Cdn. J. o f A g r i c . Economics 33 (March 1985)

Calcu

us

ating Least-Cost Machinery Size for Grain Farms

ng Electronic Spreadsheets and Microcorrputers

W i l l i a m J. Brown* and Richard A . Schoney**

Proper mach ine ry s i z i n g f o r a g i v e n f a r m has t h e p o t e n t i a l o f reduc - i n g c o s t s and t h e r e b y i n c r e a s i n g p r o f i t s s u b s t a n t i a l l y . The microcom- p u t e r and t h e e l e c t r o n i c sp readshee ts now a v a i l a b l e a r e t h e l a t e s t t o o l s f a r m b u s i n e s s managers can use t o s o l v e t h i s r e c u r r e n t , complex and i m - p o r t a n t p rob lem. T h i s paper f i n d s t h e l e a s t - c o s t c o m b i n a t i o n o f mach in- e r y t a k i n g i n t o accoun t f i x e d , v a r i a b l e and t i m e l i n e s s c o s t s . The model i s s o l v e d u s i n g a m ic rocompu te r sp readshee t .

La bonne g rosseur d 'gqu ipemen t e n p r o p o r t i o n avec l a g r o s s e u r _ d e l a fe rme v o n t d e p a i r e t donne comme r i s u l t a t une r i d u c t i o n des c o u t s e t p a r l e f a i t &me augrnente les p r o f i t s . Le m i c r o - o r d i n a t e u r e t les c h i f - f r i e r s 6 l e c t r o n i q u e s m a i n t e n a n t d i s p o n i b l e s s o n t l e s d e r n i e r s a p p a r e i l s que le i e r a n t d ' a f f a i r e s de fe rme p e u t se s e r v i r pou r r e s o u d r e le prob - lame complexe d e c h o i s i r 1 ' i q u i p e m e n t a p p r o p r i g . C e t t e G iude d e t e r m i n e l a comb ina ison de mach ines r e q u i s e s q u i e s t l a p l u s i conomique en t e n a n t compte des c o a t s f i x e s e t v a r i a b l e s a i n s i que des cou"ts o p p o r t u n s . Ce mods le e s t r i s o l u avec I ' a i d e d ' u n c h i f f r i e r de m i c r o - o r d i n a t e u r .

Introduction

S e l e c t i n g mach ine complements t h a t m i n i m i z e b o t h mach ine c o s t s and t i m e l i n e s s p e n a l t i e s i s a r e c u r r e n t , complex , and i m p o r t a n t d e c i s i o n c o n f r o n t i n g f a r m b u s i n e s s managers. Mach ine ry s i z i n g d e c i s i o n s and gen- e r a l m a c h i n e r y management a r e ma jo r f a c t o r s a f f e c t i n g f a r m p r o f i t a b i l i t y and f i n a n c i a l h e a l t h , I n Saskatchewan, fa rm mach ine ry i n v e s t m e n t d o u b l e d i n c u r r e n t d o l l a r s be tween 1976 and 1982 (Saskatchewan A g r i c u l - t u r e ) . The 1984 Top Management Workshops i n d i c a t e t h a t mach ine ry and b u i l d i n g o w n e r s h i p c o s t s accoun ted f o r a p p r o x i m a t e i y 25 p e r c e n t o f t h e t o t a l c o s t o f p r o d u c i n g wheat . The o b j e c t i v e o f t h i s paper i s t o i n v e s - t i g a t e t h e m a j o r economic f a c t o r s t h a t i n f l u e n c e mach ine ry s i z i n g , u s i n g Saskatchewan fa rms as an example. I m p o r t a n t f a c t o r s i n c h o o s i n g t h e l e a s t - c o s t mach ine s i z e a r e d i s c u s s e d as w e l l as v a r i o u s approaches t o m o d e l l i n g . I n o r d e r t o make t h e t h e o r y as b r o a d l y a p p l i c a b l e as p o s s i - ble, t h e m a j o r i t y o f t h e paper w i l l be d e v o t e d t o d e v e l o p i n g t h e founda-

9: Depar tment o f A g r i c u l t u r a l Economics, U n i v e r s i t y o f Saskatchewan > k ~ FARMLAB, U n i v e r s i t y o f Saskatchewan

48

tions for a model based on an electronic spreadsheet software package. The particular model developed uses the Version 1.0 of "Visicalc"l o n a 64K Apple I I + and the Lotus "123" for the I B M PC.

Machinery Sizing: Factors to Consider

Machinery sizing decisions are influenced by many interrelated fac- tors. While the status associated with owning a new machine is impor- tant, only the manager's risk attitude and the economic costs of owning and operating machinery, including timeliness penalties and major fac- tors are considered here. These factors cannot be considered in isola- tion from one another but must be considered jointly because of their interrelationships. A farm manager's attitude toward bearing risk is influenced by his goals and objectives, the financial ability of the farm business to assume risk, and the size of the possible gains and losses resulting from the decision (Nelson et al.). Goals and objec- tives that priorize increased leisure time or long-term business surviv- al over immediate profit maximization may result in distinctly different machinery sizing decisions. Farm managers with different net worths, debt-to-equity ratios and cash flows will have different attitudes to- ward bearing risk and thereby may choose machinery sizes (and replace- ment patterns) that are different even though all other circumstances are similar. Finally, if the potential loss is large, the farm manager may try to avoid the situation if possibie or take measures to reduce the probability of occurrence. The loss incurred from a crop failure due to under-sized machinery in any one year can produce such disastrous consequences that the farm manager may wish to invest in excess machin- ery capacity.

Economic costs are the second major factor influencing machinery se- lection. Costs are traditionally divided into fixed and variable. Fixed machinery costs include capital recovery charges, insurance and housing costs while variable machine costs include the usual operating costs such as charges for fuel, lubrication, labor. repairs and mainte- nance and timeliness penalties. While not a cost in the usual sense, timeliness i s an opportunity cost associated with reduced yield due to delayed or untimely machinery operations. The optimum machine size min- imizes the total machine costs subject to a given production plan and the manager's attitude toward risk.

Electronic spreadsheet is the name given to microcomputer programs such as Visicalc and Lotus 123. An electronic spreadsheet is a two dimensional matrix of rows and columns. Each matrix location is de- fined by a row and column and is referred to as an element. Each ele- ment can contain a number, label or formula. These types of programs derive their power from their ease of use and instant recalculation abi 1 i ty.

49

Model ling the Machinery Sizing Problem

A r e v i e w o f t h e l i t e r a t u r e d e a l i n g w i t h f a r m mach ine ry s i z i n g r e v e a l s t h r e e b a s i c approaches t o t h e p rob lem. The f i r s t approach c a n be l a - b e l l e d t h e "Prob lem S o l v i n g Model" (Canfarm, Bowers) w h i c h i s based on b u d g e t i n g p r o c e d u r e s . T h i s approach does n o t d e r i v e opt imum mach ine ry s i z e f o r a g i v e n f a r m because i t e x c l u d e s t h e i n t e r r e l a t i o n s h i p s be tween t i m e l i n e s s and y i e l d s . By o m i t t i n g t i m e l i n e s s " p e n a l t i e s " , t h i s ap- p r o a c h wou ld t e n d t o g e n e r a t e s m a l l e r t h a n opt imum s i z e s . However, t h e y do g e n e r a t e " b a l l p a r k " r e s u l t s and a r e r e l a t i v e l y s i m p l e and inexpen- s i v e t o use . The second approach can be l a b e l l e d t h e "Leas t -Cos t Model" i n w h i c h t h e l e a s t - c o s t c o m b i n a t i o n o f mach ine ry i s d e t e r m i n e d f o r a s p e c i f i c s i t u a t i o n (Hunt , O ' C o n n e l I e t a l . , Bor rows and Siemans, Chan- c e l l o r , Mc lsaac and L o v e r i n g , Hughes and H o l t m a n ) . W h i l e t h e l e a s t - c o s t mode ls a r e c o n s i s t e n t w i t h p r o f i t m a x i m i z a t i o n i n t h a t t h e " c o s t s " o f t i m e l i n e s s a r e i n c l u d e d , e n t e r p r i s e c o m b i n a t i o n s a r e n o t o p t i m i z e d . The t h i r d app roach can be c a l l e d t h e "Maximum P r o f i t Mode l " . I n t h i s model, e n t e r p r i s e s e l e c t i o n , mach ine s c h e d u l i n g and l a b o r usage a r e o p t i m i z e d s u b j e c t to v a r i o u s r e s o u r c e and t i m e c o n s t r a i n t s (Zen tne r e t a l . , Can- fa rm, Danok e t a l . ) . W h i l e many Maximum P r o f i t Mode ls a r e n o t s p e c i f i - c a l l y d e s i g n e d t o o p t i m i z e mach ine ry s i z e s , t h e y can g i v e v a l u a b l e i n - s i g h t as t o t h e e f f e c t s o f v a r i o u s mach ine s i z e s on p r o f i t s . The o b j e c t i v e h e r e i s t o p r e s e n t a r e l a t i v e l y s i m p l e model t h a t c a l c u l a t e s t h e l e a s t - c o s t c o m b i n a t i o n o f mach ines f o r a g i v e n f a r m s i t u a t i o n .

The Least -Cos t Approach Using Electronic Spreadsheets

The o b j e c t i v e o f t h e l e a s t - c o s t m a c h i n e r y s i z i n g sp readshee t model i s t o m i n i m i z e t h e sum o f f i x e d , o p e r a t i n g and t i m e l i n e s s c o s t s f o r t h e en- t i r e f a r m mach ine ry complement. The sp readshee t model bo r rows l i b e r a l l y f r o m D o n n e l l Hunt i n d e v e l o p i n g t h e t e c h n i c a l e q u a t i o n s b u t o m i t s t h e r e l a t i v e l y u n i m p o r t a n t and more t e c h n i c a l e n g i n e e r i n g v a r i a b l e s such as t i r e b a l l a s t and p e r c e n t s l i p . The l e a s t - c o s t p r o c e d u r e i s an i t e r a t i v e p r o c e d u r e w h i c h maps t h e ave rage t o t a l c o s t c u r v e o v e r a r a n g e o f t r a c - t o r s i z e s . The p r o b l e m can b e s t a t e d as

(1)

where TC = t o t a l c o s t o f mach ine complement, F C p = power u n i t f i x e d c o s t s ,

O C i = v a r i a b l e c o s t s o f o p e r a t i o n i ,

T. = t i m e l i n e s s p e n a l t i e s o f o p e r a t i o n i and

F C i = f i x e d c o s t s o f non-power u n i t s ( imp lements ) i n o p e r a t i o n i

N o t e t h a t t o t a ! c c s t c a r e t h e sum o f t h e f i x e d c o s t s a s s o c i a t e d w i t h t h e power u n i t s and b o t h t h e v a r i a b l e and f i x e d c o s t s a s s o c i a t e d w i t h pow- e r e d o r d rawn imp lements .

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Fixed Costs

Fixed costs include interest o n investment, loss in machinery value, insurance, housing and taxes. T h e first two costs are annualized into an equal annual cost figure called the capital recovery charge (CRC).

( 2 ) CRC = (PP - SV) AM;^,) + r (SV)

where CRC = capital recovery charge ($/year), PP = purchase price,

SV = salvage value,

r = interest rate,

yrs = useful life and

In this example, it is assumed that the salvage value at the end of the machine's useful life is ten percent (10%) of the original purchase price. For a discussion o n inflation rates, salvage values and the CRC refer to Schoney and Finner. Insurance, housing and taxes are set at 2.75 percent of the purchase price (Hunt). Total fixed costs expressed as a decimal percent of the purchase price are

(3) FC% = (1-.l) (AMbrS) + r(.l) + .0275

where FC% = fixed cost percentage per unit of size,

1 = purchase price per unit of size,

. 1 = salvage value (SV) at end of useful life as a percent of purchase price per unit of size and

.a275 = insurance housing and taxes as a percent of purchase price per unit of size.

Operating Costs Annual operating costs, OC;, include repairs and maintenance, oil,

fuel and labor and are a function of the area covered, speed of opera- tion, field efficiency and width of the machine.

(4) oci = &[(rmi + 0. + f i ) w + LiJ Swe

where 0ci = annual operating cost of implement i ($/year),

c = constant (8.25 English system, 10 metric),

A = area covered (a, ha),

S = speed of operation (mph, kmph) ,

e = f i e l d e f f i c i e n c y ( % ) ,

w = w i d t h o f mach ine ( f t , m),

r m =

o =

f =

L =

R e p a i r and ma Purchase D r i c e t u r e ) . p e r c e n

r e p a i r s and ma in tenance c o s t ( $ / h r ) ,

o i 1 c o s t ( f / h r ) ,

f u e l c o s t ( $ / h r ) and

l a b o r c o s t ( $ / h r ) .

n tenance c o s t a r e e s t i m a t e d as a c o n s t a n t pe rcen tage o f per hou r and v a r y by mach ine t y p e (Saskatchewan A g r i c u l -

The c o s t o f o i l , f i l t e r s , g rease , e t c . , i s e s t i m a t e d t o be 15 t of t h e f u e l c o s t (Schoney). Fue l c o s t i s a f u n c t i o n o f t h e p e r -

c e n t l o a d i n g , f u e l p r i c e and t o t a l h o u r s o f t r a c t o r use.

(HRST) (PD) (MAXPTOHP) (pL i ) / l o o

(5) f i = (1.20) (2.23 + .20PLi - .OO98(PLzi))

where f . = t r a c t o r f u e l c o s t ,

Max PTOHP = t h e s i z e o f t r a c t o r t h a t w i l l p u l l a l l imp lements w i t h i n l o a d f a c t o r of no more t h a n 80 p e r c e n t ,

PL = p e r c e n t l oad used b y t h e ith implement (maximum 80 p e r c e n t ) ,

1.20 = c o n v e r s i o n f r o m Amer ican t o i m p e r i a l g a l l o n s ,

HRST = t o t a l t r a c t o r hou rs and

PD = p r i c e o f d i e s e l f u e l p e r i m p e r i a l g a l l o n .

Timeliness Costs

T i m e l i n e s s i s t h e f i n a l annua l c o s t f a c t o r t o c o n s i d e r and perhaps t h e m o s t d i f f i c u l t t o measure w i t h any p r e c i s i o n . T o t a l t i m e l i n e s s c o s t i s a f u n c t i o n o f a r e a covered, speed o f o p e r a t i o n , w i d t h o f machine, f i e l d e f f i c i e n c y and t h e v a l u e of t h e t o t a l c r o p l o s t p e r day o f d e l a y .

(6) Ti = cA KYVCa Swe Uh(sc) ( n t )

where T. = t i m e l i n e s s c o s t o f imp lement i ($/year), I

K = t i m e l i n e s s loss f a c t o r (amount o f c r o p y i e l d l o s t p e r day of d e l a y ) ,

Y = p o t e n t i a l c r o p y i e l d ,

V = v a l u e o f c r o p ($/bu, $/kg. e t c . ) ,

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Ca = crop area (a, ha),

U = fractional utilization of total time. weather and soil texture dependent,

h = total hours available per day,

sc = 2 for premature or delayed schedules, 4 for ba 1 anced scheduling, e.g,, delayed scheduling is waiting for crop to mature before beginning to harvest usually 2 for Sask- atchewan crops (Hunt) and

nt = number of times Ca should be divided because of dispersed optimum times, e.g., different varieties of a crop or different crops mature at different times so the optimum time of harvest may be dispersed over a number of differ- ent times, usually 1 for Saskatchewan conditions (Hunt).

The two variables most difficult to measure in Equation 6 are the time- liness loss factor (K) and the fractional utilization o f total time ( U ) .

The timeliness loss factor (K) is a constant that expresses the amount of yield reduction per day of delay. Figure 1 displays the rela- tionship between barley, wheat, durum and flax yields and seeding date in Saskatchewan. These data provide the basis for estimating the K val- ues in Table 1 . In actual practice, K is generally not a constant but varies over the season by crop type and farm location. Nonconstant K values pose a problem in that K cannot be determined independently of final seeding date which is established by machine size. This problem can be overcome by iteratively varying the K value and manually checking ending planting dates associated with the optimal machine complement with the corresponding table date. Since the sizing decision is made at the margin, the initial K value should be somewhat conservative. Unfor- tunately data other than for the province of Saskatchewan and for the midwestern United States are lacking (Table 2).

U i s a decimal constant representing the total time that i s actually available for field work and is a function of weather, soil texture and down time (Table 3). As in the case of K , U is specified as a constant for each machine operation and suffers the same limitations. U may vary as seasonal weather patterns change. In addition, U is stochastic, and its value should also reflect the manager's risk preferences. Again, machine size investments should be mapped over a range of U values.

The Least -Cos t Procedure

The least-cost procedure is decomposed into two phases (Figure 2). Phase 1 optimizes implement size, wi subject to the largest available width. Total implement costs include variable and fixed costs associat- ed with implement i, plus variable costs associated with the power unit. Following Bowers and assuming that both variable and fixed implement costs are constant per unit width, then the least-cost width for a given implement i (where the i subscripts'are dropped for clarity) i s

53

I

UOg. e

900

800

700

3 X

a -4 m -4

--+- M3y 15

# I

r June June 1 15

seeding Date

Figure 1 Yield of Hard Red Spring Wheat, Durum Wheat, Barley and Flax at Saskatoon

Source of Data: H.M. Austenson, "Principles of Agronomy With Ref- erence to Saskatchewan Conditions"

54

Table 1 Timeliness of Loss Factors for Seeding Wheat at Saskatoon (Portion of Total Crop Value Lost Per Day of Delay)

Hard Red Early as Spring Wheat. Possible - Nay 1

May 1 - May 15

May 15 - June 1

June 1 - June 1 5

May 1 - June 15

May 15 - June 15

Crop Loss (+ Gain) Kq/ha Averaqe Crop Yield Kg/ha

= 140 = .078 = +.005/day - - 1790 15

Crop Loss (+ Gain) Kq/ha Average Crop Yield Kg/ha

= 60 = .031 = + .002/day - - 1930 15

Crop Loss (+ Gain) Kdha Averaqe Crop Yield Kg/ha

= 80 - 1990

- .04 = .0025/day 16

C r a n Loss (+ Gain) Kg/ha Average C r w Yield Kg/ha

= 400 = .209 = .01396/day - - 1910 15

Crop Loss (+ Gain) Kq/ha Average Crop Yield Kg/ha

= 420 = .2176 = .00473/day

Crop Loss (+ Gain) Kg/ha Averaqe Crop Yield Kg/ha

= 480 = .2412 = .00778/day

- - 1430 46

- - 1990 31

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Table 2 T i m e l i n e s s Loss F a c t o r K, by Hachine Operation

Machine Operation value

T i l l a g e Seeding Cu l t iva t ion Harvesting

Corn

Green forage Hay ( a l f a l f a ) S m l l g r a i n soybeans

rx tm

0.0001-0.0002 0.002 0.010

0.003 0.002 0.001 0.010 0.004 0.005

Source: D. Hunt, Farm Pmer and Machinery Manaqement.

Table 3: Estimated Minimum Yumkr of Wrking Days and U Values, by Location.

Heavy S o i l U Light S o i l U Working Value Norking Value

Days Days

Spring Xelfort, Yay l-June 15 (45 days) 22.8 -507 31.4 -698

Yay 1S-June 18 (30 days) 18.3 .61 21.4 .713

R q i n a , Yayl-Jurle 14 (45 days) 21.4 .476 29.7 .66 May 1 5 J u n e 24 (30 days) 15.1 .523 20.1 .67

P a l l Melfort , A L ~ . 1-Nov. 8 (100 days) 40.5 .405 12.5 .725

R q i n a , A q . 1-YW. 8 (100 days) 59.3 .593 91.4 .El4

Source: J.S. Dyer et al. "Sprinq f i e l d '.Jorkday ?robabilities fo r Selected S i t e s Across Canada" and J.S. Dyer. "Fa l l F i e ld Workdays i n Canada". Sased on a 90 m r c e n t p r o h b i l i t y .

56

2.

1. Minimize m a 1 m u a l cast of

Size TractOK Accoedinq to %ximum Power Requirement

4 .

I Ekit After 10 r q

Resize A l l Inwlemnts to F i t New “ S m l l e r “ Tractor

F i g u r e 2 Flow Char t o f Leas t -Cos t Mach ine ry S i z i n g Model

L + KYVCa Uh(sc) ( n t )

(7)

where w = t h e l e a s t c o s t w i d t h o f imp lement i .

The mach ine w i d t h , w i , f ound by t h i s p r o c e d u r e , r e p r e s e n t s t h e maximum w i d t h c o n s i s t e n t w i t h a l e a s t - c o s t mach ine ry complement and s i n c e power u n i t f i x e d c o s t s a r e y e t n o t c o n s i d e r e d , a s t a r t i n g p o i n t f o r phase 2.

Phase 2 i s an i t e r a t i v e p r o c e d u r e w h i c h s u c c e s s i v e l y maps average to- t a l c o s t s o f t h e combined power u n i t and imp lements ove r a v a r i e t y o f power u n i t s i z e s . The t r a c t o r i s i n i t i a l l y s i z e d a c c o r d i n g t o t h e max- imnum power r e q u i r e m e n t s f r o m t h e implement s i z e s d e r i v e d i n Phase I . Implement power r e q u i r e m e n t s a r e

(8) PTOHP. = 2 ’ c d l

where PTOHP = p o w e r - t a k e - o f f horsepower o f t r a c t o r (HP) o r (KW) ,

E = energy r e q u i r e m e n t i n drawbar (DB) power (Hp.hr/a) j

o r (Kw.hr /ha) ,

d = c o n s t a n t ( r a t i o o f PTO power t o 08 power) (.86), and

1 = c o n s t a n t ( l o a d f a c t o r ) ( - 8 ) .

57

The energy requi rements f o r v a r i o u s o p e r a t i o n s i n drawbar power hours pe r a c r e (HP-hr/a) ( o r (Kw-hr/ha) can be found i n Hunt. T r a c t o r s i z e s a r e based on a maximum o f 80 pe rcen t load f a c t o r ( I ) . The annual aver- age t o t a l c o s t o f t h e e n t i r e machine complement i n c l u d i n g the power u n i t i s t hen r e c a l c u l a t e d . T h i s machine complement rep resen ts the s t a r t i n g p o i n t f o r i t e r a t i n g t o a sma l le r , b u t l e a s t - c o s t machinery complement. S ince t h e f i x e d c o s t o f t h e power u n i t was n o t i nc luded i n o p t i m i z i n g t h e i n i t i a l w i d t h o f each i n d i v i d u a l o p e r a t i o n , these rep resen t good s t a r t i n g p o i n t s f o r down s i z i n g because no o v e r a l l optimum machine com- p lement can be any l a r g e r and i s l i k e l y t o b e much s m a l l e r .

T r a c t o r s i z e i s t hen decremented by t e n power t a k e - o f f (PTO) horse- power and t h e e n t i r e complement r e s i z e d , i f necessary, t o f i t t h i s "new" t r a c t o r . Machines r e q u i r i n g more PTO horsepower than a v a i l a b l e f rom t h e "new" t r a c t o r a r e r e s i z e d . The down-s iz ing o f t h e t r a c t o r i s succes- s i v e l y repeated, mapping t h e t o t a l annual c o s t s over a range o f power u n i t s and co r respond ing machinery complement s i zes . I n genera l , average t o t a l c o s t s d e c l i n e u n t i l t h e l e a s t - c o s t comb ina t ion i s reached, a f t e r which c o s t s s t a r t i nc reas ing .

Wh i le i n i t s p resen t form, the model b e s t c a l c u l a t e s o n e - t r a c t o r ma- c h i n e r y systems, i t can be extended t o approx imate t w o - t r a c t o r machinery systems by t e s t i n g combinations o f power u n i t s . For example, a two- t r a c t o r system migh t be d e f i n e d by c l a s s i f y i n g o p e r a t i o n s i n t o " b i g " t r a c t o r o p e r a t i o n s and "sma l l " t r a c t o r o p e r a t i o n s and o p t i m i z i n g t h e i r c o s t s . Several o t h e r a l t e r n a t i v e s c o u l d b e d e f i n e d and compared f o r t h e l e a s t - c o s t combinat ion. Note t h a t w h i l e t h i s procedure does n o t cap tu re a l l t h e complex l i nkages such as s h i f t s i n e n t e r p r i s e s e l e c t i o n t r a d i - t i o n a l l y embedded i n l a r g e LP models such as Danok e t a l . , i t may b e t t e r r e p r e s e n t some o f t he r e a l w o r l d r i g i d i t i e s by a l l o w i n g the user t o de- f i n e accep tab le machine combinat ions. T h i s may be p a r t i c u l a r l y impor- t a n t where some machinery a l ready e x i s t s .

Application

The model i s a p p l i e d t o an 1800 a c r e g r a i n farm i n t h e southwestern p a r t o f Saskatchewan. The case farm grows wheat p r i m a r i l y i n a one -ha l f c rop , one -ha l f summerfallow r o t a t i o n . The f o l l o w i n g c r o p o p e r a t i o n s a r e used: seeding w i t h a d iscer-seeder , ha r row ing and pack ing, sp ray ing once f o r b road lea f weeds and p a r t i a l l y f o r w i l d oa ts , swath ing and com- b i n i n g . The summerfallow o p e r a t i o n s i n c l u d e c u l t i v a t i n g t h r e e t imes, rodweeding t w i c e and ha r row ing and pack ing once. Machinery and equip- ment d a t a a r e presented i n Table 4 i n t y p i c a l spreadsheet s t y l e .

The i n i t i a l machinery complement s e l e c t e d i s p resen ted i n Table 5. The s t a r t i n g s i z e s o f t he d i sce r -seeder , harrows and packers, sprayer and swather were a l l l a r g e r than t h e c u r r e n t l y l a r g e s t a v a i l a b l e u n i t s . The model g i v e s the user the o p t i o n o f l i m i t i n g t h e s i z e t o t h e l a r g e s t a v a i l a b l e u n i t o r s o l v i n g t h e s i z i n g problem w i t h o u t rega rd f o r t h i s c o n s t r a i n t . Based on the maximum machine s i z e s f o r some opera t i ons , t he s m a l l e s t t r a c t o r t h a t w i l l p u l l a l l t he implement s i z e s chosen i s 195 PTOHP. t h e i n i t i a l t o t a l machinery system annual c o s t i s $87.610.

Tab

le 4

: The

Lea

st-C

rst

Mac

hine

ry S

izin

g M

e1

Dat

a S

prea

dske

t €o

r a

Farm

in

Sc

utk

ste

rn S

aska

tche

wan

OPERATICNS

:far

iahl

e Sy

mtu

l B

qu

atim

T

ract

or

Di?

;cer

H

arro

win

s S

pray

ing

Ra

Min

g

Cul

ti-

Swat

hins

w

inin

g

Packing

NO

. an

d va

ting

Are

a m

ered

A

Crw

Are

a Ca

nrm

bar

E: pn*e

r hr

s/ac

re

Tim

elin

ess

R F

cTto

r

Tra

lw of

Crm

/ A

cre

w

9chr

)rlu

lim

sc

Din

wrs

erl

optim

un

nt

Tlm

e nv

aila

hlr?

/ D

ay

h

Fra

ctio

nal

Uti

liza

tim

of

Tinr

U

srx3

4 9

Pie

ld

7.ff

icie

ncy

e

Max

lmm

Xt-

rhin

e w

idth

A

vail

ahle

cue1 P

rice

PD

425.

7 1800

6,7

900

8 4.

93

6.7

.014

6,7

150

6,7

2

6,7

1

5.7

18

5,7

0.59

4,6.

7.8

5.00

4.6.

7 0.

10

4s

4,s

1.35

4 .0833

.3

1800

900

1.87

.014

150 2 1

18

0.59

5.00

0.80

70

.a12

1090

900

0.55

.01

150 2 1

18

0.59

5.50

0.80

00

.9

1800

900

1.87

.002

150 2 1

18

0.59

5.00

0.80

60

-55

2700

900

4.18

.002

150 2 1 18

0.59

5.00

0.80

51

.22

900

900

2.85

.014

150 2 1

18

0.59

5.00

0.69

25

.35

900

900

7.95

.014

150 2 1

18

0.59

3.00

0.69

50

.467

Tab

le 4

con

tinu

ed

Wir

iahl

e Sy

mbo

l F

aa

tio

n

Tra

ctor

D

isce

r H

arro

win

q Sp

rayi

nq

Rdw

eedi

rq

Cul

ti-

Sw

athi

rq

Cam

bini

llg

No.

and

vati

ng

Packing

Mac

hine

I qa

se P

rice

($)

WII

hi

1 -2

081

-154

46

84

0 -2353

-316

8 0

0

Yac

hin

e Price(F/II?),ft. TP,I

397

623

169

62

186

336

303

1250

P

i

8.00

8.

00

8.00

8.

00

8.00

8.

00

8.00

Inte

rest

Rat

e r

2,2

0.12

0.

12

0.12

0.

12

0.12

0.

12

0.12

%ch

ine

Lif

e yrs.

2,2

13

15

10

15

15

15

15

12

An

nrt

izat

im

Pcx

tor

€or

Mac

hine

A$

.1

557

.146

8 .1

770

.146

8 ,1

468

.146

8 ,1

468

.161

4 yr

s *

p2

Fix

d C

mt

S V

ach

ine

=%Ii

3

.179

6 .1

716

.198

8 .1

716

.171

6 .1

716

.171

6 .1

840

Tim

elin

ess

Cmt

Per

day

($

) W

-a

6,7

$88.

98

$88.

98

$63.

56

$12.

71

$12.

71

$88.

98

$88.

98

Ta5

le 5

: In

itia

l (P

hase

I) Machinery

Ccm

plrm

ent

m

0

Tra

ctor

O

PERI

\TI(T

?S

Dis

cer

Hac

row

irq

Spr

ayin

g R

odw

eedi

ng

Cul

ti-

Swat

hing

Canhining

6 Pa

ckin

g va

ting

Mac

hine

W

idth

(ft)

Yac

hine

Wid

th

Required F

NlP

~~

~~

~ ~~

62

10 4

117

49

45

63

39

45

70

80

49

45

25

39

(195

) 19

5 11

5 43

81

16

5 63

16

3

Imnl

emen

t (f

!rs/

yr .)

55

%

94

53

26

76

125

86

92

Tra

ctor

Per

cent

lm1

80

47

17

33

67

26

67

Tra

ctor

Fue

l C

ost

($/y

r.)

$129

5 $5

42

$169

$6

61

$153

0 $6

75

$112

9

Tra

ctor

Rep

air

Co

st (

$/yr

.)

$593

$3

43

$165

$4

89

$805

$5

56

$597

Jmpl

men

t F

ix4

Cos

t (S

/yr.

) $1

3651

$4

786

5328

3 $8

51

$116

3 $2

035

$130

0 $8

964

$789

$7

11

$114

$2

82

$325

$2

28

$209

4

Tim

elin

ess

ms

t (S

/yr

.) $8390

$471

9 $1

624

$962

$1

583

$766

0 $8

225

Cah

or C

ost/

oper

atim

(S

/yr

.)

5754

$4

24

$204

$6

05

$996

$6

89

$739

$727

4 $1

1109

$2

1749

$1

6606

51

0022

$3

127

$416

1

Tah

le 6

: Phase I1 M

achi

nerv

Ca

mlm

nt

Siz

es a

r#l

Ann

ual

Ave

rage

Tot

al Costs,

by I

tera

tio

n

Iter

atio

n T

ract

or

Dls

cer

Har

row

s S

pray

er

me

r C

ulti

vato

r Sw

athe

r C

anbi

ne

Ann

ual

Ave

rage

T

ota

l C

ost

Size

b P

acke

rs

mlP

----

----

----

----

-- ft

--

--

--

--

--

--

--

--

--

$

1

19 5

45

70

80

49

45

25

39

8761

0

2 18

5 43

70

80

49

45

25

39

8679

9

3 17

5 40

70

80

49

45

25

39

86

125

4 165

38

70

80

49

45

25

39

8552

0

5 15

5 35

70

80

49

42

25

37

85

117

6 14

5 33

70

80

49

39

25

35

84

924

7 13

5 31

70

80

49

37

25

32

84

968

8 12

5 29

70

80

49

34

25

30

8530

8

9 11

5 27

70

80

49

31

25

27

8602

1

10

105

24

64

80

49

29

25

25

8753

9

Tab

lr?

7:

The

Was

t-C

ost Machinery

Can

plm

ent

Tra

ctor

OP

ERAT

ION

Dis

cer

Har

row

ing

Spra

ying

Rodweedinq

Cul

ti-

Sw

athi

ng

Can

bini

ng

& Packing

vati

ng

M3c

hb-e

Wid

th

(Et)

33

88

27

3 88

39

58

35

Yac

hin

e W

idth

Cho

sen

33

70

80

49

39

25

35

Rfg

iiKed

mi"

(145

) 11

5 43

81

14

5 63

14

5

Tra

ctor

/Im

plm

ent

(Hrs

/yr

.) 6 1

2 12

7 53

26

76

14

1 86

10

4

Tra

ctor

HP

Load

(a

) 80

63

23

44

80

35

80

Tra

ctor

Fue

l C

ost

($/yr.)

$129

5 $4

69

$143

$5

59

$144

1 $5

70

$105

9

Tractor ReDair C

ost

($/y

r.)

$5R

7 $2

46

$118

$3

51

$654

$3

99

$480

Tra

ctor

/Im

plm

nt F

ixed

Cos

t (C

/Yr.

1 $9

996

$355

4 $3

283

$851

$1

163

$173

4 $1

300

$799

5

Impl

emen

t R

epai

r C

os

t (S

/yr.

)

Tim

elin

ess

Co

st

($/y

r .)

$787

$7

11

$114

$2

82

$313

$2

28

$209

4

$112

74

$471

9 $1

624

$962

$1

792

$766

0 $9

222

Labor

Ca

t ($/YK.)

$101

4 $4

24

$204

$6

05

$112

8 $6

89

$829

Tot

al C

ost

(S/y

r.)

$195

12

$985

1 $3

055

$392

2 $7

062

$108

46

$216

79

Tot

al S

yste

m C

ost (S/yr.)

$849

24

63

Table 6 summarizes 10 phase I t iterations of the model starting with the initial 195 HP machine complement size and cost. Decrementing the initial tractor size by 10 HP requires only the discer to be down sized. Successive decrements eventually affect the harrow and packers, cultiva- tor and combine size. While downsizing the tractor horsepower initially reduces fixed costs by more than the increase in timeliness and labor costs, further downsizing eventually increases timeliness and labor costs to the point where they outweigh fixed cost savings. The least- cost system occurs at iteration No. 6 where the machine complement is based on a 145 HP tractor. Annual total cost is $84.924 or $2.686 less than the starting machine complement. The annual total costs associated with each operation from the final spreadsheet are shown in Table 7.

Conc 1 us i on

A "typical" farm in southwestern Saskatchewan can save a significant amount per year if the optimum machinery size is selected. The informa- tion needed to apply the model is available to most farm managers. The model can be adapted to handle multi-tractor systems by designating the operations by each general size or type of tractor. The true value of the model comes from running it several times for a given farm to ana- lyze the sensitivity of the variable and how they affect the optimum ma- chinery complement size.

The least-cost model can be programmed into most electronic spread- sheets and used on any o f a variety of microcomputers. In general, the microcomputer should have at least 128 of random access memory (RAM) or more. Options on some spreadsheets such as conditional "if" or "go to" statements can facilitate model construction. In addition, computer graphics can improve both the clarity and the ease of comparison between the various machine system sizes.

[Received July 1984, Accepted January 19851

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