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METHODS FOR RURAL FARMING
Mamatova Zilolakhan Khabibullokhanovna
Fergana state university associate professor ,
pedagogy sciences according to philosophy doctorate ( PhD )
Orchid : 0009-0009-9247-3510
E-mail:
Daminova Shahsanam Davlatjon kizi
Fergana State University Practical mathematics 3rd year student , group 22-09 student
E-mail:
daminovashohsanam0@gmail.com
Abstract
: This the issue of transport in the article theoretical and practical in terms of wide
is illuminated . Fergana of the province farmer farms products province in the center to the
market the most less cost with to deliver problem analysis The issue is solved step by step
with a minimum price . method through solved . Real example optimal plan based on will be
compiled and general expenses is reduced .
Keywords :
Transport issue
,
closed model transportation issues, busy cells, empty cells, cost
matrix, potentials, potential equation, closed loop.
Introduction .
The transport issue is the key to the economy. the most important and
practical from issues This issue is one of logistics , supply chain and working release
processes to optimize is focused on . Each enterprise or working release system for the
product from supply to the consumer in delivery expenses big importance has will be . In this
transportation expenses reduce and from resources effective use economic in terms of
important . The issue of transport theoretical solution through , as well as balance supply ,
consumers need satisfy , suppliers by working issued products delivery to give efficiency
increase possible.Transport The problem is usually linear . to program related is , it is in itself
resources maximum at the level effective distribution in mind holds . Each supplier and
consumer products , as well as their between
transportation expenses This issue is very
common . in the fields wide used , including rural farm products to the market delivery in
giving , industry working releases between in transporting materials and even international in
trade .
This issue is particularly limited resources there is was in conditions , economic efficiency
increase for very important . The issue minimum value in solution method and potentials
method such as separately methods These methods are used . through , transportation costs
optimization , product effective distribution and supplier and consumers in the middle
effective communication provision opportunities is studied .
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Analysis and results
Let's assume ,
m
A
A
A
,...,
,
2
1
produce the same product at each point. At a certain time
interval,
)
,1
(
m
i
A
i
=
at the point working removable product amount
i
a
to unity equal
Let it be . Work removable products
n
B
B
B
,...,
,
2
1
at points consumption let it be done
and every one
)
,1
(
n
j
B
j
=
consumer being seen time between to the product was
demand
)
,1
(
n
j
b
j
=
to unity equal Let it be .
From this outside
m
A
A
A
,...,
,
2
1
at points working removable of products general amount
n
B
B
B
,...,
,
2
1
of points to the product was requirements general to the amount equal , that
is
=
=
=
n
j
j
m
i
i
b
a
1
1
equality appropriate Suppose to be Let 's assume that every
one working release from
the point everyone consumption doer to the point product transportation opportunity
exists , and
i
A
from the point
j
B
to the point the product take to go for spending to be
done cost
ij
C
money per unit equal Let it be .
ij
x
with planned time between
i
A
from the point
j
B
to the point take to go of the
product general amount we mark .
The transportation issue given parameters and designated the unknowns following to the
table we will place .
Table 1
j
B
i
A
1
B
2
B
n
B
i / c products
amount
1
A
11
C
11
x
12
C
12
x
…
n
C
1
n
x
1
1
a
2
A
21
C
21
x
22
C
22
x
…
n
C
2
n
x
2
2
a
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…
…
…
…
…
…
m
A
1
m
C
1
m
x
2
m
C
2
m
x
…
mn
C
mn
x
m
a
demand
quantity
1
b
2
b
…
n
b
The matter economic meaning of freight so plan to compose must : 1) every one working
release at the point products full be distributed ; 2) each one consumer to the product was
demand full satisfy and this with together spending to be done road expenses general Let
the value be minimal .
The matter first condition following equations system through expression possible :
=
+
+
=
+
+
+
=
+
+
+
.
...
...
..........
..........
..........
,
...
,
...
2
1
2
2
22
21
1
1
12
11
m
mn
m
m
n
n
a
x
x
x
a
x
x
x
a
x
x
x
(1)
The matter second condition and following equations system in appearance is expressed
as :
=
+
+
=
+
+
+
=
+
+
+
.
...
......
..........
..........
..........
,
...
,
...
2
1
2
2
22
12
1
1
21
11
n
mn
n
n
m
m
b
x
x
x
b
x
x
x
b
x
x
x
(2)
The matter economic to the meaning according to unknowns negative not to be need , that
is
).
,1
;
,1
(
0
n
j
m
i
x
ij
=
=
>
(3)
-
i
working release from the point
-
j
consumption doer to the point planned
ij
x
unity
the product delivery to give for spending to be done road cost
ij
ij
x
с
money per unit equal
will be .
Planned all products transportation for spending to be done general road expenses
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=
=
=
+
+
+
+
+
+
+
+
+
+
+
+
=
m
i
n
j
ij
ij
mn
mn
m
m
m
m
n
n
n
n
x
c
x
c
x
c
x
c
x
c
x
c
x
c
x
c
x
c
x
c
Y
1
1
2
2
1
1
2
2
22
22
21
21
1
1
12
12
11
11
...
...
...
...
function through is expressed as . The problem on condition according to this function to
a minimum aspiration need , that is
=
=
®
=
m
i
n
j
ij
ij
x
c
Y
1
1
min
(4)
Relationships (1) – (4) joint transportation issue mathematician is called a model .
The transportation issue mathematician model following gathered to write in plain sight
possible .
)
,1
(
,
1
m
i
a
x
i
n
j
ij
=
=
=
(5)
)
,1
(
,
1
n
j
b
x
j
m
i
ij
=
=
=
(6)
)
,1
;
,1
(
,
0
n
j
m
i
x
ij
=
=
(7)
=
=
®
=
m
i
n
j
ij
ij
x
c
Y
1
1
min
(8)
In question every one
j
i
b
a
,
and
ij
c
non-negative numbers that is
,
0
i
a
,
0
j
b
.
0
ij
c
in problems (5) – (8)
A
b
a
n
j
j
m
i
i
=
=
=
=
1
1
equality appropriate if , that is working issued products sum ten was requirements to the
sum equal if , then this issue closed We call it a model transportation problem .
Theorem
1.
Any closed model transportation problem to the solution has .
Theorem 2. The
transport problem from the conditions structured matrix
)
(
A
r
color
1
-
+
n
m
equal to .
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Theorem 3.
If the problem all
i
i
b
va
a
all
from the numbers consists of if the
transportation issue solution whole numerical will be .
Theorem 4.
Optimal plan for the voluntary transportation problem exists .
The optimal solution to the transportation problem find for potentials method
Potentials method of transportation solution for applied first clear method was born in 1949
Russian scientists LV .Kantorovich and MKGavurin by This method is created main The idea
is related to the transportation issue. customized simplex from the method consists of is the
first times linear programming issues solution to the methods related not been without
described . Later , similar
method American scientist Danzig by created . Dancing
method linear programming main to their ideas based in American literature this method
modified distribution It is called the method .
Potentials method help with elementary basis from the plan from , to the optimal solution
closer was new basis to plans passing by go , limited on the thigh from iteration after optimal
solution to the problem is found . Each in iteration found basis plan optimal plan that it is
check for every one working issuer
)
(
i
A
and consumption to the (
j
B
) point his/her so-
called potential
i
u
and
j
v
quantity suitable These potentials are so is chosen , in which
mutual connected
i
A
and
j
B
to points suitable incoming potentials sum
ij
c
to
i
A
from
j
B
unit to the product transportation for spending ( equal to the cost of transportation ) to be
need .
Theorem 5.
If
)
(
*
*
ij
x
X
=
plan optimal plan of the transportation problem if , then to
him/her
)
0
(
*
*
*
>
=
+
ij
ij
j
i
x
c
v
u
(9)
)
0
(
*
*
*
=
+
ij
ij
j
i
x
c
v
u
(10)
the conditions satisfactory
m
n
+
one
*
i
u
and
*
j
v
potentials suitable arrival necessary and
enough .
Proof
.
Sufficiency
. Suppose ,
)
(
*
*
ij
x
X
=
plan for (9), (10) conditions appropriate Let it be .
Then optional
)
'
(
'
ij
x
X
=
plan for
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
+
=
+
=
+
=
+
>
m
i
n
j
ij
ij
n
j
m
i
ij
i
m
i
n
j
ij
i
n
j
j
j
m
i
i
i
n
j
m
i
ij
i
m
i
n
j
ij
i
m
i
n
j
ij
j
i
m
i
n
j
ij
ij
x
c
x
u
x
u
v
b
u
a
x
u
x
u
x
v
u
x
c
1
1
*
1
1
'
*
1
1
'
*
1
*
1
*
1
1
'
*
1
1
'
*
1
1
'
*
*
1
1
'
)
(
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So ,
*
X
planned linear function value his/her optional
'
X
planned from the value small It's
happening . That's why for
*
X
the plan will be optimal .
So so , potentials method algorithm from the following consists of :
1. From above built of methods from one using , initial basis plan is found .
2. Found plan optimal plan that check for potentials system is made . This from formula (15)
for using every one filled box for (17) in the form potential equations It is known that the
transport issue different from 0 in the plan was variables number
1
-
+
m
n
ta. So , the
potential equations system
m
n
+
unknown
1
-
+
m
n
equations from the system consists
of In this system unknowns number equations from the number more than happened because
of the numerical value of potentials find for from them optional to one clear one value , for
example zero value giving the rest one after another find possible . Let's assume ,
i
u
known
Let , then from (15)
j
v
found :
i
ij
j
u
c
v
-
=
If
j
v
known if , then
i
u
as follows found :
i
ij
j
u
c
v
-
=
All the numerical value of potentials clearly after all , everyone empty boxes for
)
(
ij
j
i
ij
c
v
u
-
+
=
D
is considered . If all
i
and
j
for the
)
,...,
1
;
,...,
1
(
,
0
n
j
m
i
ij
=
=
D
appropriate if , found elementary basis plan optimal plan will be .
3. If
i
and
j
of at least one value for
i
A
if , initial basis plan is replaced . This for
lk
ij
ij
D
=
D
>
D
0
max
the condition satisfactory ( l,k ) box will be filled (
lk
x
unknown) to the base is
entered ).
q
=
lk
x
suppose as ( l,k ) to the box
q
is entered . Then hour arrow according to
( l,k ) from the box Starting from the beginning , moving on , filled to the boxes order with ( -
) and ( + ) gestures placed As a result closed
K
outline harvest will be
+
-
=
K
K
K
U
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this on the ground
,
-
K
+
K
– with (-) and (+) signs the boxes own inside recipient half
contours .
By the following formula
q
the numerical value of is found .
pq
ij
K
x
x
x
ij
=
=
min
q
(11)
4. New basis plan is :
-
=
+
=
=
=
=
-
+
.
,
'
,
,
'
,
,
'
,
0
'
,
'
K
x
agar
x
x
K
x
agar
x
x
K
x
agar
x
x
x
x
ij
ij
ij
ij
ij
ij
ij
ij
ij
pq
lk
q
q
q
New basis planned filled boxes number
1
-
+
m
n
that there was for (19) condition
satisfactory boxes suddenly more than if so , from them one empty to the box turned over and
left in the boxes assume the distribution is equal to 0 Found
new basis plan for again
again potentials system will be found and new optimal plan to be condition is checked . If
new basis plan optimal plan if not , then again again in points 3, 4 made affairs The process is
repeated until the optimal solution is found . until found , that is all empty boxes for
0
-
+
=
D
ij
j
i
ij
c
v
u
condition until done repeated .
Subject :
Fergana of the province the following 4 village economy in 2025 autumn
in season apple harvest gather when taken :
1. Sixty Agro Service – 120 tons
2. Rishton Fruit - – 80 tons
3. Blood AgroPark – 100 tons
4. Besharik Harvest Agro – 100 tons
This the harvest to the 5 largest supermarket chains in the region delivery to give is being
planned . Supermarkets every in one apple The requirement is as follows :
1. Macro – Marg'ilon branch – 70 tons
2. Basket – Blood branch – 90 tons
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3. Baraka Market – Mother Farg center – 60 tons
4. Grand Market – Buwayda district – 80 tons
5. Asia Supermarket – Kuva district – 100 tons
Farmer from their farms 1 ton to supermarkets apples delivery to give expenses in the som as
follows
In our case, 4 farmers farm
and there are 5 supermarkets . Each delivery to give
direction according to expenses schedule given . Solution as follows done increased :
6 × 70 + 8 × 50 + 7 × 40 + 4 × 40 + 6 × 20 +
+ 8 × 80 + 3 × 100 = 2320 so'm
Farmer from farms apple products to supermarkets delivery to give according to structured
this transportation issue is real life logistics problems in solution how economic approaches
application obvious shows.Northwest corner method load distribution using compiled and
elementary plan calculating Then , the minimum elements method through the most cheap
transportation expenses based distribution planned . Both of the method results analysis was
done , expenses compared and potentials method optimal plans using conditions checked .
In practice such approaches enterprises and farmer farms
for from resources reasonable
usage , transportation costs reduce and logistics efficiency to increase service Through this
issue
student or specialist in transportation optimization mathematician modeling
importance understands and real problems analysis to do his/ her skills shapes .
Literature:
1. L. Kantorovich - " Mathematician programming and economic analysis " (1959).
Production release optimal plan in processes to compose and resources distribution
methods statement done .
T
B
1
B
2
B
3
B
4
B
5
Z
A
1
70
6
50
8
0
10
0
9
0
7
120
A
2
0
9
40
7
40
4
0
2
0
5
80
A
3
0
3
0
4
20
6
80
8
0
6
100
A
4
0
4
0
6
0
0
7
0
5
100
T
70
90
60
80
100
400
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Journal:
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2. GN Nemchinov , " Linear economic models " (1972). Economic in systems linear
programming and analysis methods to use dedicated .
3. VM Zhuravlev , " Linear programming and transport issues " (1993). The transport issue
solution and his/her practical application about in detail explanations given .
4. BT Pukinel , "Transport and logistics systems optimization " (2002). In transport systems
optimality provision and resources effective distribution methods seeing released .
5. AK Kolmogorov , " Linear programming : theory and practice " (1985). Linear
programming methods various in the fields use , this
including in transport matters
application .
6.
Q. Safayeva . Mathematician programming . Learning manual . TMI-2003.
