soil tillage ad sowig i srig. he climate coditios (the temerature of soil surface, the dew oit etc.) with the soil tye, the revious method of soil tillage, etc. are cosidered. Søgaard ad Sørese (2) created a model for the otimisatio of tractor-machie sets that miimises costs. It takes ito accout all items of the variable ad fixed costs, the farm size ad the cro rotatio. he outut of this model gives a roosal o the otimal machie size ad the related ower ad umber of tractors. he rogram also calculates the costs ad time eeded for the workig oeratios. Audsley (98) created aother rogram to elaborate the tractor-machie sets otimisatio ad the costs calculatio for the autum tillage followed by the soil rearatios ad sowig. It uses the weather forecastig, the effect of soil comactio ad the comliace with the timeliess of sowig. Jaot ad Cairol (99) develoed a model that allows desigig the otimal layout of cros i the farm. Based o this, it is ossible to calculate gross rofit, the demad for maower, equimet requiremets ad the size of the machie maaged lad. Camarea et al. (2) created a model for multile farms that allows the selectio of machies from a database for each farm searately. his model allows calculatig miimal costs for each of the modelled farms based o its size, the time workig rogress, the ossible Suorted by the Miistry of Educatio, Youth ad Sorts of the Czech Reublic (Projects No. MSM 66795).

2 Origial Paer Agric. Eco. Czech, 6, 2 (): 8 combiatios of machies, variable ad fixed costs redictios icludig future chages. Akarte ad Askhedkar (99) cocetrated o the calculatios of ecoomic effectiveess of tractors deloymet with regard to the break-eve oit calculatio of each oeratio as tillage, soil rearatio, sowig etc. Wa Ismail (998) moitored the tractor s deloymet ad came to the coclusio that the farms, which grow more tyes of cros, reach a higher level of tractor utilisatio tha the farms with moocultures. his is caused by the ecessity to erform more differet workig oeratios with resect to the higher umber of cros. hereby, it is efficiet to focus o limitig the umber of the mai tyes of cros ad to reduce the oeratio costs of tractors. Abrham et al. (27) described the system AGROEKIS used i the Czech Reublic. It works with tables showig ad comarig machie costs, the techical suort of oeratios, the techology ad ecoomics of cro roductio. Noe of the above metioed rograms allows for the otimisatio of the umber of tractors owed by the farm with regard to the tractors deloymet accordig to works durig the year ad the ossibility to rovide a art of works through hired services i order to reduce the costs related to the tractors deloymet. MAERIAL AND MEHODS he otimisatio of the umber of tractors based o the boudary lie aalysis is demostrated o the followig examle. he Farm Estate Láy (further SZP Láy) cultivates ha of lad, of which ha is arable lad. he farm ows tractors, whereas tractors are equied with a egie u to kw, 6 tractors u to 7 kw, 5 tractors above 7 kw ad their average age is 8 years. he umber of tractors deloyed was moitored throughout the year i differet etads ad also the umber of workig hours of the tractors was recorded. Moitorig was erformed i lie with the followig oeratio grous: soil tillage, fertilisatio, grai ad fodder cros harvestig, ad overheads. here were moitored the costs of tractors owed ad hired. he oeratio costs of tractors owed by the comay ca be determied as the sum of the aual fixed costs ad variable costs deedig o the umber of hours of the actual use durig the year at the selected itervals. he aual fixed costs cosist of dereciatio costs, costs reflectig iterest of ow caital, bak iterest or margi fiace leases, the madatory isurace ad vehicle isurace costs, the costs of storig ad garagig. he variable costs cosist of the fuel ad lubricats costs, maiteace ad reair costs, labour costs for the oerators as well as the costs of sulies. he costs of oeratios hired ca be calculated the as the cotract rice of the service multilied by the umber of hours of oeratio. he total aual costs are calculated afterwards as the sum of the costs of tractors owed by the comay ad the costs aid for the services. his relatioshi is exressed by the followig Equatio. AC i AFC ( I x i N i t v C x v t dt UVC dt) (CZK/year) () where: AC = total aual costs of tractors oeratio i the comay (CZK/year) AFC = aual fixed costs of the owed tractor oeratio (CZK/year) v = umber of the ecessary owed tractors i the comay i the iterval v = umber of tractors owed by the comay withi a year UVC = uit variable costs of the owed tractor oeratio (CZK/hour) i = itervals of tractors oeratio withi a year ( = to ) C = rice for service er hour (CZK/hour) N = umber of the hired tractors i the comay i the iterval t = hours of tractors oeratio withi the iterval (t = to x) (h) = umber of itervals of tractors oeratio (I i = i) I i he itervals of moitorig the umber of hours of tractors deloyed ca be chose differetly, e.g. a day, etad, week, decade etc. Due to the deedece of agriculture o the atural ad climatic coditios ad agro-techical deadlies, moitorig of the tractors deloymet was based o etad itervals. o register the deloymet of tractors, every etad durig the year ca be used ( = to ), whereas the actual umber of hours of the tractors deloymet i a etad is recorded (t = to x). Also the etad costat (k ) ca be used for registerig, which meas the deloymet of stadard hours of tractor use (stadard umber of hours of oe tractor i a etad, i.e. i five days 8 5 = hours of work er oe tractor er 2

3 Agric. Eco. Czech, 6, 2 (): 8 Origial Paer etad; t = ). Subsequetly, the Equatio ca be modified ito the shae of the Equatio 2, where a year is divided ito etads ad the umber of the actual tractors deloymet hours i a etad is used for cost calculatio. Alteratively, Equatio ca be adjusted ito the icremetal form as reseted i Equatio 3, if the etad costat for the calculatio of cost is alied. AC AFC ( P t v C v t dt UVC dt) (CZK/year) (2) where: t = hours of tractors oeratio withi a etad (t = ) (hour) P = umber of etads of tractors oeratio (P = ) v = umber of owed tractors used i the etad = etad of tractors oeratio withi a year ( = to ) AC AFC ( ( N C k UVC v k ) ) (CZK/year) (3) where: k = etad arameter (k = ) (h/tractor ad etad) he total costs of tractors ca be determied by multilyig the umber of hours of usig tractors ad the costs of their oeratio i accordace with the above metioed equatio. herefore, these costs rereset the area show i the chart. Usig the method of the boudary lie aalysis, the roortio of costs attributable to tractors belogig to the comay (the area uder the lie showig the umber of ow tractors) ad the costs of the oeratio outsourced (the area show i the chart above the lie) ca be illustrated. he roortio of costs attributable to the owed ad hired tractors is variable for differet combiatios of the umber of tractors. he otimal umber of tractors is the miimum iflexio oit (break-eve oit) of the total cost curve. his miimum ca be foud through the local miimum, i.e. if the first derivative of the Equatio 3 is raised to zero. Also, the result ca be derived aalytically by calculatig the total costs for differet combiatios of the umber of tractors owed by the comay ad the umber of tractors hired, resultig i the determiatio of cost miimum. RESULS AND DISCUSSION Calculatio of the total aual oeratio cost of all tractors i the comay has bee doe as reseted i the Equatio. Combiatios of the umber of owed tractors i the iterval to 3 tractors are used. he umber of 3 tractors was used due to modellig the costs above the maximum umber of tractors ecessary to erform all oeratios durig the seaso as well as the umber of tractors owed by the comay. he aim was to simulate the develomet of costs of the comay, if it ows more tractors tha it actually has. A rage of to uits was used for the hired tractors, where the uer limit corresods to the maximum umber of tractors that are ecessary to rovide all workig oeratios durig the seaso. I terms of all workig oeratios, a ecoomically otimal combiatio of the owed ad leased tractors is achieved i the miimum of the total aual costs for tractors oeratios. he cost modellig was doe usig the VBA i the MS Excel. Figure shows the tractors deloymet durig the year accordig to the realisatio of workig oeratios of basic soil tillage (ZZP), fertilisatio ad oeratios related to the cultivated cros ad overhead costs (works that caot be assiged to ay of the workig rocesses). Whe modellig the costs of oeratig tractors, the umber of the owed tractors was i the iterval to 3 uits ad the umber of the hired tractors was withi the iterval to tractors. Model calculatios were doe for differet combiatios startig with the combiatio whe all works were doe oly by the hired tractors ad o owed tractors u to the combiatio of 3 owed ad o hired tractors. As it is evidet from the Figure 2, which shows the rogress of the total aual costs of all tractors for differet combiatios of the owed ad hired tractors, there is a gradual degressive reductio of costs from the amout of CZK 7.9 millio. he reaso for this reductio is the growth of umber of owed tractors that were fully used. he curve miimum is achieved at deloymet of 9 owed tractors, whe the total costs are CZK 5 millio, whereas the costs of owed tractors achieve the amout of CZK. millio ad of hired tractors CZK.9 millio. his is the otimal umber of owed tractors i the terms of costs. From this umber of owed tractors, almost a liear icrease of costs is evidet. his is caused by the icrease of the umber of owed tractors, where the owed tractors are ot fully utilised which leads to 3

4 Origial Paer Agric. Eco. Czech, 6, 2 (): 8 Deloymet of tractors Soil tillage Fertilisatio Grai harvestig Fodder harvestig Overheads Jauary February March Aril May Jue July August Setember October November December Petads durig the year Figure. Chart of the tractors used durig a year accordig to workig rocesses the growth of the fixed costs er hour of oeratio. Hired tractors are used oly i seasoal eaks whe it is ot ossible to erform the works by ow tractors. Reachig the umber of owed tractors, o hired tractors are used ad all oeratios are rovided oly by the owed tractors. At this oit, the costs of the oeratio of owed tractors amout to CZK 7 millio. As the umber of owed tractors rises beyod this limit, the liear growth of costs is cotiuig, which is caused by the accumulatio of fixed costs that caot be traced to workig oeratios because of the tractor uder-utilisatio. he comaies that are holdig a high umber of tractors regardless their utilisatio should kee this fact i mid. Such overcaacity icreases their costs that are ot set effectively. I the terms of the total costs, it is aaret from the chart that durig the seaso, it is efficiet to lease tractors for certai oeratios which leads to costs savig. he Figure 3 shows the rogress of the hired tractors costs, of the owed tractors costs ad the total costs. he curve of the total costs is i early stage characteristic by a fast decrease with the icreasig umber of owed tractors, later it gradually slows dow. his is caused by the fact that the costs of services are higher tha the costs of the oeratio of owed tractors. herefore it comes to a quick cost reductio at the begiig as the umber of owed tractors icreases. he miimum of the total cost curve is i the oit of otimal umber of tractors oeratig i the comay. From this oit, the curve of the total costs is gradually growig. Crossig over the umber of owed tractors meas, that there is o eed to use ay hired tractor ad therefore o costs of the hired tractors occur. he curve of the cost of owed tractors is decliig with their growths; it is obvious that this is caused by decreasig the roortio of the fixed costs er hour of the Figure 2. Progress i the total aual costs for the icreasig umber of owed tractors whe other eeded oeratios are doe by hired tractors otal aual costs of all techological oeratios (i thousad CZK) Number of owed tractors

5 Agric. Eco. Czech, 6, 2 (): 8 Origial Paer Costs (i millio CZK) Cost of owed tractors Cost of hired tractors otal cost Number of owed tractors Figure 3. Develomet of the costs of owed tractors, hired tractors ad total costs tractor oeratio. After reachig the umber of owed tractors, which ca rovide all the work, the costs i the comay are created by the roortio of fixed costs because the work of these tractors is ot ecessary with regard to the scoe of the cultivated area. he shae of the total cost curve show i the Figure 3 has already bee described above. It is evidet that from the umber of tractors the curve is similar to the curve of costs of owed tractors, whe o tractors are additioally used due to the limited scoe of works which is reflected i the strog erformace of fixed costs. Figure is a curve showig the differeces betwee the costs of the oeratio of owed ad hired tractors. At 5 tractors, the oeratio costs of the owed ad hired tractors are aroximately at the same level. It is aaret from the figure that the costs are fallig raidly i the early stage, as the umber of owed tractors is goig u. he costs comared to the revious value fell by 26.7% ad at the icreased umber of owed tractors reach the rate oe to two also by 26.7%. Subsequetly, if the umber of owed tractors is icreased to three, the costs will be by 7.7%, at four tractors by 7.3% ad at five the costs are reduced by 9.%, whe their miimum is achieved. By this oit, there is evidet a fast reductio of the differece betwee the costs of the hired ad owed tractors, where the differece is gradually decreasig with the icreased umber of owed tractors. From five ow tractors, the costs ted to grow with resect to the umber of ow tractors by.3%;.3% etc., ad the differece betwee costs is gettig smaller with the icreasig umber of ow tractors. Usig ow tractors, the icremet is costat ad makes 2.5%. he costs of outsourced services are higher tha the costs of ow tractors, which ca exlai the fast cost reductio achieved. At 5 ow tractors, there is secured the eed of most workig oeratios durig the year ad icreasig the umber of tractors results i the cost growth maily due to the icreased Differeces betwee the costs of owed ad hered tractors (i millio CZK) Number of owed tractors Figure. Chart of absolute differeces betwee the costs of owed ad hired tractors 5

6 Origial Paer Agric. Eco. Czech, 6, 2 (): 8 3 Costs of hired tractors Costs of owed tractors 3 Number of tractors 2 Number of owed tractors 2 Costs (i thousad CZK) Jauary February March Aril May Jue July August Setember October November December Petads durig the year Figure 5. he structure ad timig costs of owed ad hired tractors roortio of fixed costs ad the fast reductio of the costs of hired tractors that are used oly if eeded. he otimum of the total costs is achieved oly whe 9 ow tractors are used, because at this umber of tractors the lowest sum of costs of the owed ad hired tractors is achieved, i.e. the miimum of the total costs. he total costs of tractors ca be calculated by the Equatio (2). hese costs i lie with the etads are show i the chart o Figure 5 i the colums. As it is aaret from the Figure 5, usig the method of the boudary lie aalysis divides the chart ito two arts. he area uder the lie shows the costs of the work rovided by owed tractors. he area above the lie shows the costs of the work of hired tractors, i.e. the situatio whe the umber of owed tractors i the etad is ot able to rovide all oeratios. here is also evidet a higher umber of tractors, which are eeded i te etads oly, esecially durig the harvest time whe differet workig oeratios cumulate. From this ersective, it is ossible to solve the otimisatio by orgaisatioal measures (e.g. by icreasig the tractors shifts, by the chage of the structure of cros etc.). Usig the method of the boudary lie aalysis that itegrates the area of the chart ad summarises the total aual costs i each etad of the year, the develomet of the total aual costs ca be modelled usig differet combiatios of the umber of owed ad hired tractors. From Figures 6, 7 ad 8, there is oticeable the chage of costs (the areas of the chart) at usig owed tractor i the amout of ; ad 3 vehicles. It shows also the icrease of the costs i the etads. Comarig Figures 6 ad 7 shows that i the case of works rovided by owed tractors, the costs are higher i the etads whe the tractors are ot fully used due to the fixed costs er hour of work. O the cotrary, the costs of hired tractors are higher i the etads whe the eaks are comared to the works doe by owed tractors 3 Costs of hired tractors Number of owed tractors Costs of owed tractors 3 Number of tractors 2 2 Costs (i thousad CZK) Jauary February March Aril May Jue July August Setember October November December Figure 6. he costs i each etad durig the realisatio of work by hired tractors oly 6 Petads durig the year

7 Agric. Eco. Czech, 6, 2 (): 8 Origial Paer 3 Costs of hired tractors Costs of owed tractors Number of owed tractors 3 Number of tractors 2 2 Costs (i thousad CZK) Jauary February March Aril May Jue July August Setember October November December Petads durig the year Figure 7. he costs i each etad durig the realisatio of work by owed tractors solved by rovidig the services. As it is show i Figures 7 ad 8, the icreasig umber of owed tractors that are ot fully used leads to the icrease of the costs due to the fixed costs growth. CONCLUSIONS May agriculture comaies kee usig tractors of a high average oeratio age which ofte reflects the bad techical coditios or high fuel cosumtio. Also the umber of tractors owed by the comaies is higher tha ecessary for the workig oeratios. If the comay wats to reduce its cost, it is essetial to evaluate the structure of tractors ad to get rid of the useless tractors. he otimisatios caot be solved oly from the ecoomic ersective, as it is imortat to cosider the agro-techical requiremets too. he boudary lie aalysis method ca hel the comay to decide what umber of tractors is ecoomically otimal with resect to their deloymet durig the year i the etads. Furthermore, the results of the aalysis ca be used to determie which volume of works ca be rovided by services, ad based o the workig oeratios i the etads, to select the aroriate oeratios to be rovided by services. he results of the aalysis show that outsourcig may be efficiet esecially durig the seaso eaks with regard to the costs that are related to the ossessio of ow tractors ad their use durig the year. he seaso eaks occur oly i a few short eriods of time whe a high umber of tractors is eeded i the comay. Providig works i these eriods ca be doe by sigificatly reduced total costs related to tractor oeratios. Reducig the umber of tractors i the comay ca also icrease the use of tractors, thus itroducig Costs of hired tractors Costs of owed tractors Number of owed tractors 3 Number of tractors Costs (i thousad CZK) Jauary February March Aril May Jue July August Setember October November December Petads durig the year Figure 8. he costs i each etad durig the realisatio of work by 3 owed tractors 7

8 Origial Paer Agric. Eco. Czech, 6, 2 (): 8 more shifts durig the eak times. For this to occur, agriculture comaies have to focus o the reewal of tractors. By urchasig ew tractors with a higher reliability, it is ossible to esure a timely imlemetatio of the work required i the eterrise. More shifts ca be used esecially for the oeratio with the basic soil tillage ad sowig. Oe of the crucial factors eeded for the otimisatio of the umber of machies i the comay is the cosideratio of the egative imact of delayed work oeratios. It is imortat to erform all the work oeratios i a timely maer i order to avoid uecessary losses or additioal costs. Kolek et al. (997) focused o the tolerace of witer rae, witer wheat ad srig barley with regard to their delayed harvest. he aim of this observatio was to determie the biological rocess of the losses ad quality chages of the above whe harvested after their otimal maturity eriod. Higher losses were recorded o rae, relatively small losses o witer wheat ad srig barley. Qualitative traits such as the weight of oe thousad seeds, oil ad rotei cotet, the roortio of frot grai ad other remaied uchaged. However, a higher risk of losig food quality or maltig quality was oticed. he amout of the losses deeds o the harvested cro as well as the weather coditios durig the give year. Kavka et al. (997) cocluded from their observatios that the ossibility of usig combie harvesters from the exteral service roviders makes the ow cro more rofitable durig oor weather coditios (esecially whe the bad weather lasts log which affects egatively the cro eaks). Determied by the bad weather, oly short eriods of time are roitious for the harvest. his meas that the ecessary tools ad machies are eeded at the same time ad caot be used gradually (as it would be alicable durig the ormal weather coditios). herefore, eve a comay which is able to erform all the oeratios with its ow machies eeds to cooerate with other agriculture comaies or to outsource the services if the challege of a foul weather occurs. his is imortat so that the uecessary costs ca be miimised. REFERENCES Abrham Z. Kovářová M., Kociáová V., Herout M., Scheufler V. (27): echické a techologické ormativy ro zemědělskou výrobu. (echical ad techological orms for agricultural roductio.) VÚZ, Praha, PDF documet. Available at htt://svt.i.gi.cz/vuzt/orade/ rirucky/27-5.df?meuid=63 (accessed 3.7.2). Akarte M.M., Askhedkar R.D. (99): Ecoomics of tractor utilizatio for agricultural oeratios. Joural of Modelig, Measuremet & Cotrol, : 6. Audsley E. (98): Use of weather ucertaity, comactio ad timeliess i the selectio of otimum machiery for autum field work: A dyamic rogramme. Joural of Agricultural Egieerig Research, 29: 9. Camarea E.A., Gracia C., Cabrera Sixto J.M. (2): A mixed iteger liear rogrammig machiery selectio model for multifarm systems. Biosystems Egieerig, 87: 5 5. Jaot P., Cairol D. (99): Liear rogrammig as a aid to decisio-makig for ivestmets i farm equimet for arable farms. Joural of Agricultural Egieerig Research, 59: 79. Kavka M., Kolek L., Vašák J., Faměra O., Pošar B. (997): Otimalizace očtu a využití sklízecích mlátiček s ohledem a faktor včasosti sklizě. (Otimisatio of the umber ad utilisatio of combies accordig to the term of harvest.) Zemědělská techika, 3: 59. Kolek, L., Vašák, J., Faměra, O., Kavka. M. (997): Vliv termíu sklizě a ztráty a kvalitu rodukce řeky, šeice a ječmee. (he effect of time of harvest o losses ad quality of roductio of rae, wheat ad barley.) Rostliá výroba, 3: Pulley R.A., Chali J. (28): A rogram to combie climate, soil, ad tractive modelig techiques to redict agricultural field-days ad otimize tractor selectio. I: ASABE Aual Iteratioal Meetig 28, 3: Providece, Rhode Islad, 29 Jue 2 July, 28. Søgaard H.., Sørese C.G. (2): A model for otimal selectio of machiery sizes withi the farm machiery system. Biosystems Egieerig, 89: Wa Ismail W.I. (998): Cost aalysis model for cro roductio machiery system. Agricultural Mechaizatio i Asia, Africa ad Lati America, 29: 6. Received: th Jauary 23 Acceted: 9 th May 23 Cotact address: Miroslav Kavka, Czech Uiversity of Life Scieces Prague, Kamýcká 9, 65 2 Prague 6, Czech Reublic kvk@tf.czu.cz 8