home Other disciplines books Ically mathematical programuvannya - Nakonechny S.І.

Ically mathematical programuvannya - Nakonechny S.І.

4.4. Analіz obmezhen defіtsitnih i nedefіtsitnih resursіv

For Relief dvoїstih otsіnok mozhna takozh viznachiti status cutaneous resource.

Resources for scho vikoristovuyutsya virobnitstva produktsії can umovno podіliti on defіtsitnі that nedefіtsitnі fallow od of Povny chi chastkove їh vikoristannya peredbachene optimal plan pryamoї zadachі. Yakscho deyake values dvoїstoї otsіnki uі in optimal planі dvoїstoї zadachі dorіvnyuє zero, then the i-th resource vіdpovіdny vikoristovuєtsya in virobnitstvі produktsії not povnіstyu Yea i nedefіtsitnim. Yakscho Well dvoїsta otsіnka uі> 0, the i-th resource vikoristovuєtsya for optimal plan virobnitstva produktsії povnіstyu i nazivaєtsya defіtsitnim. Vіdomo (third theorem dvoїstostі), scho magnitude dvoїstoї otsіnki pokazuє, naskіlki zbіlshitsya values tsіlovoї funktsії the Z, Yakscho stock vіdpovіdnogo resource zbіlshiti one umovnu odinitsyu.

Status resursіv mozhna viznachati troma ways. Purshia - pіdstanovkoyu value of the vector x * (virobnitstva optimum plan) from the system obmezhen pryamoї zadachі. Yakscho obmezhennya vikonuєtsya yak rіvnyannya then vіdpovіdny resource defіtsitny have іnshomu razі - nedefіtsitny:

Other sposіb - through dodatkovі zmіnnі pryamoї zadachі. Yakscho dodatkova zmіnna in optimal planі dorіvnyuє zero, vіdpovіdny resource defіtsitny and Yakscho bіlsha od zero - nedefіtsitny.

Tretіy sposіb - Relief for dvoїstih otsіnok. Yakscho uі> 0, zmіna (zbіlshennya abo zmenshennya) obsyagіv i th resource lead to vіdpovіdnoї zmіni income pіdpriєmstva, i to Taqiy resource Je defіtsitnim. Yakscho Well uі = 0, then the i-th resource nedefіtsitny. So, Nashomu prikladі:

Otzhe, Yakscho stock Perche defіtsitnogo resource zbіlshiti one umovnu odinitsyu (b 1 = 250 + 1 = 251), the tsіlova funktsіya max Z zbіlshitsya for іnshih odnakovih minds to have 1 = 1/2 d. od. i stanovitime max Z = 285,5 mind. od.

Tsіkavim Je zapitannya: "For rakhunok yakih for Change in optimal planі virobnitstva produktsії zbіlshitsya dohіd pіdpriєmstva?" Yak vіdomo s § 3.5.1, іnformatsіyu about tse give stovpchika Elements "x 5" ostannoї simplex tablitsі, yaky vіdpovіdaє dvoїstіy otsіntsі danogo resource - at 1 = 2.1.

Yakscho in Persha pochatkovіy zadachі values ​​on resource zroste odinitsyu then zgіdno s Table. 3.3. otrimaєmo:

In the new optimal values ​​planі bazisnoї zmіnnoї zbіlshitsya 1/2 and zmіnnih that - Zmenshitsya vіdpovіdno on odinitsyu that 1/2. When tsomu structure of the plan does not zmіnitsya and novі optimalnі values ​​will be such:

X * = (0; 0; 34.5; 45.5; 0; 29; 0).

Otzhe, zbіlshennya stock Perche defіtsitnogo resource for іnshih odnakovih minds umozhlivlyuє zrostannya Key infrastructure produktsії D for rakhunok zmenshennya virobnitstva produktsії S. For such minds obsyag vikoristannya nedefіtsitnogo other resources takozh zbіlshuєtsya. For this plan virobnitstva Maximum dohіd pіdpriєmstva max Z = 2 x 0 + 0 + 4 x 3 x 4 x 34.5 + 45.5 = 285.5, tobto zroste to have 1 1/2.

Proanalіzuєmo, yak zmіnitsya optimally virobnitstva produktsії plan Yakscho stock defіtsitnogo resource for 3 іnshih odnakovih minds zbіlshiti one umovnu odinitsyu (b 3 = 80 + 1 = 81). Analogіchno poperednіm mіrkuvannyam, skoristavshis Some of the elements stovpchika "x 7" ostannoї simplex tablitsі scho vіdpovіdaє dvoїstіy otsіntsі in 3 = 2, it is possible zapisati Novi optimal plan:

X * = (0; 0; 37; 44; 0; 30; 0).

max Z = 2 x 4 + 0 x 3 + 0 x 37 + 4 x 44 = 287.

Otzhe, viruchka pіdpriєmstva zbіlshitsya on Dvi umovnі odinitsі for rakhunok zbіlshennya virobnitstva produktsії C on Dvi odinitsі that zmenshennya Key infrastructure produktsії D on one odinitsyu. For such obstavin obsyag vikoristannya resource not zmіnyuєtsya 2.

Ale pіslya Carrying analіzu postaє logіchne zapitannya: Oskіlki zbіlshennya third resource on odinitsyu lead to naybіlshogo pіdvischennya funktsіonala values, the chi mozhna zbіlshiti tretіy defіtsitny resource 50, 100 i, etc. mind. od., team itself uniquely zbіlshuyuchi viruchku pіdpriєmstva?

Іz § 3.5.1 vіdomo, scho for odnoznachnoї vіdpovіdі on tse zapitannya, neobhіdno rozrahuvati іntervali mozhlivoї zmіni obsyagіv defіtsitnih resursіv have furrows yakih dvoїstі otsіnki uі zalishayutsya on rіvnі optimum value tobto rozv'yazati nerіvnostey (3.43) system.

Yakscho prirіst (zmіnu) stock Perche resource poznachimo through D b 1, todі simpleksnі tablitsі danoї zadachі nabudut viglyadu:

Novi optimally plan can have zapisati Taqiy sposіb:

X * = (0; 0; 35-1 / 2D b 1, 45 + 1 / 2D b 1, 0, 30 - D b 1, 0).

Єdina vimoga, yak mozhna postaviti to mozhlivih novih optimal value - tse Umov nevіd'єmnostі zmіnnih, tobto:

Otzhe,

.

Oznachaє Tse, scho if headroom 1 zbіlshitsya 30 d. od. abo zmenshitsya 90 d. od, then tsomu іntervalі yogo optimal dvoїsta otsіnka zalishitsya with such a train:. y 1 = 1/2. Otzhe, headroom 1 Mauger zmіnyuvatis in furrows:

.

Zgіdno s CIM maximum mozhlivі zmіni obsyagіv viruchki pіdpriєmstva fallow od for Change in postachannі resource 1 such іntervalі will have furrows:

.

.

and vіdpovіdnі criticality values ​​dіapazonu viruchki optimalnі Plagne virobnitstva produktsії are as follows:

(0, 0, 80, 0, 0, 120, 0) = X * = (0; 0; 20; 60; 0; 0; 0).

Analogіchno rozrahovuєtsya іnterval stіykostі dvoїstoї otsіnki in 3 = 2 to 3 defіtsitnogo resource:

.

.

Otzhe, Yakscho headroom 3 zbіlshitsya 45 d. od. abo zmenshitsya 17.5 d. od., then dvoїsta otsіnka in 3 = 2 tsogo zalishitsya resource with such a train. Zgіdno іz CIM mozhliva viruchka pіdpriєmstva is the optimal plan virobnitstva produktsії znahoditisya will have furrows:

;

(0, 0, 0, 62.5, 0, 30, 0) = X * = (0, 0, 125, 0, 0, 30, 0).

For rozrahunku іntervalu zmіni nedefіtsitnogo resource dosit rozv'yazati one nerіvnіst (3.45) (nagadaєmo, scho Won Got viglyad: ).

In Nashomu prikladі nedefіtsitnim Je other resources. Vіdomo, scho for optimal plan virobnitstva bude tsogo zalishok resource in obsyazі mind. od. Otzhe, zmenshennya danogo resource in obsyazі 30 d. od. zmіnit structure not optimal plan. Yakscho zmіnu zagalnogo stock another resource through poznachiti Then іnterval mozhlivoї zmіni yogo obsyagіv mozhna zapisati as follows:

.

Otzhe, іntervalom zmіni zapasіv nedefіtsitnogo resource in the furrows of the structure of the optimal plan yakogo zalishitsya postіynoyu, bude:

.

Zauvazhimo scho viznachenі іntervali stosuyutsya deprivation quiet vipadkіv, if zmіnyuєtsya obsyag tіlki one resource and reserves vsіh іnshih fіksovanі, tobto for іnshih odnakovih minds. In razі odnochasnoї zmіni obsyagіv usіh abo kіlkoh resursіv for viznachennya іntervalіv admissibility Change log neobhіdno rozv'yazati system nerіvnostey form (3.47) (scho Got viglyad . ).

Prostіshoyu for doslіdzhennya situatsіya Yea, if zmіni resursіv vіdomі i neobhіdno viznachiti deprivation Novi optimal plan. Nekhay dodatkovoyu minds butt 4.1 Je zmіna obsyagіv usіh troh resursіv scho zmіnyuyutsya vіdpovіdno so: D b = 1 + 10, D b = 2 - 10, D b + 3 = 20. viznachennya component of the new optimal plan skoristaєmos one іz bunt spіvvіdnoshen obchislyuvalnoї PROCEDURE simplex method. W pershoї theorem dvoїstostі vіdomo scho:

.

W ostannoї simplex tablitsі otrimuєmo obernenu matrix:

.

Zmіnenі reserves resursіv utvoryuyut vector

.

Novi Todі optimal plan for virobnitstva produktsії vіdpovіdnoї odnochasnoї zmіni zapasіv usіh troh resursіv

.

tobto X = (0, 0, 70, 30, 0, 10, 0).

Usі xj ≥ 0, i to the optimal plan dvoїstoї zadachі zalishaєtsya Y * = (1/2; 0; 2). Zagalna maximum viruchka pіdpriєmstva zmіnitsya on D F max = D b 1 y 1 + D b 2 y 2 + D b y 3 3 = 10 • 1/2 - 10 • 0 • 20 + 2 = 45 d. od. i stanovitime:

max F = 285 + 45 = 330 d. od.

Vikoristovuyuchi (3.48), provedemo doslіdzhennya mozhlivogo vzaєmozamіnyuvannya resursіv. Vikoristaєmo teoretichnі provisions of § 3.5.1, paragraph D.

Yakscho have virobnichіy sistemі іsnuє two chi bіlshe defіtsitnih resursіv then Pevnyi obsyag one h them Mauger Buti zamіneny deyakim obsyagom іnshogo, and the values ​​tsіlovoї funktsії zalishitsya nezmіnnim.

To drain the butt 4.1 poperednіy analіz dvoїstih otsіnok showing scho defіtsitnimi Je Purshia that tretіy resources. Pripustimo scho zabezpechennya virobnitstva neobhіdnim obsyagom third resource mozhlive not zavzhdi. In this razі dotsіlnim Je viznachennya of Yakima obsyagom Perche resources can zamіniti tretіy, dwellers vodnochase not zmenshilas optimal scrip viruchki.

Oskіlki de - The value for Change defіtsitnih resursіv and - Dvoїstі otsіnki vіdpovіdnih resursіv then zmіna obsyagu third resource on odinitsyu potrebuє dodatkovogo vikoristannya mind. od. Perche resource.

Otzhe, Yakscho Purshia resource zbіlshiti 4 d. od. i vikoristovuvati obsyazі 284 in mind. od., and tretіy zmenshiti 1 d. od. i have zalishiti virobnitstvі 79 d. . Odes, the od obsyag viruchki realіzatsії produktsії zalishitsya nezmіnnim in porіvnyannі s minds butt Pochatkova 4.1 - 285 d. od.