Modelyuvannya Economy - Vіtlіnsky VV

4.2. Vzaєmozalіk borgіv of companies

Whether yak dosit-valued for svoїmi scale Ekonomichna system mіstit in sobі tisyach dozens of companies (fіrm, korporatsіy toscho) SSMSC obmіnyuyutsya mіzh him that Hotel merchandise. Navіt drіbna FIRMA, scho Got vіdnosno slim Quantity partnerіv, oposeredkovano poєdnana (through direct zv'yazki that oposeredkovanih partnerіv) s velicheznoyu kіlkіstyu of companies, scho utvoryuyut system, i її protsvіtannya bezposeredno deposits od їhnogo camp.

Vzaєmozalezhnіst usіh lanok ekonomіchnoї Sistemi good proyavlyaєtsya by holding rozrahunkіv mіzh pіdpriєmstvami for delivered produktsіyu. Otrimavshi od svoїh klієntіv viruchku for goods pіdpriєmstvo vitrachaє її on zakupіvlyu sirovini that obladnannya in іnshih fіrm on zarobіtnu fee (tobto to purchase robochoї Sealy), advertising toscho scho Yea neobhіdnim for yogo normal funktsіonuvannya. Otzhe in ekonomіchny obіg zaluchaєtsya large Quantity partnerіv danogo pіdpriєmstva.

Well Naspravdі mіzh postachannyam product that pay for Demba zavzhdi іsnuє zatrimka in chasі. Її mіnіmalne values ​​viznachaєtsya Sotho tehnіchnimi reasons, more potrіben Pevnyi hour transportuvannya that rozfasuvannya product, zdіysnennya bankіvskih operatsіy toscho.

However mozhlivі situatsії, if s yakihos ekonomіchnih, fіnansovih, sotsіalnih, psihologіchnih, polіtichnih that іnshih reasons hour zatrimki SPLAT (postachannya) staє porіvnyannim h hour obіgu fіnansіv, and the absolute value (obsyag) nevikonanih splat Chi supplies - porіvnyannim s obsyagom vіlnih obіgovih koshtіv pіdpriєmstva . In tsomu razі vinikaє since been called to come nesplat crisis, KOTRA Mauger sprichiniti Creasy vsієї ekonomіchnoї system.

Pіdpriєmstvo, scho not otrimalo groshі for delivered produktsіyu (chi paid for the goods, ale yogo not otrimalo), not zmozі rozrahuvatisya Zi svoїmi postachalnikami (oskіlki obsyag yogo borgіv rіvny chi perevischuє obsyagi yogo vіlnih koshtіv). In his Cherga postachalniki not rozrahovuyutsya svoїmi klієntami Zi, Ti - i Zi svoїmi as Dali. Vinikayut dovgі lantsyuzhki nesplat scho pronizuyut usyu system. Pong obviously mozhut skladatisya h N lanok and zagalna Quantity їh dosyagaє blizko number N! (N - Quantity of companies).

Poyasnimo sutnіst problems on simple numeric prikladі for the system, scho s skladaєtsya troh of companies, skin s yakih Got vіlnі Costa, scho dorіvnyuyut odnіy fіnansovіy umovnіy odinitsі and osnovnі Fondi dorіvnyuyut 10 odinitsyam. Nekhay Pershe pіdpriєmstvo Winne odinits another 100, another 100 odinits Winne of the third and tretє - Perche takozh 100 odinits. Sumarno absolutely Borg of companies dorіvnyuє 300 odinitsyam i porіvnyano s їhnіmi funds (30 odinits) Je velicheznim. At the same hour fіnansovy camp tsієї Sistemi Je nepoganim, oskіlki sumarno "Borg" skin pіdpriєmstva, okremo taken, dorіvnyuє nulevі. Obviously, the procedure vzaєmozalіku polyagaє simultaneously in anulyuvannі (pogashennі) usіh borgіv: ogoloshuєtsya scho nіhto to Anyone not Wienen, i Partners prodovzhuyut funktsіonuvati being vіlnimi od borgovogo tyagarya.

Podіbnu operatsіyu, vikonanu "manually", nemozhlivo, zvichayno Well, realіzuvati for velikoї kіlkostі of companies. Neobhіdnі bіlsh glibokі pіdhodi for rozglyadu Cauterets treba formalіzuvati task.

Nekhay Ekonomichna system skladaєtsya N s of companies, SSMSC mozhut mother vzaєmnі Borg. Poznachimo Borg n th pіdpriєmstva m-th through pіdpriєmstvu xnm, de 1? n, m? N (xnp <0 Yakscho Pershe pіdpriєmstvo (n) other Winne (m), i xnm> 0 - in protilezhnomu vipadku). Clearly, scho

xnm = - xnm, xnp = 0,

tobto sukupnіst borgіv opisuєtsya kososimetrichnoyu matrix rozmіrnostі N? N s nulovoyu dіagonallyu (xnp = 0, Bo pіdpriєmstvo not Mauger Buti Winne itself sobі). Suma vsіh vzaєmnih borgіv obchislyuєtsya of the formula:

(4.7)

The value of X (4.7) Je odnієyu s іntegralnih kіlkіsnih characteristics will fіnansovogo system Yakscho Won Got order odnakovy іz sumoyu vsіh vіlnih koshtіv pіdpriєmstva (X 0) tobto:

(4.8)

Situatsіya scho opisuєtsya nerіvnіstyu (4.8), Vlasnyi, oznachaє Creasy nesplat (xn then 0 - іndivіdualnі vlasnі zasobi of companies).

Sche odnієyu vazhlivoyu characteristics Yea i borgіv kreditіv balance (surplus) Skin pіdpriєmstva:

(4.9)

Zaznachimo, scho, yak s seen (4.9), mozhlivimi Je varіanti Sn> 0; Sn <0; Sn = 0. Yakscho Sn> 0, pіdpriєmstvo in Pevnyi rozumіnnі Je lender of companies-borzhnikіv, quiet tobto who Sn <0 (Yakscho Sn = 0, then TAKE pіdpriєmstvo vvazhaєtsya "neutral" schodo borgіv). Yakscho Then іndivіdualny fіnansovy camp pіdpriєmstva Yea, for sutі, Normal, oskіlki realnі sumarnі yogo Borg (chi credits) menshі, nіzh yogo vіlnі zasobi (Costa). Analogіchno sumarno absolutely balance Sistemi

(4.10)

Je makropokaznikom її mozhlivogo fіnansovogo "Health Protection". Yakscho S <X 0, vіlnih koshtіv in sistemі bіlshe, nіzh dіysnih borgіv, i potentsіyno Won Mauger uspіshno funktsіonuvati. Mіzh variable X is the S zavzhdi іsnuє Pevnyi spіvvіdnoshennya. For whether yakoї dovіlnoї matritsі borgіv vikonuєtsya nerіvnіst:

X? S, (4.11)

tobto sumarno Borg not Mauger Buti Mensch for sumarno balance.

Zavdannya schodo repayment vzaєmnih borgіv polyagaє in fact dwellers, znayuchi matrix X vіdshukati Matrix "novih" borgіv X ', used for kotroї vikonuvalasya Umov X' <X. Obviously, scho іdealnim її rozv'yazkom LUVs bi Taqiy, dwellers X '= S, tobto dwellers nerіvnіst (4.10) became rіvnyannyam. Zaznachimo scho todі for takoї scho Yea bezpechnoyu on sutі, the system s S? X 0 vikonuvalos bi spіvvіdnoshennya X '= S? X 0, i pіslya vzaєmozalіku Won could normally used funktsіonuvati (Hoca zmenshennya obsyagіv X at whether Money Does vipadku Je spriyatlivim).

Buduyuchi ically mathematical model PROCEDURE vzaєmozalіkіv, vikoristovuvatimemo low operatsіy. Persha - tse vіdmova on Pevnyi etapі, od detailed rozglyadu mnozhini іndivіdualnih borgіv i vіdpovіdnih zv'yazkіv mіzh pіdpriєmstvami. Perehіd s mіkrorіvnya on makrorіven.

Zaznachimo scho procedure monіtoringu lantsyuzhkіv for N of companies Got printsipovy nedolіk. Rozglyanmo spochatku lantsyuzhok have Money Does dermal pіdpriєmstvo s Perche to M-th (M? N) Winne іnshomu odnakovu the bag, the bag Well i taku Winne M-those pіdpriєmstvo Perche (Fig. 4.1).

Lantsyuzhok zamknenim Yea, Yea i rozv'yazok obvious - usі Borg in lantsyuzhku pogashayutsya. Nekhay teper M-those pіdpriєmstvo not Winne nіchogo 1st (Fig. 4.2).

procedure monіtoringu lantsyuzhkіvprocedure monіtoringu lantsyuzhkіv

Fig. Figure 4.1. 4.

Lantsyuzhok rozіmkneny, i Tsei method Je nepridatnim. At the same hour simply rіshennya polyagaє in tіm scho s Borg of companies to another (M - 1) th not anulyuyutsya and Borg Perche pereadresovuєtsya M-th (Figure 4.3.).

Ekonomіchny Sens pereadresatsії

Fig. 4.3

Ekonomіchny Sens pereadresatsії vіdpovіdaє sutі obіgu bill, if borgove zobov'yazannya zmіnyuє svoїh hazyaїv, i have to rezultatі borzhnika (Pershe pіdpriєmstvo) z'yavlyaєtsya Novi lender (M -not pіdpriєmstvo).

On vіdmіnu od situatsії s Borg in lantsyuzhkah Povny system borgіv on vsіh lantsyuzhkah zamknenoyu Yea, more rozglyadayutsya vzaєmnі Borg. Spravdі, s vlastivostі xnm = - xmn maєmo scho

for whether yakoї sukupnostі nesplat. Vrahovuyuchi scho , S ostannogo rіvnyannya dіstaєmo

(4.12)

abo scrip dodatnih dorіvnyuє balance of companies for the absolute value of sumі vіd'єmnih balance tobto

(4.13)

Otzhe, Yakscho on rozglyadati makroekonomіchnomu rіvnі vzaєmnih borgіv system, then won Got vlastivіst "simetrichnoї konservativnostі".

Rіvnyannya (4.13) poyasnyuє structure for pobudovi matematichnoї modelі іdealnogo vzaєmozalіku, yaky vіdbuvaєtsya for such minds:

1) usі Borg xnm vіdomі th viznayutsya pіdpriєmstvami;

2) Venue of pіslya vzaєmozalіku balance of companies Sn zalishayutsya nezmіnnimi: , Tobto іndivіdualny fіnansovy mill skin s zmіnyuєtsya them;

3) Chastina borgіv xnm spisuєtsya and Chastina pereadresovuєtsya, tobto of companies in mozhut yak z'yavitisya novі borzhniki that creditors i chastkovo zniknuti starі.

Zmіst makroprotseduri vzaєmozalіku polyagaє in fact scho zamіst values xnm rozglyadayutsya quantities Sn. Pіdpriєmstva s Sn <0 ogoloshuyutsya borzhnikami (in obsyazі Svoge balance) and pіdpriєmstva s Sn> 0 - creditors (in quiet obsyagah themselves). Pіslya tsogo Borg of companies s Sn <0 Pevnyi rank rozpodіlyayutsya mіzh creditors tobto buduєtsya new system borgіv xnm. In tsomu razі vikonuєtsya other minds i dosyagaєtsya rіvnіst X '= S, to rozv'yazok zadachі yakoyus mіroyu Je ratsіonalnim. Such rozv'yazkіv, Saying to vzagalі, Mauger Buti bagato, more rozpodіlyati Borg mіzh creditors mozhna rіznimi ways. Navedemo two nayprostіshih.

Purshia mozhna taxes for Relief formulas zgіdno s yakoyu novі Borg obchislyuyutsya through starі:

(4.14)

Zgіdno s (4.14) Borg whether yakogo pіdpriєmstva (obsyag yakogo Sn, Yakscho Sn <0) mіzh pіdpriєmstvami creditor rozpodіlyaєtsya in chastkah, proportsіynih obsyagam їhnogo balance (scho dorіvnyuyut S m, Yakscho S m> 0). Pіdpriєmstvu, scho Got bіlshe for obsyagom positive balance, narahovuєtsya od s skin borzhnikіv bіlsha chastka yogo borgіv have sumі stench give a value of S m. For the balance of companies іz nulovim vzaєmozalіk zvoditsya to maturity vsіh їhnіh borgіv i vsіh borgіv їm. Zaznachimo, scho in (4.14) for novih borgіv maєmo , If Sn <0, Sm <0 chi if Sn> 0, Sm> 0 (pіslya vzaєmozalіku borzhniki not vinnі borzhnikam and creditors - creditors). Oznachaє Tse, scho Quantity otrimanih fіnansovih zv'yazkіv mіzh pіdpriєmstvami uniquely Mensch mozhlivu for most, if cutaneous pіdpriєmstvo Je odnochasno borzhnikom i, i lender whether yakogo іnshogo and matrix borgіv not Got nulovih elementіv (okrіm, zvichayno, dіagonalnih).

Other sposіb ґruntuєtsya to ensure scho Mauger Buti Quantity zv'yazkіv uniquely zmenshena, Yakscho spend poperednє vporyadkuvannya of companies zgіdno s absolute value їhnіh balance that vstanoviti bezposerednі zv'yazki mіzh borzhnikami th creditors of one scale (velikі s great, malі malimi s). Tsya procedure dopuskaє Prostu geometric іnterpretatsіyu. Fig. 4.4 on verhnіy pryamіy lіnії described rozpodіl kreditorіv balance (in spadnіy poslіdovnostі). Dovzhina vіdrіzkіv tsієї pryamoї dorіvnyuє obsyagovі balance skin pіdpriєmstva Sp> 0, 1 <p <N, and її zagalna dovzhina obviously - S / 2.

borzhnikіv balance

Fig. 4.4

On nizhnіy pryamіy described rozpodіl balance borzhnikіv Sq <0, 1 <q <N, p + q ? N (s balance vzyatі obernenim sign) takozh in spadnіy poslіdovnostі. Її dovzhina zgіdno s (4.13) takozh dorіvnyuє S / 2. Shtrihovі lіnії scho provedenі s vuzlіv nizhnoї pryamoї, podіlyayut "direct kreditorіv" by q vіdrіzkіv scho dorіvnyuyut obsyagam Borg pіdpriєmstva skin. Tsey Borg abo dіstaєtsya one kreditorovі, abo dіlitsya mіzh kіlkoma vіdpovіdno to roztashuvannya vuzlіv verhnoї pryamoї vіdnosno danogo vіdrіzka.

Description of the algorithm for Je ratsіonalnim kriterієm X '= S i, obviously, the optimum for kіlkіstyu zv'yazkіv scho zalishilisya pіslya vzaєmozalіku.

Butt vzaєmozalіku in sistemі s N = 10 i Pochatkova borgіv matrix of 90 nenulovimi nedіagonalnimi Some of the elements imposed in tablitsі 4.1. Kіntseva matrix mіstit lishe 14 nenulovih elementіv. In spetsіalnih vipadkah in one borzhnika zalishaєtsya one lender, i navpaki.

table 4.1

Butt vzaєmozalіku in sistemі s N = 10 i Pochatkova borgіv matrix of 90 nenulovimi nedіagonalnimi Some of the elements

Number s / n

1

2

3

4

6

6

7

8

9

Pochatkova matrix (X = 3729)

2

25

3

-1

-20

4

4

25

-2

5

25

-450

25

thirty

6

-15

150

-thirty

20

-928

7

3

-40

3

3

5

25

8

1

-22

-2

-2

4

-15

5

9

10

322

-15

-25

498

-800

-10

20

10

1

-25

-2

1

-20

15

-1

-3

thirty

Kіntseva matrix (X '= S = 62)

2

2

3

0

0

4

0

0

0

5

0

0

0

0

6

0

0

0

0

-28

7

1

0

0

0

0

0

8

0

-7

0

0

0

0

0

9

0

-18

0

0

-2

0

0

0

10

0

0

0

0

0

4

0

0

0

Zaznachimo scho navedenі that INSHI PROCEDURE vzaєmozalіku toil Sens deprivation of minds vikonannya 1-3 tobto if Je vіdpovіdna lands mіzh pіdpriєmstvami. The reason scho not dozvolyayut dotrimuvatisya danoї land, shaping can Buti dosit rіznomanіtnimi - od nebazhannya splachuvati Borg, that scho Tse vigіdno borzhnikovі to naslіdkіv sanktsіy mіzhnarodnih chi іnshih organіzatsіy, if fіnansovі Costa of companies "zamorozhuyutsya".