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Воронежский государственный технический университет

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Учебное пособие 800649

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			T* T		max,		(9)
			j	i
Dijmax —		,				Sijmax.	,
Dijmax		, .moo	.			,
			.
		Sijmax,	i≠j, i, j = l, ..., k,			,	,
		S,	Smax.			,	Dmax
Smax,		S				,
Smax,
			Dmax Dmax				(10)
			i	j	ij
γ=k(k—1).	,	,	Sijmax,				Smax,
γ=k(k—1).	,	,			S
	,	γ*= k1k2.	Sijmax,				Smax,
		γ*= k1k2.					Smax
S.	Sijmax,	i —			Smax	, a j —
S.		k1 = k2=l			Smax	S
	.	max,
	.	(10),				,	.
	Dmax	(10),	'			,	.
	Dmax		'				S
		,	(			,	).
.		,	Dmax
.
				«		»	, . .
			(		)	.
			(		)

T	T	ij	(t, x), i, j N,
j	i	ij
l t, x T L t, x ,
	t M,
m	t M,

a x b,

121314

T= (T1, T2, ..., Tk)' —						,
t=(t1, t2,..., tk)' —						,
= ( 1	2, ..., xk)' —					,
αij(t, x)	—						t	x, l (t, x)
L(t, x) —			,	-		, m = (m1, m2, ..., mk) > 0		= (	1
2, ..., Mk)' —				k —		,	b —	x, N —•
,	(i,	j),		Д1Ж		, k —		x, N —•
.	(i,	j),		Д1Ж		, k —	(13) — (14).
.			,		,	,	(13) — (14).
			,		,	,
(					,	Д1Ж		.)
(				(	,	,		.)
.).				(		,
.).
	(11)	— (14)	,			,
		Д1Ж (		,		)		,
(i, j)		i						αij, li, Li	a
				91

	αij(t, x), li(t, x)		Li(t, x)		bi.	t .		,
	i		mi, Mi	i	bi.	G	,
			(11) —(14).			k	,	k
—		(11) — (14),			(i0, j0)	,
	(11) — (14)		Tj0—Tf0 > αi0j0 (t, x).			αij (t, x)
		(i,	j),		li(t, x),	Li(t, x)
i		G	(11) — (14).		,			(
,	)	G						.
	Д1Ж,	(11) — (14)						,
			,			(11) —	(14)


	T0		0i (t,x), li t,x					i 1,...,k,	15
Ti	T0		0i (t,x), li t,x					i 1,...,k,	15
T		T		i0	(t,x), L t,x			i 1,...,k,,	16
0		i		i0		i
			T			0
0			T			0
				0			,		17
							,		17
	min					max
l			T			L

lmin	Lmax
	li(t, x)	Li(t, x)	(13) — (14).
,				G0
,						ρ
				1		ρ.
	G0, S = 1, ..., ρ,			φ0(t, x) ≡ 0,
,	δ= ρ,	G0	0			.
Д1Ж		xi, i = l, ..., k,
		xi, i = l, ..., k,				,
	(11), (13) -(17),					,
	,		max s ij (t,x),
			max s ij (t,x),
			0 s

			m t M,
			a x b,


			(11) - (14),
			Tj Ti			ij (t),
			l t	T L t ,

			m t M,

		(18) — (20)			(t) 0,
			max		(t) 0,
			0 s	s
				M,
			m t	M,
Ω
Ω
(21) — (23), . .
Min —	-		Д2Ж			Ω
t			).
	t* Min		).
	t* Min					-

(11), (13) — (17)
	Д4Ж	,
,	φs(t, x) —	s- o
	,	G0
.	Tj, j = l, ..., k.
	Tj, j = l, ..., k.
(11) — (14)
i, j N,		18
		19
		20
:
i, j N,		21
		22
		23

2425

(24) —(25),

-f(t)≡t (

(

)

(21) —(23),

T
p		,		T* = T + t,
	*
T
= t* —					.	,				t*,
						(21) —(23),
						1		k
						1		ti	min,
								ti	min,
				Ω,			k i 1
	Д2Ж,			Ω,		-				—
	Д2Ж,									—
			T
p									,
				*
			T			е t \|2
						е t \|2			t,
								k
						t2 ti2 min,
				t**				i 1		.
				t**						.
αij(t, x), li(t, x), Li(t, x),								.	(11) — (14).
				,		Ω		.
				,		Ω			( ,
				,		,			( ,
				,		,
			,		).				,
									,	.
		t		p* Min D,		D —			-	.
				p* Min D,		D —
					p
	,				** MaxD —					-
						p

(26)

t**

		(27)
	(13) — (14)
	t
,	)	.
	(	,

(11) — (14),

.	Min D
	p

MaxD —			T
MaxD —	-	D	p
p				*
			T

	.	,	T
	.	,	p
				*
			T
(	)		,

2Ti ti min(max),

i 1k

	(11) — (14),	(	)	-	(11) — (14).
	-				.
	,	(11) —	(14)	,	,
	-	2,	,		,
	. 15		.
	-		.
	,
.	Tmin, Tmax, Tmin, m , tmin, tmax, xmin, xmax				,
k,	(11) — (14).				Ti, Ti*, ti, xi, i = l, ...,
k,	(11) — (14).
	(11) — (14),
		93

(14)RT = Tmax—Tmin, RT* = T*max—T*min

,RT = Tmax—Tmin, Rx = xmax—xmin —

		[Timin, Timax], [Timin, Timax]				xi
		[Timin, Timax], [Timin, Timax]
		[timin, timax],		[ximin, ximax] —
		—		Ti, Ti, ti, xi,				.
		—			(11)	— (14),		.
			xi		(11)	— (14),
				.	,		.
		(11) —	(14)				.
		(11) —	(14)				,
	.						,
-	.
				( )	p	T
				( )	p
							*
(14)						T
(14)	,	,		min				max
				min				max
min							(11) —(14).
min
Х				щ
			.				T
			.				p
								*
							T
,	Δ( )≥0,	,	Δ(	)≤Diag t(p),		Δ(	) -	,
ij( )

(11) —

ij p ti tj ij p ,

ij p max Ti*, Tj* min Ti*, Tj* 0,

t(p)-		ti(p)					,	Diag	t -
Δ*( )						,		ti ,
Δ*( )	~	~
ij( )ж,	~	~
ij( )ж,	ij p	p
~	p min 0, ij	p .
ij	p min 0, ij	p .
							(21) — (23)
		Tµ -			≥	- tµ,
						µ — T		≥ — min + t .
			,					,	(24) — (25).
(21) — (23)					,			,	1
(21) — (23)
		T T		2	t		T T t ,
µ≠ .
µ≠ .	(21) — (23), (28)							.
	(21) — (23), (28)							.
	(28),

ij*( )

ij*( ) =max{0,

(28)

min=

(

αij(t),	li(t), Li(t)
Д4].					-
Д4].
,								(
)	,						.					.
	,											.
								.
	(28)							(21) — (23)						.
	(28)													.
	.	(28)
	.
	.		,				,
			,				,					.
												.
				-
	(9),	,			.						µ	— T	≥ — max	- t ,
	(9),	,											,
	.
	(3),	(4),											,	,
													S
			(		,					max	—		),
min		max	max			min	max	min	,	max
*	( )	=	*			,		*	,	*			,
	( )							S					,
S.													f = f(t,	),
													f = f(t,	),
		,										αij, li, Li
		,										,
	(11) —(14)						.
(11) — (14),		,
)	.												-
)		.
	,	.	,										(	)
	,		,							-			(	)
	xi		(11) — (14),									.	xj
									(			.	)
	(								(	)			)
	(						Δ(	)		)			.
							Δ(	)					.	,
							«					»	.	,
							«					»	.	.
-		(			)									.
		(			)
	-		q( ) ≥ 0,										—	-
Q( )	≥ 0.		q( )											.
,													(21) —(23).

T
		t

T

) ≥ 0 Q*(T, t, )>0,	ё
)>0,


q* T,t, d	q d ,

Q T,t, Q .

q*(T, t, Q*(T, t,

(29)

(30)

(	)
λi>0	( . .
),

					f	iti min					(31)
t Ω (	,			,	t,	i			(21) — (23))
t Ω (	,	t*		,	t,		.		(21) — (23))
-		t*					.
	«	»				t = t*			,	,	,
					,		i, j N,				32
					Tj	Ti ij (t),	i, j N,				32
					l T L,						33

					T* T t*,						34

	t*.										-
	T	t	*				(31)	—
									(33)
									(33)
	T*								«	» Д1Ж.
									«	» Д1Ж.
						(33)		,	(31),
								,		.
				(				)		.
				(				)
								t*
	,			,	t* —			(33).
	,				«			»	.
								-	.
				,
.									(	,
)								,	(	,
)								,	.
	,			,				,	.		.
	,			,				,			.
Д1Ж	(31) — (33),										,
											,
										:	,
	Д1Ж			.	ё	,				(32) — (33)
	Д1Ж				ё
						96

,	Д1Ж,	ё	—
,
z		Д1Ж.	z
z0		Д1Ж.
,	R		.
			.
	(32) — (33)		.

				,	,
		,		Д1Ж.	,
					,
		Д1Ж.
		[1].		(31)—(33),
				(31)—(33),
(	)		,		.
	,	«		»,	:
	.
		,			,
	,	,	,		,
	.				,
	.		-
			,	,	Д3—4]
		.	,	,
		(	,	,	,
					,
					)
		,			.

1.		.	.,		,		.	//
					. №3.1(53). 2013. - C. - 116-119.			//
			. .		. №3.1(53). 2013. - C. - 116-119.
2.			. .		Д	Ж/	. .,	. .//
					Д	Ж/	. .,	. .//
			. № 3.2 (17). 2015. -				C. 227-232.
3.		. .
Д	Ж/		.	.,		. .,	. .//
			. №4(62), 2015. –			. 31-33.
4.		.	.,	.	.,		.
					Д		Ж// «	:	,
	,		,		».	.			-
			.		(17-18		2015 ):	-
			,	.1,	2015. - C. 342-346.
					97

PARAMETRICAL NETWORK MODELS OF DISTRIBUTION OF LIMITED

RESOURCES IN TASKS OF LINE CONSTRUCTION

V. E. Belousov, O. Yu. Karchevsky, I. S. Sokha

Abrosimov Ivan Petrovich, VUNTs Air Force "Military and air academy of N. E. professor of Zhukovsky and Yu. A. Gagarin", teacher

Russia, Voronezh, e-mail: abros80@mail.ru, ph. +7-919-188-69-18

Karchevsky Oleg Yuryevich, Voronezh state technical university, graduate student of department of management of construction

Russia, Voronezh, e-mail: upr_stroy_kaf@vgasu.vrn.ru, ph.: +7-473-2-76-40-07

Sokha Ilya Sergeyevich, VUNTs Air Force "Military and air academy of N. E. professor of Zhukovsky and Yu. A. Gagarin", teacher

Russia, Voronezh, e-mail: catasroph17@rambler.ru, ph. +7-952-577-43-92

Abstract. In article effective methods of the temporary analysis and calculation of the generalized network models are offered. On their basis the class of parametrical network models is under construction and applications of such models to problems of distribution of limited resources of the construction organizations in the conditions of a production intensification are considered. A number of terms of scheduling is specified. Conditions of consistency and criteria of resource resolvability of some classes of tasks on such models are investigated.

Keywords: algorithm, method, model, project, production, construction, resources.

References

1.Barkalov S.A., Nguyen Wang Rangg, Nguyen Than Rangg. An algorithm of calculation of temporary parameters of the count and forecasting of a date of completion of the modelled process//Control systems and information technologies. No. 3.1(53). 2013. . 116-119.

2.Belousov V. E. An algorithm for expeditious definition of conditions of objects in multilevel technical systems [Text] . Belousov of V.E., Konchakov S.A.//Economy and management of control systems. No. 3.2 (17). 2015. C. 227-232.

3.Belousov V. E. An algorithm for the analysis of versions of decisions in multicriteria tasks of [Text] / Aksyonenko of Item Yu., Belousov V. E., Konchakov S.A.//Control systems and information technologies. No. 4(62), 2015. P. 31-33.

4.Belousov V. E., Lyutova K. G., Nguyen Vyet Tuang. Models of qualimetrical assessment of conditions of difficult technical systems [Electronic]//"Quality of production: control, management, increase, planning". Mater. International youth scientific and practical conference.

Kursk (on November 17-18, 2015): Publishing house of Southwest state university, T.1, 2015. - . 342-346.

519.8

				.	.	, . .

		Ю	я		*,	В	ы		,
			,	,		ы
Р	,	. В	, e-mail: bond.julia@mail.ru,				.: +7-910-341-29-46
О	ы	Д			, В		ы		,
	ы
Р	,	. В	, e-mail: obdim@yandex.ru,				.: +7-920-220-30-99
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©		. .,	.	., 2018
						99

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	5 –								482,4	2 (45%);
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	14 –					0,7 124 .			(100%);
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100

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