Ically mathematical programuvannya - Nakonechny S.І.

6. ROZDІL TSІLOCHISLOVІ ZADACHІ LІNІYNOGO PROGRAMUVANNYA. OSNOVNІ Method ЇH ROZV'YAZUVANNYA TA ANALІZU

"Until tabunnika priyshli three Cossacks kupuvati horses," Good, I'll selling horses -. Saying tabunnik - Perche I'm selling pіvtabuna i slit pіvkonya, another - half horse, scho zalishatsya, i slit pіvkonya, tretіy takozh zdobude half horses, scho zalishatsya , s pіvkonem. Sobі Well I zalishu tіlki 5 horses. " Zdivuvalisya Cossacks, yak Tse bude tabunnik rozdіlyati horses at Chastain. Ale pіslya deyakih rozdumіv zaspokoїlisya stink, i lands vіdbulasya "

(Task s books have vidanoї stolіttі XVIII)

6.1. Ekonomichna i ically mathematical formulation tsіlochislovoї zadachі lіnіynogo programuvannya

Іsnuє dovolі wider colo ically mathematical tasks programuvannya in ekonomіko-ically mathematical models yakih one abo kіlka zmіnnih toil nabuvati tsіlih values. Napriklad, if just past pro Quantity verstatіv in the shop, at tvarin sіlskogospodarskih pіdpriєmstvah toscho.

Zustrіchayutsya takozh zadachі, SSMSC s Persha Look no toil nіchogo spіlnogo s tsіlochislovimi models against formulyuyutsya yak zadachі tsіlochislovogo programuvannya. Vimogi diskretnostі zmіnnih in yavnіy chi neyavnіy forms pritamannі such practicality problems, yak vibіr poslіdovnostі virobnichih protsesіv; calendar planuvannya robots pіdpriєmstva; planuvannya that zabezpechennya materіalno-tehnіchnogo postachannya, rozmіschennya of companies, rozpodіl kapіtalovkladen, planuvannya vikoristannya obladnannya toscho.

Ically mathematical task programuvannya, zmіnnі yakoї toil nabuvati tsіlih value nazivaєtsya tasks tsіlochislovogo programuvannya. In addition razі, if tsіlochislovih values toil not nabuvati OAO All but one chi kіlka zmіnnih task nazivaєtsya chastkovo tsіlochislovoyu.

Before tsіlochislovogo programuvannya nalezhat takozh Ti zadachі optimіzatsії in yakih zmіnnі carols deprivation dvoh values: 0 abo 1 (bulovі, abo bіnarnі zmіnnі).

Umov tsіlochislovostі Je by sutі nelіnіynoyu i Mauger zustrіchatisya in problems, scho mіstyat lіnіynі yak, so i Nonlinear funktsії. In danomu rozdіlі rozglyanemo zadachі ically mathematical programuvannya in yakih minds krіm tsіlochislovostі OAO All obmezhennya that tsіlova funktsіya Je lіnіynimi scho toil titles tsіlochislovih tasks lіnіynogo programuvannya.

Zagalna tsіlochislova task lіnіynogo programuvannya zapisuєtsya as follows:

(6.1)

of minds:

; (6.2)

; (6.3)

- Tsіlі number . (6.4)

Slіd zaznachiti, scho in rozglyanutih in poperednomu rozdіlі klasichnіy transportnіy zadachі problems that іnshih vehicle type (in problems about priznachennya, about naykorotshy Way toscho) s tsіlochislovimi parameters Pochatkova minds zabezpechuєtsya tsіlochislovy rozv'yazok without zastosuvannya spetsіalnih metodіv, but the zagalnomu vipadku vimoga tsіlochislovostі zmіnnih uniquely uskladnyuє rozv'yazuvannya ically mathematical tasks programuvannya.