University of Nigeria Research Publications

KEMBE, Moses Msugh

Aut

hor

PG/MSC/90/9490

Title

Optimal Allocation of Farm Tractors: A Case Study of

Benue State Tractor Hiring Agency (BENTHA)

Facu

lty

Physical Sciences

Dep

artm

ent

Statistics

Dat

e December, 1992

Sign

atur

e

O P T I X A L A L L O C A T I O N O F FARH T R A C T O R S :

A C A S E STUDY OF BEMJE S T A T E TRACTOR

HIRING AGENCY (BENTHA).

KEMBE, MOSES MSUGH \

B. S C . (EIONS) M A T I I U l A T I C S ( JOS) . REG. IT0 . X / N . ~ C / 9 0 / 9 4 9 0

A T R O J E C T REPOTtT STll3MT'rTED TO TIIE

D12'ARrI!M E;NT 0 I? L '2 A l l 1 1 C S , PAC I I 1,'P Y

OP I'IIY SZCAL 321 ICNCFS IN PAIITIAL

F l l I ~ l ~ l LMLN'L' 019' 'Y l i 11; I~E<~Ul l~LT" l C N T S k'OH

TTIE DECREE OF MASTER OF SCIENCE O F THE U N I V E R S l T Y O F N I G E R I A , NSUKKA.

DEDICATION

To my l a t e son, d1.o died be fo re he

was naned..

i i i

CERTIFICATION

This p r o j e c t r e p o r t h a s n o t b e e n a c c e p t e d

i n s u b s t a n c e f o r a n y d e g r e e and i s n o t 5 e i n g

c o n c u r r e n t:y s u b m i t t e d f o r a n o t h e r degree.

C a n d i d a t e : KEMBE PiOSLS NSUGW

S u p e r v i s o r : REV. (DR.) C.C. AGUN1.4AMRA.

I am v r r y much i n d e n t e d LCJ many p e o p l e who

ccr? t r i b u t e d i nmense ly to khe cornplet ior~ o f this p r o j e c t .

S p e c i a l t h a n k s goes t o sev . (r3r.) C.C. ~gun?.ramba,

m y humble 5ut i n t e l l i g ~ n t s u p c t r v i s o r who made f a r

r e a c h i n y c o m m e n t s and sugges t ions t o t i - ~ e whole w r i t e - u p

or this project. I also acknowl~dge p r o t . U.G.N.

k h e r n a t c r i a l s n e e d e d for t h i s work. My special

y r a t i t u d e and a p p r s c l a t i u n goes to, P r b f . P.I. U C h e

tor his ~verwlielming i n t e r ~ s t in my welfare in h i s

d u a l c a p a c i t y as m y ~ e c t u r e 2 s nrra Head of D e p a r t m e n t

of s t a t i s t i c s , University of hl lge r la , i J r ;ukka ; t o

P r o f . J .>I. Aaic h i e 'for h i s e n c o u r a q m e n t; to

o t i d . l q r r l a , N s u k k a f o r v e r y u s e r u l s u g ~ ~ ! s t i o n s and

quldancr ; to my lecturers in the Depar tmen t of

s t a t i s t i c s University of N i g e r i a Nsukka f o r t h e i r

u n t i r i n g l o v e and concern; to m y s p e c i a l f r i e n d s ,

~ i d e l l s Uquowo, c h i k e Nwankwo, E. Asogwa, ~ i v l u m u n G e

for t h ~ i r encouragement.

he i n t e re s t shown b y t h c General manager of

B E N T H A , J.T. Tscqha a n d t h e Mnnagcr p i e l c i o p e r a t i o n s

and maintenance, S.A. ~ k c d e g b a f o r t h e i r c o o p e r a t i o n

and assistance i n collect in(^ t h e r e l e v a n t data i s

y r a t e f u l l y a c k n o w l e d g ~ d . P a r t i c u l a r l y , I ~ A i s h t o

a c k n o w l e d g e my wife and s o n , F i n q u s e n and Dooyurn f o r

t h e i r e n c o a u r d q e m e n t , e n d u r a n c e and u n d e r s t a n d i n g

i n allowing me t o d e v o t e s o much o f o u r time t t l a t

r e a l l y b e l o n g t o then; on t h i s p r o j e c t .

y i n a l l y , I t h a n k the a u t h o r i t i e s o f t h e c o l l e g e

oi : : t i u c a t i ~ n , Katsina- la f o r g r m t i n c = , m c s t u d y

lpave f o r t h e M - S C . Programme. I am a l s o gratcful

t o t h e U n i v e r s i t y of ~ u b l i n - u n i v e r s i t y of iYfgeria

~ i n k a i 2 e programme f o r o f f - s e t t i n g part of t h e c o s t

of production of t h i s p r o j e c t . ~ a s t l y , I thank

m y ~ o b for g i v i n g m e g o o d h e a l t h and p a t i e n c e t o

complete t h i s work.

M.M. Kernbc Depar tment of s ta t i s t i c s U n i v e r s i t y D Z ~ i g e r i a , ivsukka.

C o v e r Page : - - . ... . . D e d i c a t i o n : -. . . ,. . . . C e r t i f i c a k i o n : * . ... ... Acknowledgement: . . . ... ... C o n t e n t s : * . - ... ... L i s t of T a b l e s and C h a r t s . , . . . . CHAPTER 1

1.1 M o t i v a t i o n f o r t h e S t u d y : .- . 1 . 2 A i m s and O b j e c t i v e s of t h e S t u d y :

1.3 Scope of the S t u d y : . . . . - . 1.4 D e s c r i p t i o n . of t h e Case S t u d y : . . 1 . 4 ; 1 iqanaqernent S t r u c t u r e : . . . 1.4: 3 T y p e s of F i e l d O p e r a t i o n s a n d

Revenue S o u r c e s : ... ... 1.4 5 M a i n t e n a n c e : ... . . -

R E V I E W O F LITERATURE ... a . . 2.2 G e n e r a l I n t r o d u c t i o n t o

Allocation Problem:... ... 2 . 2 Farm Power and 2-lachinery

Performance: . . . ... 2 . 3 T r a c t o r Perforrnancc: . . . 2.4 Timeliness: ... . . .

iii

v i i i

v i i

c o s t of Operation .. . ... Psrm Power and Kachinery Select ion . . . . . . . . . 20

Tractor Size : . + ..- 21

p o l i t i c a l Considerat ion: . . . 21

Foundation Work: . . . ... 2 1

Recent Con t r ibu t ion t o the Alloca t ion o f T r a c t o r s and Implements: ... ... 23

C K r n E R 3

3- 1 T h e o r e t i c a l Framework: .. . 26

3.2 The Model: . . . . . . 26

7 . 3 Data C o l l e c t i o n . . . ... 31

C H m E R 4 PiODEL ANALYSIE AND RESULTS 33

4.1 H e u r i s t i c S o l u t i o n of the ;Yodel ,. , . . , 33

4.2 The H e u r i s t i c Procedure f o r T r a c t o r A l l o c a t i o n . . . a * a 54

C I I r W E H 5 CONCLUSIOK AND 1IECO?.lllEIJDATIO1TS . . . 4-4 5.1 Conclusion . . . ,. . . 4-4-

5.2 Recommendations . . . . .. 44

REE'ERENCES: ... ... 47

viii

LIST OF TABLES AND CRARTS

chart 'l.4: 2 Orgmogram of t he Agency:

Table 1.4:4 Charges on T r a c t o r ~ervices/ Hecta re : e m .

T a b l e 4.3 ??umber o f hectarage h . ( k ) ploughed by k tractors i n t h e $ th day in all zones based on the geoerafed data - . . w m m

Fages

6

Table 4.4 ~ ( k , m .) = Probability distribution J

of k t r a c t o r s working on t h e t th day when m, o f t h e t o t a l tractors

J a r e al loca ted t o a l l zones when m+ = 22 based on the generated data. 37

Table 4.5 Expected number of bectarage ( I I ( m ; ) ) J

p e r t th day Plou&hed by m; t r a c t o r s f o r J

a l l the zones based o n t h e generated d a t a =.. -.- 38

~ a b l c 4.6 T h e Muginal. increase i n the number o f h e c t s a g e p1oue;hed by the t r a c t o r s H(m . + A ) - 11(m .) based

J J on t h e generat d d ~ t a = m a 39

T a b l e 4.7 Number of T r a c t o r s a l h c a t e d t o t he Zones Dased on t h e proposed Nodel when m* = 22 based on the generated d a t a . . . 40

T a b l e 4.13 Actual Allocat ion b y g ~ m f l h ... 41

T a b l e 4-.9 Cmpmison of Allocat ion P o l i c i e s m e - 42

8enue S t a t e Trac to r Hiring AgPncy 135NT!+l)

is usually c o n f r o n t e d w i t h the problem of

d e t ~ r r n i n i n g the optimum number of t r a c t o r s to

be allocated t o different zones i n t h z state.

T h e number of tractors al1oc:a ted t o a zone is

normal l y d e c i d e d without a n y p r o p e r s t u d y of

t r a c t o r n e ~ d s of t h e zones , Sometimes allocation

is based on mere1 y p o l i t i c a l cons iderc i t i u n s .

T h e problen of a l l o c a t i o n i s formulated and

h e u r i s k i c p r o c e d u r e s a r e a p p l i e d t u o? t ima l ly

a 2 l o c a t c t h e l i r n i t e d tractors.

CHAPTER O N E --

INT?Ol2UCTIO,i4 --

I . i 4 0 t j . v a t i o n for t h e s t u d y ;

acnue s t a k e i s one of t h e b i g g e s t s t a t e s i n

the p l idd l e B e l t of ~ i g e r i a b o t h in its s i z e a n d

p o p u l a t i o n . I t h a s a t o t a l area of a h u t

6 7 , 7 4 0 sq.km. s u r r o u n d e d b y P la tee tu , ~ a r a b a ,

C r o s s ~ i v e r , Enugu a n d K o y i s t a t e s w i t h a t o t a l

p o p u l a t i o n o f a b o u t 4,721,717 pebple- Bcnue

s t a t e of ~ i g e r i a ~ i a r y ( 1989 ) .

~ i s t o r i c a l l y , khc p e o p l e of Denue 5 thte

generally have a common a g r i c u l t u r a l Sackground.

A good p e r c e n t a g e of thc p o p u l a t i o n are farmers.

B e n u e s t a t e remains a major producer of yams,

soyabeans termed ' t h e secd o f life' as well as

a producer af b e n i s e ~ d in Nigeri, . crops l i k e

r i ce , maize, groundnu ts , cassava, melldn, guinea

corn, millet are a l s o produced i n large quantities

i n t h e s t a t e . Tamatocs, p e p p e r , o k r o and

d i f f e r e n t . t y p e s of vegetables a r e also p r o d u c e d

i n t h e s t a t e . Tsegba ( 1992 ) .

B U ~ a c a . r e f u l l o o k at the f a r m i n g p r a c t i c e s

of t h e C e n u c p e o p l e s h o w s t h e u s e of p r i m i t i v e

and c r u d e f a r m i n g i m p l e m e n t s and s u b s i s t e n c e

a g r i c u l t r u a l a p p r o a c h e s . Benue s t a t e c a n n o t

boast o f o p t i m a l food p r o d u c t i o n u n l e s s t h e r e

i s a m a j o r r i e v e l o p m e n t and improvement sf t h e

a g r i c u l t r u ~ l p o t e n t i a l s of t he s t a t e , Such

i m p r o v e m e n t s musk be a s h i f t f r o m t h e

p r i m i t i v e and crud^ m e t h o d s of farming t o t h e

m o d e r n and s c i e n t i f i c a p p r o a c h e s of o u r t i m e

w h i c h i n c l u d e i n p u t s s u c h 2s inproved s e e d l i n g s ,

fertilizer a p p l i c a t i o n , u s e of agro-chemicals,

t r a c t o r s , e tc.

TO achieve m o d @ r n i z s t i o n i n a g r i c u l t r u a l

p r o b u c t i o n , t h e B c n u e s tat^ G o v e r n m e n t e s t a b l i s h e d

a Tractor ~ i r i n y Agency t o o f f ~ r tractor se rv ices

in the state is n o t based o n any s o u n d criterion.

A p p a r e n t l y , a l l o c a t i o n i s a r b i t r a r y s i nce i t i s

n o t based o n t h e s i z e o f farm and d e m a n d s o f t h e

v a r i o u s areas .

A i m s and Objectives o f t h e S t u d y :

The a i m s and o b j e c t i v e s o f t h i s s t u d y i n c l u d e :

i) Heview e x i s t i n g a l l o c a t i o n models.

i i ) To d e v e l o p a n a l l o c a t i o n mode l for t h e

case s t u d y .

i i i ) T o a p p l y t h ~ m o d e l o n the case s t u d y area.

i v ) 5ugqes t ways on haw 3 E P I T H A will make more

v i a b l e improvements .

l . 3 S c o p e of t h e S t u d y :

T h i s r e s e a r c h i s aimed a t d e v e l o p i n g a n

o p t i m a l t e c n n i q u e o r method f o r a l l o c a t i n t j F a r m

t r a c t o r s t o a f a r m i n g c o m m u n i t y . k m d t h e m a t i c a l

model h a s been f o r m u l a t e d w h i c h i s based o n t h e

number of t ractors allocateci to a zone s u b j e c t t o

t h e d e m a n d of t h e zone.

The model is such t n a t i t Can be used for

such farm o p e r a t i o n s like p l o u g h i n g , h a r r o w i n g ,

r i d q i n g , h a r v e s t i n g etc.

H o w e v e r , d u e t o limi t& rescurces , time

a n d d a t a available, t h e researcher u s e d p l o u g h i n g

a 5 a unit of o p e r a k i o n .

Description of t h e Case S t u d y :

T h e Benuc S t a t e T r a c t o r I i i r i n g Aqcncy

IuENTHA) was e s t a b l i s h e d by a n E d i c t of tne

G o v e r n m e n t of t k n u e S t a t e of N i g e r i a in 1988.

!Benu* State Government Gazzette V o l u m e 2 2 , 2988 ) .

Thc A q e n c y was g i v e n the r e s p o n s i b i l i t y of

~ r o v i d i n g tractor s e r v i c e s to t h e p e o p l e of

u e n u e S t a t e f o r t h e p u r F o s e of promoting

a g r i c u l t u r ~ i n t h e S t a t e , i n c r s a s i n g food o u t p u t

a n d qenerally i m p r o v i n g t h e s t a n d a r d o f l i v i n g

of h c r i n d i g e n e s . BENTHA B u l l e t i n (19891.

T h o s e o b j e c t i v e s h o w e v e r , seems to be a

m i r a g e , T r a c t o r s are not d i s t r i b u t e d at t h e

t i m e when n e e b ~ d . S o many factors accounts f o r

t h i s . ' T i l e major f a c t o r r e s p o n s i b l e f o r t h e

p a r t i a l f a i l u r e o f t h e se t o b j e c t i v e s of HLNTHA

is the bureaucratic n a L u r e of g o v e r n m e n t , a s i t

t a k e s Longer than necessary to allocatr a t r a c t o r

e v e n a f t e r payment for the t r a c t o r has b e e n effected.

Tractors are allocated t o a r e a s on p o l i t i c a l

reasons: even t h o u g h t r a c t o r s may n o t be needed

by s u c h areas.

B ~ T H A started o p ~ r a t i c m s i n ibydy, ~ 9 0 9 w i t h

a f l e e t of I00 s t q r t r a c t o r s a n d 5 6 F i a t t raCtors .

~ h i . r t y ( 3 0 ) more ~ t e y r t r a c t o r s w r e ;rEd~d to

t h e f l e e t i n 1990, t h u s b r i n g i n g klle tmtal number

of tractors u n d e r BENTHAIS c o n t r o l to 180.

BEKTHA a l s o h a s 120 plougi l s , 120 t iarrcd2,

220 ~ i d g e r s a n d 10 Bool-il S p r a y e r s . bZik~ Z l : k B u l l l e t i n

(2999)

4 : 1 I q a n a g m e n t s t r u c t u r e : - C u r r p n t l y , t h e Board of Benue s t a t e Tractor

' { i r i n g ,>,gpncy i s headel:; by tile ~ i r e c t o r ~ e n e r a l ,

i , ' i n i s k r y 01 ~ o i - i c u l t u r c . Ministry of , ~ g r i c u l t u r e

i s t h e s u p c r v i s i n g ministry of the agency. he

Planaoernen t Team of t h e Agency is hcadcd by a

Gencr I3Z Xanager w h o has u n d e r h i s d i r e c t

s u p e r v i s i o n three manayers n amply:

Flanaqer j d m i n i s t r a t i o n , Manager ~ i n , i n c c an6

pianaqer y i e l d Ol;crationr; and 14ainten;;ni;e.

charts 1.4:2 Orqanoqran! of the A q e n c y :

G e n e r a l Manager t

M a n a g e r O p e r a t i o n s

I F i n a n c e

I X a n a g e r

A d m i n i s t r a t i o n

Accoun ban t s A d m i n i s t r a t i v e Otficers

Stores p f f t c e r s

C a s h i e r s Cl?ricai O f f i c e r s .

O p e r a t o r s

T h e kqency h a s s t r u c t u r e d i t s o p e r a t i o n s into

f o u r co-ordina tinq zones and s u b s t a t i o n s as Lis tea

'>elow:

N o r t n e r n Zone:

- G w e r E a s t

- : * i a k u r d i - G a a d i

- Guma

- Daubu

N o r t h - E a s t Z o n e :

- ~ n o k o

- i l shongo

- Konshisha

- :3uruku

E a s t e r n L o n e :

- Ksts ina -Ala

- i i :-.i a r l d e

- Ukum

- Ja to-Aka

- O j u

- Ado

The overall t- i t?adguarters of BENTHA is i n

X a k u s d i , t h e S t a t e c a p i t a l . The zones a re

adminis t ~ r e b ~y co-ordina t o r s . BETiTiiA has

s t a t i o n s i n a11 t he e i g h t e e n (18) Local

G o v e r n m e n t Areas of t h e S t a t e headed hy s u p e r v i s o r s .

The A g e n c y h a s a t p r e s e n t a b o u t 211 s t a f f ,

Some of t h e Agency s t a f f a r e jot-roued f rom some

o t h e r m i n i s t r i e s i n the S t a t e w h i l e a few are

1.4:3 T y p e s . of F i ~ l d Operations an d R e v ~ l n u e Sources:

A t p r e s e n t BENTHA u n d e r t a k e s t h e f o l l o w i n g

m a jar o p e r a t i o n s :

i ) Ploughing

ii) S a r r o w i n g

lii) K i d q i n y

i v ) S p r a y i n g

V ) T r a i l i n g

T a b l e 1.4 : 4 C h a r q e s on T r a c t o r S e r v i c e s / H e c t a r e :

I n a d d i t i o n t o t h e revenue g e n e r a t e d by t h e

Agency through t h e f i e l d o p e r a t i o n s , g o v e r n m e n t

o c c a s i o n a l l y gives a t o k e n amount as subvent ion

t o t h e Agency,

1.4: 5 Maintenance:

Repairs of t r a c t o r s a r e d o n e w h ~ n t h e r e i s

a b r e a k down of t r a c t o r a t the s t a t e h e a d q u a r t e r s ,

M a k u r d i . T h e r e i s a spare p a r t store w h i c h i s

c o n s t a n t l y b e i n g r e p l e n i s h e d f o r use on D E N T H A

Tractors. T h o u g h s p a r e p a r t s are a v a i l a b l e t h e

b u r e a u c r a t i c p r a c t i c e s O F government makes

r e p a i r s on b r o k e n down tractors t a k e s l o n g e r

t h a n npcessary.

CHAPTER 2

2.1 G ~ n e r r 3 1 Introduction to A l l o c a t i o n ~ ' r o b l e m :

Allocation generally h a s b e e n q n a r z a o f

c.on t i n u o u s research s i n e e 1;: te 19410s t i l l d a t e .

A lot of t e x t s , papers a n d a r t i c l e s h a v e b e e n

p u b l i s h ? d on t h e s u b j e c t since t h e n . T h e t h e o r y

of a l l o c a t i o n i s c o n c e r n e d w i t h t h e a1 loca t i o n

or deployment o f r e s o u r c e s t o j o b s i n s u c h a

way t h a t t h e o v e r a l l e f f i c i e n c y i s ~naxirn ized;

for e x a m p l e , s o t h a t cost is m i n i m i ~ e d o r

maximize t h e t o t a l returns amonq other things.

o n a1 laca t i o n p r ~ b l e m s a r e t e c h n i q u e s

for s o l v i n g a general class of o p t i m i z a t i o n

problems dealing w i t h t h e i t e r a t i o n o f many

v a r i a S l e s s u b j e c t t o a s ~ t of r e s k r a i n i n g

c o n d i t i o n s . A 1 l o c a t i o n p r o b l e m s t h e n a r i s e

p r i m a r i l y w h e n t h e r e are a number of a c t i v i t i e s

to be performed and t h ~ a l t e r n a t i v e w a y s of

d o i n g t h ~ m and r e s o u r c e s o r f a c i l i k i e s are n o t

a v a i l a b l e for p e r f o r m i n g e z c h a c t i v i t y i n t h e

most e f f e c t i v e ,$ay. A 1 l o c a k i o n mode l s t h e n

combine a c t i v i t i e s a n d r e s o u r c e s i n s u c h a way

to m a x i m i z e o v e r ~ l l e f f e c t i v e n e s s . k c k o f f a n d

S a s i e n i %968 1.

A1 l o c a t i o n p r o b l e m s treat o r c o m b i n e

different t y p e s of resources. T h ~ s e i n c l u d e :

P l a n p o ~ e r , c a p i t a l , space and machinery arnonq o t h c r s ,

T h e resource of i n t e r e s t i n the l i t e r a t u r e here

i s m a c h i n e r y ( f a r m T r a c t o r ) .

To optimize t h e a l l o c a t i o n of farm t r a c t o r s

a n d i rnp le rnen t s , s e v e r a l p r i n c i p l e s a n d m e thnds

a r e a d o p t e d t o ach ieve t h i s objective. These

p r i n c i p l e s and methods a r e b5sed on t h e following

p a r a m e t e r s .

i T r a c t o r performance

ii! Farm p o w e r and machinery se l ec t i on

i i i ) F a r m p o w e r and m a c h i n e r y performance

i v ) T i m e l i n e s s

v ) F a r m s i z e

v i ) C o s t of o p e r a t i o n .

2.2 F a r m P o w e r a n d M a c h i n e r y

Accord ing t o Anazndo ( 1975 1 e v a l u a t i o n o f

t h e p e r f o r m a n c e o f a piece o f m a c h i n e r y i s n o t

a n e a s y t a s k . I t r e q u i r e s p r o f e s s i o n s 1 sk i l l s .

H e stated t h a t q u a l i t a t i v e a s s e s s m e n t o f t h e

p e r f o r m a n c e of e q u i p m e n t may D e d o n e by

c o n s i d e r i n q t n e f o l l o - . < i n g :

i) H o w s u i t a b l e i t i s t o t h e e c o l o q i c a l

cond i t i o n s a n d c u l t u r a l p r a c t i c e s i n

qlles t i o n .

ii) E a s y m a n i p u l a t i o n b y a l o c a l o p e r a t o r o n

t h e f i e l d ; a n d

i i i ) How qood the q u a l i t y o f j o b t h e e q u i p m e n t , d o c s u n d e r t h e prevailinq c i r c u m s t a n c e s .

Some u s e f u l exp ress ions are m o d e l l e d f o r

quqn t i t a t i v e e v a l u a t i o n o f t h e p e r f o r m a n c e

of mosL a q r i c u l t u r a l r n a c h i n 5 : r y .

( i l l F k c l d C a p a c i t y IFJ)

FC m Speed of O p e r a t i o n ;< n i d t h o f m a c h i n e . . . . . . ... 2.21

(b) Theorc t i c a l Field C a p a c i l r y ( '1 I ;C)

TFC = Zated speed A o p t i m u m ; . i id t i i o f

Implernen t ... 2 . 2 2

( c ) ~f f ~ c t i v c ~ i e l d c a p a c i t y ( E F C )

EFC = , \c tual average speed X ~ f f e c t i v e

w i d t h of machine). . - 2 2 3

( b : ~ i e l d ~f f i c k e n c y (FE:

when the e q u i p m e n t is a t

all t i m e s o p s r a t i n g w i t h

r a ted speed V and r a t e 0

w i d t h b,

Te ;= € 5 f e c t i v e f i e l d o p e r a t i n g time

, e = Percentage of i r n p l c m ~ n t w i d t h

a c t u a l l y u t i l i z e d .

;". = ~ i ~ e l o s t p e r hectare auc? LO n

i n t c r u p t i o n s t h a t a r e n o t

p r o p o r t i o n a l t o area .

T h e e f f ? c t i v e f i e l d c a p a c i t y is t h e n g i v e n by

v b F E EFC = TFC + P E = -

10 b , / h .., 2 . 2 5

!adhere: V = ground speed

:,I = nach ine w i d t h

= F i e l d Efficiency

Onovo I l 3 9 l ) found EFC expressed b y 2.25

i n a d e q u z t e . He skated t h a t FE i r ; a f u n c t i o n of

s e v e r a l non-productive i t e m s such as break-douns,

a d j u s t m e n t s , t u r n i n q a t farm heads and o t h e r s .

Since FE is the sum of many d i f f e r e n t f a c t o r s ,

i t is d i f f i c u l t to o b t a i n reliable v a l u e s f o r ?L . He d e v e l o p e d a mathema t i c a l model f o r p r e d i c t i n g

farm n a c h i n e r y performanc~ r a t e s u s i n g 14

i n p u t s co-efficients i n c l u d i , i g i terns re1 a k i n g t o

t h e a c t u a l machine and i t s use, f i e l d shape,

size, physical conditions and m a c h i n e m a n a g e m e n t .

T h i s e s t i m a t e s m a c h i n e c a p a c i t y f o r i n d i v i d u a l

field c o n d i t i o n s r a t h e r than f o r a v e r a g e f i e l d

condi. L i o n s .

The r n o d ~ l i s given s i i l l u l taneousiy a s

T = A + Y ( h r / a ) ... 2 . 2 6

iaJhere: A = Time s p e n t a c t u a l l y p e r f ~ ~ r n i n q t h e

s p e c i f i c o p e r a t i o n h r / h a .

d = T i m p used f o i - a c t - i v i t i e s , row e n d

t u r n i n g s a n d o t h e r d e l a y s h r / h a

T =I T o t a l time h a / h r

C = P e r F o r m a n c e r a t e h a / h r .

2 . 2 : 5 Field Machine I n d e x :

Renoll ( 1 9 7 0 ) d e v e l o p e d a m o d e l x h i c h

i n d i c a t e d how w e l l a d a p t e d a s p e c i f i c f i e l d i s

t h e u s e of a g i v e n m a c h i n e r y , . I t i s q i v e n a s

Where T = Tota l time f o r p r o d u c t i v e f i e l d 3

o p e r a t i o n .

TZ = T o t a l n o n - p r o d u c t i v e time e x c l u d i n g

t u r n i n g s ; a n d

7 * L i .= T o t a l t i r n c ? f o r t - ~ r n i n g at r o w - e n d s . 2

The h i q h e r t h e F N I v a l u e s t h e bet ter s u i k e d

a f i e l d is ta t h c machine.

2.3 Tractor Performance:

Maximum draw-bar h o r s e power i s the most

useful performance criterion for evaluating t h e

performance of f a r m t r a c t o r . Reece ('19G71

d e v e l o p ~ d on algorithm for ? v a l u a t i n g maximum

draw-bar horsepower. The a L g o r i t h r n i s qiven

below:

S t e p 1. Determine w e i g h t w, on d r i v i n g w h e e l s

u n d e r the p a r t i c u l a r c o n d i t i o n . ; of

b a l l a s t , load transfer a n d s l o p e u n d e r

c o n s i d ~ r a t i o n . C a l c u l a t e tyre contact

r e . Assume a 25% m a x i m u m d e f l e c t i o n

of t y r e - section h e i g h t .

S t e p 11. C a l c u l a t e t h e m a x i m u m t r a c t i v e t h r u s t

P!Rcrc bl = w i d t h o f Lyre c o n t a c t

1 = l e n q t h of t y t c c o n t a c t

c = c o h e s i o n of soil

O = a n g l e o f i n t ~ r n a l s h e a r i n g

r e s i s t a n c e of t h e s o i l .

S t ~ g 111. Deter,mine the s l i p f u n c t i o n , x , at

maximum d r a w b a r horse po:+er u s i n g a

p r e v i o u s l y p l o t t e d c u r v e of s l i p a s a

f u n c t i o n of l / k here k i s d e f i n e d as

t h e s h s a r displacement e x p o n e n t ,

E s t i m a t e the rolling resistance R

%b w 1 1

= -c- . . 2.29 E = ED-efficient which ref lec t t h e

r e l a t i v c con tact p r e s s u r e and s o i l

s t r e n g t h which rnus t b e d e t e r m i n e d

during tractor o p e r a t i o n .

= total v e h i c l e w e i g h t .

Determine t h e d r a ~ i - b a r p u l l ( r j ) a t

max imum draw-ba r h o r s e p o w e r .

ir = hi! - ... 2 - 3 0 m3x

X = S l i p f u n c t i o n .

S t e p V I . Calculate t h e working speed a l l o q d i n g

for s l i p .

'.ihere: 31+p = i3reak horsepower

TTE = Tractor Transmission E f f i c i e n c y

i = S l i p

El = C o n v e r s i o n f a c t o r

= 556 i j r i t i s h U n i t s

= 1100 S.I. U , ? i t s .

S t e p ViI: C a l c u l a t e m a x i m u m d r a w - b a r horscpooer ( p )

a t t h e l i m i t i n g s p e e d p = DV + L 1 * - .

2 . 3 2

Where: 2 = ~rhw-bar Pull

Sl = C o n v e r s i o n facLor as d e f i n e d before.

2 .4 T i r n e l i n ~ s s :

3oyce e t a1 (1971) s t a t e d t h a t t i m e l i n e s s o f

operation is p a r t i c u l a r 1 y important in f a r m i n g

since c ~ o ; ) p r o d u c t i o n operations a r c time s p e c i f i c .

T h e t imeliness of o p e r a t i o n can only be a c h i e v e d

through opt imum a c t i v i t y schedcrl ing . i3u t o p t i m u m

a c t i v i t y s c h e d u l i n q c a n o n l y be p r a c t i s e d by

making u s c of t h e a p p r o p r i a t e c a p a c i t y of farm

equ ipment or m a c h i n e f o r each o p e r a t i o n . T h e

u s e of a farm m a c h i n e o f large capacity on a

small f i ~ l d would result in under-utilization

of machinpry and t h i s is uneconomical. O n the

o t h e r hand, u s e of low c a p a c i t y t r a c t o r on a

l a r g e f i e l d would r e s u l t i n over-utilization of

m a c h i n e r y and the consequencies are m a c h i n e

areak-down and inefficient crop p r o d u c t i o n .

C e r v i n k a and Chancellor (1975).

2.5 C a s t cf O p ~ r a t i o n :

The t o t a l cask f o r o p e r a t i o n ok a f i e l d

r n a c h i n ~ r y is usually e x p r e s s e d o n a pc r h e c t a r e

or h o u r l y b a s i s or on a p r o d u c t i o n u n i t Bases .

The cost is d i v i d e d i n t o t w o . F i x ? d c o s t s and

v a r i a b l e cos ts . Fixed c o s t s a r e bas.?d on

machine o . q n e r s h i p .

T h e y a r e incurred i r r e s p ~ c t i v e of machine

use. T h e y i n c l u d e c o s t of i n t e r e s t o n m a c h i n e r y ,

i n v e s t m e n t , taxes , h o u r ~ i n q and i n s ~ r ~ ~ n c e and

a n n u a l depreciation, F i x e d costs. Adelhem and

Stack t 1376) s t a t e d t h a t fixed c o s t s due to

t a x e s she1 t e r , i n s u r a n c e a n d interest v a r y

s i q n i f i c a n t l y w i t h time and l o c a t i o n . V a r i a b l e ,

c o s t s on the o t h e r h a n d a r e cost i n c u r r e d o n

~ q a i n t e n a n c e , r e p a i r , power and Paimur, oil,

l u b r i c a n t s and f u e l .

2.6 Farw i 7 o ~ ~ ( e r a n d M a c h i n a r y S e l ~ c t i o n :

A v a r i e t y of f a r m m a c h i n e s a r e a v a i l a b l e i n

various c a p a c i t i e s f o r f a r m o p e r a t i o n s . H o ~ , ~ e v e r

f o r rnos t efficient and economical p r o d u c t i o n

systcrn k i i t h timeliness of o p e r a t i o n to be

a c h i e v e d o n l y one m a c h i n e w i t h khe s p e c i f i e d

c a p a c i t y will p e r f o r m the f a r m o p e r a t i o n . The

seiection at a p p r o p r i a t e sizes of fa rm t r ac to r s

a n d i m p l e m ? n t s i s t h u s o n e of t h e most i m p o r t a n t

d e c i s i o n p a r a m e t e r s i n t h ~ overall a g r i c u l t u r a l

manaqemcnt program.

Ef F i c i e n t s e l e c t i o n of f i e l d mach ine ry

r p q u i r e s t h c a v a i l a b i l i t y o f power , service and

s p ? r ? p a r t s , labour a n d calculation of t i m e - u s e

and c o s t s i n order to a c h i e v e an o p t i m u m r e t u r n .

Anazodo ( 1 9 7 5 ) .

2 . 7 T r a c t o r S i z e :

This is us u a l l y expressed i n h o r s e p w e r

or Xilowatt. T h e t r a c t o r size must be matched

a d e q u a t e l y w i t h t h e ficld irnplemen t i n o r d e r t o

a c h i e v e o p t i m u m r e s u l t . Hunt ( 1 9 7 0 ) .

2.8 P ~ l i t i c a l C o n s i d e r a t i o n :

T h i s cannot be d e t e r m i n e d q u a n t i t a t i v e l y

but i t is s t i l l a v e r y i m p o r t a n t f a c t o r i n

tractor allocation. EkedcqSa ( 1991).

2.9 Founds t i o n work:

r#- ! Lnc h i s t o r y of t r ac to r c l e v ~ l o p m e n t is t oo

l o n q to reia te ih t5is l i t e r a t u r ~ . Accord ing to

C u p i n (l975), l a n d m a r k s a l o n g t h e road of

tractor deve lopment i n c l u d e the f i r s t I J ~ P of a n

i n t e r n a l combus t ion e n g i n e i n a tractor i n t h e

U n i t e d S t a t e of America in lE9C; thr. 'Ivcl

t rac tor 7 3 G 1 ; t h e A m e r i c a n Ford of 1917 and

t h e i ~ t e r n a t i o n a l 'Farmall ' of 1923. U ~ l r i n y

t h e 1 4 3 0 s t h e u s e of low-pressure pneumatic

t y p c of t r a c t o r s became p o p u l a r . A s u r v e y of

t r a c t o r u s e i n the E a s t e r n c o u n t r i e s a l s o snowed

a p p r e c i a ~ l e i n c r e a s e i n t h e 1930s. ::it11 all

t h e s e l i t t l e r e s e a r c h has Seen ca r r i ed o u t o n

economic a s p e c t s of t r a c t o r u t i l i z a t i o n and

managernen k,

I n M i n e r i a , t h e i n t r o d u c t i o n of f a r m tractor

dates b a c k t o t h e 1930s a n d m s f i r s t utilized

o n G o v e r n m e n t farms o r p l a n t a t i o n s . I t gained

widespread utilization when :he f a r m e r r e g i o n a l

G o v o r n m e n t i n t r o d u c e d t r a c t o r h i r e s e rv i ce s i n

t h e 19GOs. K a k o n j u o l a ( 2 9 8 3 ) .

H o w e v e r , a p i o n e e r e l a b o r a t e and

comprehensive s t u d y of t h e f u n c t i o n s and

operations of t r a c t o r h i r e u n i t s was made by

Kolawolo (1974). He s t u d i e d t h e overall

p ~ ~ r f o r m a n c c , viability and problems of p r i v a t e

a a r t i c i p a t i o n i n mechanized f a r m i n g i n 'vies t e r n

N i g e r i a . i l ~ s t a t e d t h a t G o v e r n r n ~ n t o w n e d t r a c t o r

h i r e u n i t s performed below e x p e c t a t i o n . T h e

consequence of t h i s was h i s r eco rnnenda t lon of

t n e p r i v a t i 7 . a t i o n :>f t r a c t o r h i r e u n i t s .

AL..royemi I l s 8 3 ) i n his s t u d y exnressed

similar v i e w s w i t n Kolowale. He s t a t e d t h a t

qove rn rncn t t r ec t a r h i r e u n i t s h a s v e r y l o w

o u t p u t a n d p r o v i d e u n r e l i a b l e j a u n d i c e d se rv ices

to farmers .

2-10 R e c e n t C o n t r i b u t i o n to the Allocation of T r a c t o r s a n d Implements:

Anazodo ( 1 9 8 5 ) i n his s t u d y t o e v a l u a t e t h e

a p p r o p r i a t e sys tem o f maize p r o d u c t i o n i n a

cornrnuni ty he compared traditional and s e l e c t i v c . l y

n e c h a n i z e d s y s t ~ m s on t h e b a s i s of t i m e l i n e s s and

p r o f i t a b i l i t y . He established t h a t a f t e r a b r e a k -

e v e n analysis Mas made, t h e f i n a n c i a l e f f i c i e n c y

of the tracJi t i o n a l system was 85% while t h a t of

se lec t ive ly m a c h a n i z e d system was 158%.

Okereke (199.1,) compared r i c e - o u t p u t from

k r a d i t i o n a l f a r m s u s i n g o n l y m a n u a l labar and

thosp t h a t use,? t rac tors . Ite e s t i m a t e d labor

i n p u t s a n d the cos t s a n d returns of production

i n nnkh sys tems of f a r m i n ? . He used t h e

Cobb-Uouqlass produc t ion nodel for- a n a l y s i s .

Thc model used i s g i v e n b y :

Where Y = r i c e o u t p u t ( % g / n a )

A = scale F a c t o r , w h i c h i s g r e a t e r t h a n

zero a n d w h i c h i s a s s u m e d to a r o d a t

a s t e a d y r a t e .

X, = farm size ( h a ) ..

A = amount of f a r m l a b o r 3

X I = t r a c t o r - h i r e c h a r g e p c r h e c t a r e a n d 2

c a p i t a l d e p r e c i a t i o n of e q u i p m e n t I 1 4 1

?: = V a r i a b l e c a p i t a l c o s t ( J / n a ) /I

U - S t o c k a s t i c v a r i a b l e of error term w h i l e

t a k e s a c c o u n t of u n e x p l a i n e d F a c t o r s

a f f e c t i n g r ice p r o d u c t i o n .

T h e exponents 5 .. . b4, r e p r e s ~ n t t h e

r c l a t f v e p r o p o r t i o n of r i ce o u t p u t c o n t r i b u t e d

by t h e v a r i o u s i n p u t s .... X and a l s o 4 '

i n d i c a t e t h e e l a s t i c i t y o f otl 'l:put with respect

to chanqes i n t h e S s ,

He however s t a t e d t h a t f a r m s i z c was not

s i g n i f i c a n t l y r e l a t e d to r icc o u t p u t S u t l a b o r

i n p u t was s i ~ n i f i c a n k t-o r i ce o u t p u t .

Onouo (1991) developed a c o m p u t e s a i d e d

i ' !etnv~ork a n a l y s i s for optimum tractor and irnplenen t

alLoca t i on . He considered t i m e 1 i n e s s a s t h e

major interest in tractor allocation.

Determination of the t i m e f o r e a c h w o r k and t h e

d ~ c i s i o n t o alloca t~ tractors and i m p l c m c n t s ,

time i t takes to complete t h e operation were

covered in t h e programme. T h e t i m e it takes to

complete a particular field operation showed a

great r e d u c t i o n w i t h h e l p of t h e n e t w o r k programme.

CHAPTER 3

3 . 1 Themre t i c a l Framework;

l i l tnis c h a p t e r we wish to deve lop a model

for t h e a l l o c a t i o n of t r a c t o r s by t h e Benue S t a t e

T r a c t o r H i r i n q Agency ( i 3 E N T H i i ) . To make dSNTHA

v i a b l e m e a n s a l o t t o i t s management. These

m a c h i n e s a n d p e o p l e . Zfforts should bc rnadc to

e f f ~ c t s c i e n t i f i c manaqernen t of f i e l d o p e r a t i o n s

w h i l e technical workeps outpuk should be assessed

based on real eng inee r i n9 e x p e r t i s e .

3.2 The S o d e l ;

T h e model will c o n s i d e r t w o o b j ~ c t i v e s

narr-ely, t he s o c i e t a l oSjective and government/

p a r a s t a t a l o b j e c t i v e . T h e s o c l e t a l o b j e c t i v e

i s that of r n a x i m i z i n q food o u t p u t ta m e e t t h e

demand of h e r ever increasing popu la t ion .

T h i s could be realized t h r o u g h i m p r o v e d f a r m i n g

methods s u c h as t h e use of t r ac to r s , f e r t i l i z e r ,

aqro-chemicals and o t h ~ r imp lenen t s . Tsegha ( 1992 1.

Thc : ;ovcrnmen t / i 2 a r a s t a t a l o n t h e Q t h e r

h a n d l w i s h e s to ass i s t f a r m e r s to a c h i e v e t h e i r

se t ob j ec t i ve s o f maximizing food o u t p u t b y

p r o v i d i n g t r a c t o r s , f e r t i l i z e r , ag ro-chemica l s

a n d o t h e r i n p u t s a t s u b s i d i z e d r a t e to farm-rs.

9ENTHA d u l l e t i n (1989).

The i n p u t o f i n t e r e s t i n t h i s s t u d y i s t n e

f a r m tractor a n d i ts rnanaqemen t .

P r e a r n b l ~ :

L e t F i be t h e p r o d u c t i o n o f the i t h f o o d .

H = H ~ c t a r a g e to bc p l o u g h e d i n d i f f e r e n t

z o n e s .

U = Inputs (seeds, f e r t i l i z e r , t r a c t o r s ,

Agro-chemicals, l e v e l of m e c h a n i z a t i o n ) .

T = Timeliness

V = Inveskmen t

d = : ; ~ a t h = r .

Y h c t n t a l p r o d u c t i o n o f t h e i t h crop in t h e

j t11 z ~ n c = F i j

:. F- i ' i: F - Tota l p r o d u c t i o n o f t h e i t h j='f l j

f o o d c r o p i n a l l zones .

C l ~ a r l y Fi i s m o n o t o n i c w i t h H . T h a t i s F i

i n c r e a s e s when H a l s o i n c r e a s e s p r o v i d e d t h e

f - o l l a w i n q a s s u m p t i o n s o n t h e v a r i a b l e s U , T , V

a n d :.j h o l d .

(a) U: Good seeds, correct a m o u n t of fertilizer

a p p l i c a t i o n and o t h e r agro-ch~mical s and

then reasonable l e v e l of m e c h a n i z a t i o n .

( b ) T: Land is c l e a r ~ d on t ime, p l a n t i n g is

done on t i m e , a p p l i c a t i o n of fertilizer

i s on t i m e and weeding i s done on time

a n d h a r v e s t i n g is bone on t i m e .

( c ) V : T h e r e i s adequ?ke i n v ~ s t m e n t .

( Q ! Good w e a t h e r and enough rainfall.

Since F , is monotonic w i t h t l , w e have I

5 F i j (H, u, T , Y ,

Our i n t 2 r e s t t h e n is t o maximize t h e total

h e c t a r a q e to be p l o u q h c d w i t h o p t i m a l d i s t r i b u t i o n

of the f e w available t r a c t o r s n;.::ned b y BENTHA.

:i = T o t a l n u m b e r 05 t r a c t o r s o v ~ n e d S y

d2NTHA and a v a i l a b l e for a l l o c a t i o n .

H t = Total number of h e c t a r a q e p l o u q h e d o n

t h e t t h day a t all zones.

For t h e j t h zone , l e t

m.! = Number o f t r a c t o r s allocated. i

P i = P r o b a b i l i t y of a t r a c t o r warking a t J

t t h d a y i n t h e j t h z o n e .

I). = Number of tracizor d e m a n d e d by t h e j t i 7 J

zone,

P ik , m . = Probability of k tractors working j J

on t h e t t h d a y .

i? ( !< 1 = Numb?r of i-icctarage ploughed by j

k t ractors i n t h e t t h d a y .

-. B, {rn . ) = s x p e c ted n u m b e r of hec t a r a g e p e r J 3

t th d a y p l o u g h e d by t r a c t o r s .

A s s u r n ~ t i o n s ;

i) The t o t a l nurnbcr of h e c t a r a g e t o bc p l o u g h ~ d

is zzsumed discrete.

ii)

iii)

i v )

30

.?he number o E tractors work inq i n B: yhven

d a y t, fol lows Sinornial d i s t r i i : u t i o n .

g u f f i c i c n t l a n d i s a l w a y s a v a i l a i s l e for a l l

t r a c t o k s a ~ l o c s t e d .

T h e o p e r a t i o n is t i m e l y .

he e x p e c t e d n u m b e r of h e c t a r a q e r-l plughed " t

by a l l k r a c k o r s a t t h e j k h zone is given by

tience t h e t o t a l nurnbcr

by t h ~ t r a c to r s in a11 ~ o n e s / u n l t s on t h ~ t t h

day is given by:

~ u b j w t to t h e cons t r a i n t s

r i j r i r n D whcre rn* is the minimum t h a t can

'113 qiven to c7 zone l r r e s p c t l v e of d~rnand a n d

= M = t o t a l ::umber of t r a c t o r s a v a i l a b l e

f o r allocation.

3.3 3 a t a C o l l e c t i o n :

T ~ E d a t a usca as I n p u t t o r t h i s s t u d y were

collected kron t h e Benue s t a t Tractor i l l i r inq

A q e n c y ( B E N T H A ) . I n order t o neterrnine opt imum

h e c t a r a g e of l a n d t h e number of t r a c t o r s

a l l ~ c i i t e d t o v a r i o u s zones a n d h e c t a r a g e p loughed

arc n e ~ d ~ d . ~ a t a were a l s o neebe?, on t h e

[ E- h&Jb..rp b-"Y p a r t i c u l a r b,ay, t P - w c t,-, >,dtbl~% ,ft> +-- L, -7 ',d .-A !"U- ;;9~_c"+J4 W

- he da ta collection exercise w a s v e r y

l a h r l o u s , 1 t took ser ies of r e p ~ a t e d v i s i t s to

w i t h t , rm~e i n , - c h a r g e to q i v ~ ~ u t ; information on

x t i v i t i c s and o p c r a t i a n s of U ~ t ! y ! h . c o n s e q ~ i e n t l y ,

they would be i n complicated form and i n s u f f i c i e n t .

T i ~ e i r e x t r a c t i o n i n t o a s u i t a b l e form was q ~ i t e

t ime-consuming.

The record on demand o f t r a c t o r s f rom each

zone d u r i n g a f a r m season was not kept;.

It was assumed tha t a l l the available tractors could

be a l loca ted t o one zone. 3Inwever., f o r p o l i t i c a l

c o n s i d e r a t i o n s , a ~uinimum of 22 t r a c t o r s were a l loca ted

t o each zone,

C R U T E R 4

MODEL APTALYSXS AND RESULTS

4.1 H e u r i s t i c s o l u t i o n of t he Model

The marginal increase in t h e number of hectarage

plowzhed by the t r a c t o r s as a r e s u l t a f allocatiw t h e

rn-tn tractor t o t h e j t h zone i s given by J

The j t h zone is t hen a l l o c a t e d t h e m.' th t r a c t o r on ly S when t h a t t r a c t o r results i n maximum mmginal increase i n

the number of hectarw,e ploughed.

4.2 The H e u r i s t i c Fracadure f o r Trac to r Al loca t ion

I. Determine P .(k.m .) for every in teger rn such that J J j

m - m & R and f o r every i n t e g e r k such that O j, O k k 4 m f o r every zone.

j

2. Determiae h . ( k ) f o r every i n t ege r 06kCi i l J

3. S e t r=1 where r represents t he number of i t e r a t i o n s

4. S e t m .(r) = m* f 3r every J (minimum that can b e 3

a l l o c a t e d t o a zone).

5. Betermine A . ( r ) J = A J L m j ( r ) +I, mj(r)_/ f o r every j

6. Determine J * such that h . * ( r ) = max A . ( r ) ,I j J

7. S e t r = r + . ;

8. Set rcj(r) = m .(r-I) f o r every j +j* J

9. S e t m . + ( r ) - m ( I * - , I ) + I J j

I . s t o p the m,(r) i s the accepted b e s t value o f m - j. J J

A se t of data was generated f o r anabgsis. It was

b a s e d on the f ac t that a total ol" 95 t r a c t o r s i n good workim

c o n d i t i o n :Irere ava i l ab le f o r a l l o c a t i o n in t h e y e a r 1990.

~f a m i n i m u of s q 22 t r ac to r s were a l l o c a t e d t o each zone,

t h e n the re were 7 tractors remaining t o be shared between t h e

f o u r zones. We t h e n appl ied t h e model developed f o r t h e

a l l o c a t i o n of t h e remaining 7 t r a c t o r s . F o r easy

appl ica t ion o f model on the generated data, t h e generated

da t a has been s i m p l i f i e d as ziven i n t h e t a b l e s below

T a b l e 4.3 Number of hectarage hj(k) ploughed by k t r a c t o r s in t h e t th dqy I n a l l zones based on t h e trsnerfited data

Table 4.4 p k j ) = p r o b a b i l i t y distribution o f k t ractors && on t h e t t h d a y when m, of the t o t a l

V

t r a c t o r s a re allocated t o a l l zones when - m* = 22 based on the generated data.

0.004 0.008 0.01 2 0-02 0.024 0.028 0.032 0.036 0.04 0,044 0.0443 o. 052 0.056 0.06 0.06 3.06 0.062 0.052 0, ma 0.044 0.08. 0.04 0, O'F 0,028 0.024 3.02 0.015 0.004

dar Ploughed by m i t r a c t o r s f o r a i l the Zones * I

based on t h e ~ e n e r a t e d ;rc: data

Table 4.6 The Marginal increase in the number of hectarage

ploughed by the t r a c t o r s H(m .+'I) - H(m .) based J J

on the generated data.

T a b l e 4.7 ITumber of T rac to r s a l loca ted t o the Zones Rased

on t h e proposed M o d e l when m* = 22 based on t h e

gcnera.ted data.

L'.

T a b l e 4.8 ~ c t u a l A l l o c a t i o n By BE'WHA

L!,.

T o t a1 ---TY

H(m J . ) (Avere,~e h e c t c v w e

p e r t- th day) .

T a b l e 4.9 Comparisnn o f Allocation Policies

Actual Allocation / ~llocation Based on The By OENTHA 'I990 Proposed Model usin; t h e

qwerated data

ZOIES m . H(lo - j 5 3

T ~ b l e k.8 .g ives t h e a c t u a l a l l o c n t i o n as was dons

b y F , E Y ~ I I A in the y e a r 1990 u s i n g t h e ava i l ab le t r a c t o r s

that were i n perf 'ect working c o n d i t i o n . Tab l e 4.9 shows a

cornpa lson between the a l l o c a t i o n policies. T h e increase

in t h e t o t a l hectL,-85e ploughed by t h e allocation based on

t h e proposed model usinl ; t he generated dpta is given as

There is an increass i n t h e t o t a l hectarage ploughed

when the model developed is used f o r a l l o c a t i o n of t r a c t o r s ,

e v e n though t h e increase is small, This is because

h e u r i s t i c procedures a r e used. hn increase in total hecta-

r G e ploughed c a n be improved upon if t h e a1l;orithm is

f u r t h e r improved upon. A l s o if t h e P . va lues a r e increased J

as a resul t of p r u y r supervision of t r a c t o r o p e r a t a r s and

proper m i n t encvlcs of t ractors .

In this study we reviewed models of t r a c t o r management

o r a l locat ion. A mathematical ~ o d e l was formulated t o

aid t r a c t o r a l l oca t i on based o n t h e p r o b a b i l i t y of a t r a c t o r

work i=~ in a ziVen da,y and t h e h e c t u a g e ploughed in t ha t day.

i i e u r i s t i c procedures snow tha* t h e r e is increase in the

t o t a l number of hectarage p l o u ~ h e d if a l l o c a t i o n is done

based on t h e proposed model.

5.2 Recommendations

Based on the r e sea rch we c s s r i ed o u t , we make the

f o l l o w i n g r e ~ o ~ e n d a t i o n s :

(a) BE?JTHA shou ld be keep in^ yecords on a l l t r ac to r s owned

by it. These should inc lude

(i) N a m e of t r a c t o r

(ii) !lame of Operator

(iii) Make of tractor

(iv) YeL= b o u ~ n t

( v > Horsepower

v i j Ma in tenance history, t h a t is, t i m e it

b r o k e d o w n , r e a s o n f o r h - p a l - d o w n ,

4. ,lme ' t a k e n before r e p a i r s a n d cost

of r e p a i r s . T h i s w i l l h e l p to f i n d

n u t w h e t h e r a t r ac to r is w o r k l n g on

a d a y t or n o t .

( b i 'I'he number of t r a c t o r s allocated to a zone

m u s t b e d e c i d e d based on the tractor needs

o f t h ~ zone.

( c ) I t may be p o s s i b l e to i n c r e a s e t h ~ e f f e c t i v e -

n e s s of zones a s a r e s u l t of a l l c x a t i n g more

t r ac to r s to arcas where t h e w o r k l o a d

( n u m b e r of h e c t a r a g ? to be ploughed is more

even i f t h e y a r e from the same geo-e thn ic

arpa.

!ti) Farmcr s who come to p a y for t r a c t o r s s h o u l d

h c v a d e t o s u p p l y t h e f o l l o w i n g information:

i) T y p e of o p ~ c 3 t i o n

ii I Nurnh~r of h ~ c t a r e s

iii N u m b e r of t rac tors r e q u i r e d

iv! S i t e of f a r m

v ; Type of crop to be p l a n t e d

(vi) Loca t ion of farm

( v i i ) Kame of f a r m e r .

( 2 ) BENTI% s t d f should be s e n t to 5nspect t h e

f i e l d so as t o ascertair, t h e seal fam s h e .

(f) Further work shou ld be done in improving the

algorithm of t h e proposal model l 'o r

o p t i m a l allccation.

(g] F u r t h e r work should b e done to determine t h e

e f f e c t of cos t o f ope ra t ion on the a l l oca t i on

of tractors.

-E

J=

Ln

C

UC

Q

w

O ,a -

4

0-t c

-4

.< u

d1

3U

rd

C E R V I ? $ K A , V . and CHANCELLOR, N.J. (1975) Regional Economic Implications of V d r i o u s I n t e n s i t i p s of u s e of C r o p P r c d u c t i o n E q u i p m e n t . T r a n s of Arner. 5OC of Aqric 5ng. 1813) 453-8.

C U P I N , C. (1976) Farm P l a c h i n e r y . 9 t h E d i t i o n E L a S and CLS London.

Z K S D F G J A , S.A. 11991) Oral I n t e r v i e w w i t h Manager , F i e l d Operations, B E N T H A , E a k u r d i , aenue S t a t e .

IIUPIT, D.H. ( '1970): Farm P o w e r and C.iachin?ry Manaaernen t , F i f t h S d i t i o n , I o ~ a 5tate U n i v e r s i t y P r e s s A m p s Iowa.

:;avannah %ones of l i e s t e r n Nigeria. 2 h S R Vol. -13, ido. 4. A c a d e m i c Press, London.

NAK5?!JUULA, G.A. 11983). The I m p a c t of Yorris J. 2,382 Technology C h o i c e in S m a l l Holder M e c h a n i z a t i o n , pp. l l 3 - l ' l 4 .

; J ~ A K K X , A . 1 IWU), R a d i o d r o a d c a s t to the P e o p l e of L3~nue S t a t e , N i g e r i a .

O S I J I , €.I. (1983) : Farm M a c h i n e r y Selection Cos t i n q and klanage inenk f o r O k p u j c R u r a l C o m m u n i t y ; 8.Sng. T h e s i s , D e p a r t m e n t of AqriculturaI Engineering, U n i v e r s i t y of Nigeria, Nsukka ,

O K L R E K E , 0. (1991) " I n c r e a s i n g Rice O u t g u t T h r o u a h T r a c t o r u s e in A n a m b r a S t a t e , N i g e r i a " . + ; i n r a c k I n t e r n a t i o n a l I n s t i t u t e f o r A g r i c u l t u r a l D e v e l o p m e n t . A f r i c a n R u r a l Science Series Research > p p o r t , Number 14.

1 9 . ONOVO, S.A. ( 1 9 9 1 ) Opt imum A l l o c a t i o n o f Farm T r a c t o r s a n d E q u i p m e n t u s i n g N e t w o r k A n a l y s i s . U n p u b l i s h e d B. Enq. T h e s i s D e p a r t m e n t o f A g r i c u l t u r a l E n g i n e e r i n g , U n i v e r s i t y o f N i g e r i a , N s u k k a .

20. R E E C E , A . R . ( 1 3 6 7 ) " T r a c t o r D e s i g n a n d T r a c t i v e P e r f o r m a n c e " A p a p e r p r e s e n t e d a t t h e A g r i c u l t u r a l E n g i n e e r i n g Sympos ium o f t h d I n s t i t u t i o n o f A g r i c u l t u r a l L n g i n e e r s . Bed f o r d E n g l a n d .

21 . KENOLL, E . S . ( 1 9 7 0 ) . A M e t h o d f o r P r e d i c t i n g Field M a c h i n e r y E f f i c i e n c y a n d C a p a c i t y . T r a n s a c t i o n s of t h e A S A E 1314) pp . 448-9.

2 2 . TSEGHA, J . T . (1992) V i a b i l i t y P a c k a g e f o r t h e B e n u e S t a t e T r a c t o r H i r i n g A g e n c y " . R e p o r t p r e s e n t e d t o t h e G o v e r n m e n t o f Uenue S t a t e b y t h e G e n e r a l M a n a g e r , dENTMA, M a k u r d i .