{"id":37108,"date":"2019-10-31T22:15:47","date_gmt":"2019-10-31T19:15:47","guid":{"rendered":"https:\/\/prohoster.info\/blog\/diskretnaya-matematika-dlya-wms-algoritm-szhatiya-tovarov-v-yachejkah-chast-1\/"},"modified":"2019-10-31T22:15:47","modified_gmt":"2019-10-31T19:15:47","slug":"diskretnaya-matematika-dlya-wms-algoritm-szhatiya-tovarov-v-yachejkah-chast-1","status":"publish","type":"post","link":"https:\/\/prohoster.info\/sq\/blog\/news\/diskretnaya-matematika-dlya-wms-algoritm-szhatiya-tovarov-v-yachejkah-chast-1","title":{"rendered":"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"<p><img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/89e9927c86cd36ee5b4ab37b5c0753c9.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<br \/>\nN\u00eb k\u00ebt\u00eb artikull ne do t\u00eb flasim se si e zgjidh\u00ebm problemin e munges\u00ebs s\u00eb vendeve t\u00eb lira n\u00eb magazin\u00eb dhe mbi zhvillimin e nj\u00eb algoritmi t\u00eb optimizimit t\u00eb disktret t\u00eb zgjidhjes s\u00eb k\u00ebtij problemi. Do t\u00eb flasim p\u00ebr m\u00ebnyr\u00ebn si 'nd\u00ebrtuam' modelin matematikor t\u00eb detyr\u00ebs s\u00eb optimizimit dhe p\u00ebr v\u00ebshtir\u00ebsit\u00eb me t\u00eb cilat papritur u p\u00ebrball\u00ebm gjat\u00eb p\u00ebrpunimit t\u00eb t\u00eb dh\u00ebnave hyr\u00ebse p\u00ebr algoritmin.<\/p>\n<p>N\u00ebse jeni t\u00eb interesuar p\u00ebr aplikimet e matematik\u00ebs n\u00eb biznes dhe nuk keni frik\u00eb nga transformimet e forta identike t\u00eb formula n\u00eb nivelin e klas\u00ebs s\u00eb 5-t\u00eb, at\u00ebher\u00eb mir\u00eb se vini n\u00ebn kat!<\/p>\n<p>Artikulli do t\u00eb jet\u00eb i dobish\u00ebm p\u00ebr ata q\u00eb aplikojn\u00eb <i>sistemat WMS, punojn\u00eb n\u00eb industrin\u00eb e logjistik\u00ebs s\u00eb magazinave ose prodhimit, si dhe p\u00ebr programuesit q\u00eb jan\u00eb t\u00eb interesuar p\u00ebr aplikimet e matematik\u00ebs n\u00eb biznes dhe optimizimin e proceseve n\u00eb nd\u00ebrmarrje.<\/i>-sistemat, punon n\u00eb industrin\u00eb e logjistik\u00ebs s\u00eb magazinave ose prodhimit, si dhe p\u00ebr programuesit q\u00eb jan\u00eb t\u00eb interesuar p\u00ebr aplikacionet e matematik\u00ebs n\u00eb biznes dhe optimizimin e proceseve n\u00eb nd\u00ebrmarrje.<\/p>\n<p><noindex><a rel=\"nofollow\" name=\"habracut\"><\/a><\/noindex><\/p>\n<h4>Pjesa hyr\u00ebse<\/h4>\n<p>\nKy publikim vazhdon ciklin e artikujve, ku ne ndajn\u00eb p\u00ebrvoj\u00ebn ton\u00eb t\u00eb suksesshme n\u00eb zbatimin e algoritmeve t\u00eb optimizimit n\u00eb proceset e magazinimit. <\/p>\n<p>N\u00eb <noindex><a rel=\"nofollow\" href=\"https:\/\/habr.com\/ru\/post\/463289\/\">artikulli i m\u00ebparsh\u00ebm<\/a><\/noindex> P\u00ebrshkruhet specifika e magazin\u00ebs, ku ne kemi zbatuar <i>sistemat WMS, punojn\u00eb n\u00eb industrin\u00eb e logjistik\u00ebs s\u00eb magazinave ose prodhimit, si dhe p\u00ebr programuesit q\u00eb jan\u00eb t\u00eb interesuar p\u00ebr aplikimet e matematik\u00ebs n\u00eb biznes dhe optimizimin e proceseve n\u00eb nd\u00ebrmarrje.<\/i>-sistemin, si dhe tregohet p\u00ebrse na nevojitej t\u00eb zgjidhnim detyr\u00ebn e klasifikimit t\u00eb grumbujve t\u00eb mbetjeve t\u00eb produkteve gjat\u00eb zbatimit t\u00eb <i>sistemat WMS, punojn\u00eb n\u00eb industrin\u00eb e logjistik\u00ebs s\u00eb magazinave ose prodhimit, si dhe p\u00ebr programuesit q\u00eb jan\u00eb t\u00eb interesuar p\u00ebr aplikimet e matematik\u00ebs n\u00eb biznes dhe optimizimin e proceseve n\u00eb nd\u00ebrmarrje.<\/i>-sistemit dhe si e b\u00ebm\u00eb k\u00ebt\u00eb.<\/p>\n<p>Kur p\u00ebrfunduam s\u00eb shkruari artikullin mbi algorithmat e optimizimit, rezultoi shum\u00eb i gjat\u00eb, ndaj materiali i akumuluar vendos\u00ebm ta ndajm\u00eb n\u00eb 2 pjes\u00eb:<\/p>\n<ul>\n<li>N\u00eb pjes\u00ebn e par\u00eb (ky artikull) ne do t\u00eb flasim p\u00ebr m\u00ebnyr\u00ebn si 'nd\u00ebrtuam' modelin matematikor t\u00eb detyr\u00ebs, dhe p\u00ebr v\u00ebshtir\u00ebsit\u00eb e m\u00ebdha me t\u00eb cilat papritur u p\u00ebrball\u00ebm gjat\u00eb p\u00ebrpunimit dhe transformimit t\u00eb t\u00eb dh\u00ebnave hyr\u00ebse p\u00ebr algoritmin.<\/li>\n<li>N\u00eb pjes\u00ebn e dyt\u00eb ne do t\u00eb shqyrtojm\u00eb n\u00eb detaje realizimin e algoritmit me gjuh\u00ebn <i>C++<\/i>, do t\u00eb zhvillojm\u00eb nj\u00eb eksperiment llogaritar dhe do t\u00eb p\u00ebrmbledhim p\u00ebrvoj\u00ebn q\u00eb mor\u00ebm gjat\u00eb zbatimit t\u00eb k\u00ebtyre 'teknologjive inteligjente' n\u00eb proceset e biznesit t\u00eb klientit.<\/li>\n<\/ul>\n<p>\nSi ta lexoni artikullin. N\u00ebse keni lexuar artikullin e m\u00ebparsh\u00ebm, mund t\u00eb kaloni drejtp\u00ebrdrejt n\u00eb kapitullin 'P\u00ebrmbledhja e zgjidhjeve ekzistuese', n\u00ebse jo, p\u00ebrshkrimi i problemit t\u00eb zgjidhur ndodhet n\u00eb spoilerin m\u00eb posht\u00eb.<\/p>\n<p><b class=\"spoiler_title\">P\u00ebrshkrimi i problemit t\u00eb zgjidhur n\u00eb magazin\u00ebn e klientit<\/b><\/p>\n<h4>Ngushtica n\u00eb proceset<\/h4>\n<p>\nN\u00eb vitin 2018 ne realizuam nj\u00eb projekt p\u00ebr zbatimin e <i>sistemat WMS, punojn\u00eb n\u00eb industrin\u00eb e logjistik\u00ebs s\u00eb magazinave ose prodhimit, si dhe p\u00ebr programuesit q\u00eb jan\u00eb t\u00eb interesuar p\u00ebr aplikimet e matematik\u00ebs n\u00eb biznes dhe optimizimin e proceseve n\u00eb nd\u00ebrmarrje.<\/i>-sistemit n\u00eb magazin\u00ebn 'Sht\u00ebpia e Tregtis\u00eb \"LD\" n\u00eb qytetin \u00c7eljabinsk. Zbatova produktin '1C-Logistika: Menaxhimi i magazin\u00ebs 3' n\u00eb 20 vende pune: operator\u00ebt <i>sistemat WMS, punojn\u00eb n\u00eb industrin\u00eb e logjistik\u00ebs s\u00eb magazinave ose prodhimit, si dhe p\u00ebr programuesit q\u00eb jan\u00eb t\u00eb interesuar p\u00ebr aplikimet e matematik\u00ebs n\u00eb biznes dhe optimizimin e proceseve n\u00eb nd\u00ebrmarrje.<\/i>, magazinier\u00eb, shofer\u00eb ngarkuesish. Depo mesatare rreth 4 mij\u00eb m2, numri i qelizave 5000 dhe numri i SKU 4500. N\u00eb depo ruhen krane sferike t\u00eb prodhimit ton\u00eb n\u00eb madh\u00ebsi t\u00eb ndryshme nga 1 kg deri n\u00eb 400 kg. Stoku n\u00eb depo ruhet sipas grupeve, pasi ka nevoj\u00eb p\u00ebr p\u00ebrzgjedhjen e mallrave sipas FIFO.<\/p>\n<p>Gjat\u00eb projektimit t\u00eb skemave p\u00ebr automatizimin e proceseve n\u00eb depo, u p\u00ebrball\u00ebm me problemin ekzistues t\u00eb ruajtjes jo optimale t\u00eb stokut. Specifika e ruajtjes dhe renditjes s\u00eb kran\u00ebve \u00ebsht\u00eb e till\u00eb q\u00eb n\u00eb nj\u00eb qeliz\u00eb t\u00eb ruajtjes individuale mund t\u00eb ndodhet vet\u00ebm nj\u00eb nomenklatur\u00eb e nj\u00eb grupi (shih. fig. 1). Produkti arrin n\u00eb depo \u00e7do dit\u00eb dhe \u00e7do ardhje \u00ebsht\u00eb nj\u00eb grup i ve\u00e7ant\u00eb. P\u00ebrve\u00e7 k\u00ebsaj, si rezultat i 1 muaji funksionimi t\u00eb depos krijohen 30 grupe t\u00eb ve\u00e7anta, p\u00ebrkund\u00ebr faktit se secila duhet t\u00eb ruhet n\u00eb nj\u00eb qeliz\u00eb t\u00eb ve\u00e7ant\u00eb. Malli shpesh p\u00ebrzgjidhet jo n\u00eb paleta t\u00eb plota, por nj\u00ebsi, dhe si rezultat, n\u00eb zon\u00ebn e p\u00ebrzgjedhjes individuale n\u00eb shum\u00eb qeliza v\u00ebrehet nj\u00eb pamje e till\u00eb: n\u00eb nj\u00eb qeliz\u00eb me volum m\u00eb shum\u00eb se 1m3 ndodhen disa styk\u00eb kranesh, t\u00eb cilat z\u00ebn\u00eb m\u00eb pak se 5-10% t\u00eb volumit t\u00eb qeliz\u00ebs. <\/p>\n<p><img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/a7c03f2302c3be02c00c670453353f16.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>Fig. 1. Foto e disa styk\u00ebve n\u00eb nj\u00eb qeliz\u00eb<\/i><\/p>\n<p>Dallohet nj\u00eb p\u00ebrdorim jo optimal i kapaciteteve t\u00eb depos. N\u00eb m\u00ebnyr\u00eb q\u00eb t\u00eb paraqesim shkall\u00ebn e katastrof\u00ebs, mund t\u00eb japim numra: mesatarisht, ka nga 100 deri n\u00eb 300 qeliza t\u00eb tilla me volum m\u00eb shum\u00eb se 1m3 me \"restitucione t\u00eb minushme\" n\u00eb periudha t\u00eb ndryshme t\u00eb funksionimit t\u00eb depos. Duke qen\u00eb se depoja \u00ebsht\u00eb relativisht e vog\u00ebl, n\u00eb sezonet e ngarkes\u00ebs s\u00eb depos, ky faktor b\u00ebhet \"ngushtic\u00eb\" q\u00eb r\u00ebndon shum\u00eb proceset e pranuara dhe d\u00ebrgimit.<\/p>\n<h4>Ideja p\u00ebr zgjidhjen e problemit<\/h4>\n<p>\nLindi ideja: grupet e mbetjeve me datat m\u00eb t\u00eb af\u00ebrta t\u00eb p\u00ebrzgjidhen n\u00eb nj\u00eb grup t\u00eb vet\u00ebm dhe k\u00ebto mbetje me grupin e unifikuar vendosen kompaktet s\u00eb bashku n\u00eb nj\u00eb qeliz\u00eb, ose n\u00eb disa, n\u00ebse vendi n\u00eb nj\u00eb nuk do t\u00eb mjaftoj\u00eb p\u00ebr vendosjen e gjith\u00eb numrit t\u00eb mbetjeve. Nj\u00eb shembull i k\u00ebtij \"tkurrjeje\" \u00ebsht\u00eb ilustruar n\u00eb fig. 2.<\/p>\n<p><img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/792f114a7afa6272a6d152a784650681.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>Fig. 2. Skema e tkurrjes s\u00eb mbetjeve n\u00eb qeliza<\/i><\/p>\n<p>Kjo lejon nj\u00eb reduktim t\u00eb ndjesh\u00ebm t\u00eb hap\u00ebsirave magazinuese, t\u00eb cilat do t\u00eb p\u00ebrdoren p\u00ebr mallrat e reja q\u00eb do t\u00eb vendosen. N\u00eb raste t\u00eb mbipopullimit t\u00eb kapaciteteve magazinuese, nj\u00eb mas\u00eb e till\u00eb \u00ebsht\u00eb jasht\u00ebzakonisht e nevojshme, p\u00ebrndryshe mund t\u00eb mos ket\u00eb hap\u00ebsir\u00eb t\u00eb mjaftueshme p\u00ebr t\u00eb vendosur mallra t\u00eb rinj, e cila do t\u00eb \u00e7onte n\u00eb bllokimin e proceseve t\u00eb vendosjes dhe furnizimit dhe, si pasoj\u00eb, n\u00eb bllokimin e pranimeve dhe shkarkimeve. M\u00eb par\u00eb, para se t\u00eb implementohej sistemi WMS, kjo operacion b\u00ebhej manualisht, e cila ishte e paefektshme, pasi procesi i k\u00ebrkimit t\u00eb stockeve t\u00eb p\u00ebrshtatshme n\u00eb qeliza ishte mjaft i gjat\u00eb. Tani, me implementimin e sistemit WMS, vendos\u00ebm ta automatizojm\u00eb, ta p\u00ebrshpejtojm\u00eb dhe ta b\u00ebjm\u00eb at\u00eb inteligjent.<\/p>\n<p>Procesi i zgjidhjes s\u00eb nj\u00eb detyre t\u00eb till\u00eb ndahet n\u00eb 2 faza: <\/p>\n<ul>\n<li>n\u00eb faz\u00ebn e par\u00eb ne gjejm\u00eb grupe partiresh t\u00eb af\u00ebrta n\u00eb dat\u00eb p\u00ebr kompresimin (kjo detyr\u00eb \u00ebsht\u00eb e dedikuar) <noindex><a rel=\"nofollow\" href=\"https:\/\/habr.com\/ru\/post\/463289\/\">artikulli i m\u00ebparsh\u00ebm<\/a><\/noindex>);<\/li>\n<li>n\u00eb faz\u00ebn e dyt\u00eb ne llogarisim vendosjen m\u00eb kompakte t\u00eb stockeve t\u00eb mallrave n\u00eb qeliza p\u00ebr \u00e7do grup partie. <\/li>\n<\/ul>\n<p>\nN\u00eb artikullin aktual ne do t\u00eb ndalem n\u00eb faz\u00ebn e dyt\u00eb t\u00eb algoritmit.<\/p>\n<h4>P\u00ebrmbledhje e zgjidhjeve ekzistuese<\/h4>\n<p>\nPara se t\u00eb kalojm\u00eb n\u00eb p\u00ebrshkrimin e algoritmeve t\u00eb zhvilluara nga ne, \u00ebsht\u00eb e r\u00ebnd\u00ebsishme t\u00eb b\u00ebjm\u00eb nj\u00eb p\u00ebrmbledhje t\u00eb shkurt\u00ebr t\u00eb sistemeve tashm\u00eb ekzistuese n\u00eb treg <i>sistemat WMS, punojn\u00eb n\u00eb industrin\u00eb e logjistik\u00ebs s\u00eb magazinave ose prodhimit, si dhe p\u00ebr programuesit q\u00eb jan\u00eb t\u00eb interesuar p\u00ebr aplikimet e matematik\u00ebs n\u00eb biznes dhe optimizimin e proceseve n\u00eb nd\u00ebrmarrje.<\/i>, n\u00eb t\u00eb cilat \u00ebsht\u00eb realizuar funksionaliteti i ngjeshjes optimale.<\/p>\n<p>N\u00eb radh\u00eb t\u00eb par\u00eb, \u00ebsht\u00eb e nevojshme t\u00eb theksohet produkti \"1C: Enterprise 8. WMS Logistika. Menaxhimi i Magazinit 4\", i cili i p\u00ebrket dhe shp\u00ebrndahet nga firma 1C dhe i p\u00ebrket gjenerat\u00ebs s\u00eb kat\u00ebrt <i>sistemat WMS, punojn\u00eb n\u00eb industrin\u00eb e logjistik\u00ebs s\u00eb magazinave ose prodhimit, si dhe p\u00ebr programuesit q\u00eb jan\u00eb t\u00eb interesuar p\u00ebr aplikimet e matematik\u00ebs n\u00eb biznes dhe optimizimin e proceseve n\u00eb nd\u00ebrmarrje.<\/i>-sistemeve t\u00eb zhvilluara nga kompania AXELOT. N\u00eb k\u00ebt\u00eb sistem \u00ebsht\u00eb deklaruar funksionaliteti i ngjeshjes, i cili ka p\u00ebr q\u00ebllim t\u00eb bashkoj\u00eb stocket e ndryshme t\u00eb mallrave n\u00eb nj\u00eb qelize t\u00eb vetme. \u00cbsht\u00eb e r\u00ebnd\u00ebsishme t\u00eb p\u00ebrmendet se funksionaliteti i ngjeshjes n\u00eb nj\u00eb sistem t\u00eb till\u00eb p\u00ebrfshin gjithashtu mund\u00ebsi t\u00eb tjera, p\u00ebr shembull, rregullimin e vendosjes s\u00eb mallrave n\u00eb qeliza sipas klasave t\u00eb tyre ABC, por ne nuk do t\u00eb ndalemi n\u00eb to. <\/p>\n<p>N\u00ebse analizojm\u00eb kodin e sistemit \"1C: Nd\u00ebrmarrja 8. WMS Logjistika. Menaxhimi i Magazin\u00ebs 4\" (i cili n\u00eb k\u00ebt\u00eb pjes\u00eb funksionaliteti \u00ebsht\u00eb i hapur), mund t\u00eb arrijm\u00eb n\u00eb p\u00ebrfundimin e m\u00ebposht\u00ebm. Algoritmi i kompresimit t\u00eb mbetjeve zbret nj\u00eb logjik\u00eb relativisht primitive lineare dhe nuk mund t\u00eb flitet p\u00ebr nj\u00eb kompresim \"optimal\". Sigurisht, ai nuk parashikon klasifikimin e grupeve. Disa klient\u00eb, t\u00eb cil\u00ebt kishin implementuar nj\u00eb sistem t\u00eb till\u00eb, u ankua mbi rezultatet e planifikimit t\u00eb kompresimit. P\u00ebr shembull, shpesh ndodhte q\u00eb n\u00eb praktik\u00eb, gjat\u00eb kompresimit, ndodhte kjo situat\u00eb: 100 cop\u00eb mbetjeve t\u00eb nj\u00eb produkti nga nj\u00eb kuti planifikoheshin t\u00eb zhvendoseshin n\u00eb nj\u00eb kuti tjet\u00ebr, ku ndodhej 1 cop\u00eb produkti, kur n\u00eb fakt do t\u00eb ishte optimal n\u00eb aspektin e shpenzimeve t\u00eb koh\u00ebs t\u00eb b\u00ebhej p\u00ebrndryshe.<\/p>\n<p>T\u00eb nj\u00ebjt\u00ebn funksionalitet t\u00eb kompresimit t\u00eb mbetjeve t\u00eb produkteve n\u00eb kutit\u00eb e magazin\u00ebs e kan\u00eb shpallur edhe shum\u00eb sisteme t\u00eb huaja. <i>sistemat WMS, punojn\u00eb n\u00eb industrin\u00eb e logjistik\u00ebs s\u00eb magazinave ose prodhimit, si dhe p\u00ebr programuesit q\u00eb jan\u00eb t\u00eb interesuar p\u00ebr aplikimet e matematik\u00ebs n\u00eb biznes dhe optimizimin e proceseve n\u00eb nd\u00ebrmarrje.<\/i>-sisteme, por, fatkeq\u00ebsisht, asnj\u00eb rishikim real mbi efikasitetin e pun\u00ebs s\u00eb algoritmeve (kjo \u00ebsht\u00eb nj\u00eb sekret tregtar), as p\u00ebr m\u00eb shum\u00eb nj\u00eb ide mbi thell\u00ebsin\u00eb e logjik\u00ebs s\u00eb tyre (softuer pronar me kod t\u00eb mbyllur) nuk kemi, prandaj nuk mund t\u00eb gjykojm\u00eb.<\/p>\n<h4>K\u00ebrkimi i nj\u00eb modeli matematikor t\u00eb problemit<\/h4>\n<p>\nP\u00ebr t\u00eb projektuar algoritme cil\u00ebsore p\u00ebr zgjidhjen e problemit, \u00ebsht\u00eb e nevojshme fillimisht q\u00eb ky problem t\u00eb formulohet qart\u00eb n\u00eb m\u00ebnyr\u00eb matematikore, dhe k\u00ebt\u00eb do ta b\u00ebjm\u00eb.<\/p>\n<p>Ka shum\u00eb kuti <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/bfff1fb95dd0c633ada02b9398778eab.jpeg\" style=\"display:block;margin: 0 auto;\" \/>, n\u00eb t\u00eb cilat ndodhen mbetjet e nj\u00eb produkti t\u00eb caktuar. M\u00eb pas, k\u00ebto kuti do t\u2019i quajm\u00eb kuti-dh\u00ebn\u00ebse. Do t\u00eb sh\u00ebnojm\u00eb <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/50ef693482cd4cb27410b30b0bc107b1.jpeg\" style=\"display:block;margin: 0 auto;\" \/> v\u00ebllimin e produktit q\u00eb ndodhet n\u00eb kuti <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/dc7faf1656fb12c8e467fe3a5b8977fa.jpeg\" style=\"display:block;margin: 0 auto;\" \/>$.<\/p>\n<p>\u00cbsht\u00eb e r\u00ebnd\u00ebsishme t\u00eb thuhet se n\u00eb procedur\u00ebn e kompresimit mund t\u00eb marr\u00eb pjes\u00eb vet\u00ebm nj\u00eb produkt nga nj\u00eb grup, ose disa grupe, t\u00eb bashkuara paraprakisht n\u00eb nj\u00eb kluster (lexo <noindex><a rel=\"nofollow\" href=\"https:\/\/habr.com\/ru\/post\/463289\/\">artikullin e kaluar<\/a><\/noindex>), q\u00eb shpjegohet nga specifika e ruajtjes dhe vendosjes s\u00eb produkteve. P\u00ebr produkte t\u00eb ndryshme ose grupe t\u00eb ndryshme, duhet t\u00eb nis\u00eb nj\u00eb procedur\u00eb e ve\u00e7ant\u00eb kompresimi.<\/p>\n<p>Ka shum\u00eb kuti <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/b9aafca691626263d8ecc2faed8dfcfe.jpeg\" style=\"display:block;margin: 0 auto;\" \/>, n\u00eb t\u00eb cilat mund t\u00eb vendosen potencialisht mbetjet nga kutit\u00eb-dh\u00ebn\u00ebse. K\u00ebto kuti do t\u2019i quajm\u00eb m\u00eb pas kuti-kontejner. K\u00ebto mund t\u00eb jen\u00eb si kuti t\u00eb lira n\u00eb magazin\u00eb, ashtu edhe kuti-dh\u00ebn\u00ebse nga shum\u00eb. <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/25731bc72091e2284e76c434d2abdcfd.jpeg\" style=\"display:block;margin: 0 auto;\" \/>. Gjithmon\u00eb shum\u00eb <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/d407f97344131a3056b1eab1d3dd7dcd.jpeg\" style=\"display:block;margin: 0 auto;\" \/> \u00ebsht\u00eb nj\u00eb n\u00ebngrup <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/581806d446f3d8c91927045249698e71.jpeg\" style=\"display:block;margin: 0 auto;\" \/>.<\/p>\n<p>P\u00ebr \u00e7do kuti <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/b084d5852a1e4f00d2498640534d66e9.jpeg\" style=\"display:block;margin: 0 auto;\" \/> nga shum\u00eb <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/236efb40a21865f78240c8e14303cc2e.jpeg\" style=\"display:block;margin: 0 auto;\" \/> jan\u00eb t\u00eb caktuara kufizime mbi kapacitetin <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/fe253cfe5f2aa39bc8e064674fb206f8.jpeg\" style=\"display:block;margin: 0 auto;\" \/>, e mat\u00eb n\u00eb dm3. Nj\u00eb dm3 p\u00ebrfaq\u00ebson nj\u00eb kub me an\u00ebt 10 cm. Produktet e ruajtura n\u00eb magazin\u00eb jan\u00eb mjaft t\u00eb m\u00ebdha, prandaj n\u00eb k\u00ebt\u00eb rast kjo diskriminim \u00ebsht\u00eb m\u00eb se e mjaftueshme. <\/p>\n<p>\u00cbsht\u00eb caktuar nj\u00eb matrice e distancave m\u00eb t\u00eb shkurtra <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/48c133b0affa17f6a2367a02241d5f17.jpeg\" style=\"display:block;margin: 0 auto;\" \/> n\u00eb metra midis \u00e7do \u00e7ift qelie <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/8fd860e331a8e42dd258857bdf580c05.jpeg\" style=\"display:block;margin: 0 auto;\" \/>index <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/feb9a48c6e9e4ccd8e9fa1db5565e96e.jpeg\" style=\"display:block;margin: 0 auto;\" \/> dhe <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/d9a48a8a22ea984d0769373c5620c99a.jpeg\" style=\"display:block;margin: 0 auto;\" \/> i p\u00ebrkasin grupeve <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/e2dd20fda8a8b0b5ea2173c14f04fe00.jpeg\" style=\"display:block;margin: 0 auto;\" \/> dhe <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/0dabafdb55ac6b8495f6d5f657d6c01d.jpeg\" style=\"display:block;margin: 0 auto;\" \/> p\u00ebrkat\u00ebsisht. <\/p>\n<p>Le t\u00eb p\u00ebrfaq\u00ebsojm\u00eb <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/2994defad9bb0a44741f31a85273abf2.jpeg\" style=\"display:block;margin: 0 auto;\" \/> kostot p\u00ebr transferimin e mallrave nga qelia<img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/a2e54425ec786d3a88290dda47f4b9cb.jpeg\" style=\"display:block;margin: 0 auto;\" \/> n\u00eb qeli <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/bf4a9f1a1f396a9b7b6244cf8c77ecc8.jpeg\" style=\"display:block;margin: 0 auto;\" \/>. Le t\u00eb p\u00ebrfaq\u00ebsojm\u00eb <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/6f4c10386fc638f6ca37e0ccdcf4ccb4.jpeg\" style=\"display:block;margin: 0 auto;\" \/> kostot p\u00ebr zgjedhjen e kontejnerit <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/613d619ea5951551427f0cd45c7f79bf.jpeg\" style=\"display:block;margin: 0 auto;\" \/> p\u00ebr t\u00eb transferuar n\u00eb t\u00eb mbetje nga qelia t\u00eb tjera. Si do llogariten dhe n\u00eb cilat nj\u00ebsi t\u00eb matjes do t\u00eb llogariten vlerat <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/22130f203fde6271e33cba0db14d6a80.jpeg\" style=\"display:block;margin: 0 auto;\" \/> dhe <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/d75c50be3ee4f8e02a9523f2d2109f0d.jpeg\" style=\"display:block;margin: 0 auto;\" \/> do ta shqyrtojm\u00eb m\u00eb von\u00eb (shihni seksionin p\u00ebrgatitja e t\u00eb dh\u00ebnave hyr\u00ebse), tani \u00ebsht\u00eb e mjaftueshme t\u00eb thuhet se k\u00ebto sasi do t\u00eb jen\u00eb proporcionale drejtp\u00ebrdrejt me sasin\u00eb <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/5e4e80f122ac1fe43f94de2726c0d3b7.jpeg\" style=\"display:block;margin: 0 auto;\" \/> dhe <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/1b6a9d41ba4ad68d5a5fbae883b80596.jpeg\" style=\"display:block;margin: 0 auto;\" \/> p\u00ebrkat\u00ebsisht.<\/p>\n<p>Le t\u00eb p\u00ebrfaq\u00ebsojm\u00eb me <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/1ebfe4179740aff474a78d11a004aaa7.jpeg\" style=\"display:block;margin: 0 auto;\" \/> nj\u00eb variab\u00ebl q\u00eb merr vler\u00ebn 1, n\u00ebse mbetjet nga qelia <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/48f9789788c38746ba4ac0c947e0a4ca.jpeg\" style=\"display:block;margin: 0 auto;\" \/> sht\u00eb transferuar n\u00eb kontejner <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/58ce0b4c9bfb946c00bffdc0c50a05d6.jpeg\" style=\"display:block;margin: 0 auto;\" \/>, dhe 0 n\u00eb rastin e kund\u00ebrt. Le t\u00eb p\u00ebrfaq\u00ebsojm\u00eb me <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/642d5627193c55922be5274826b75cb4.jpeg\" style=\"display:block;margin: 0 auto;\" \/> nj\u00eb variab\u00ebl q\u00eb merr vler\u00ebn 1, n\u00ebse kontejneri <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/6939c9f4daf2ecd531d9c2518c03401d.jpeg\" style=\"display:block;margin: 0 auto;\" \/> p\u00ebrmban mbetjet e mallrave, dhe 0 n\u00eb rastin e kund\u00ebrt.<\/p>\n<p><b>Problemi formulon si<\/b>: \u00ebsht\u00eb e nevojshme t\u00eb gjejm\u00eb nj\u00eb grup kontejner\u00ebsh <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/d6065db66f210083181dabb39f0e9e16.jpeg\" style=\"display:block;margin: 0 auto;\" \/> dhe k\u00ebshtu \"prikemi\" qelit\u00eb-donator\u00eb me qelit\u00eb e kontejner\u00ebve, n\u00eb m\u00ebnyr\u00eb q\u00eb t\u00eb minimizojm\u00eb funksionin<\/p>\n<p><img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/68d7f0271f9761fff2c762e0fe6f5207.jpeg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>n\u00eb kushtet<\/p>\n<p><img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/d57b8752aa4a8140e239dfa7fdc9ec36.jpeg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>N\u00eb p\u00ebrfundim, gjat\u00eb llogaritjes s\u00eb zgjidhjes s\u00eb problemit ne mundohemi: <\/p>\n<ul>\n<li>s\u00eb pari, t\u00eb kursejm\u00eb kapacitetin e magazin\u00ebs; <\/li>\n<li>s\u00eb dyti, t\u00eb kursejm\u00eb koh\u00ebn e magazinier\u00ebve. <\/li>\n<\/ul>\n<p>\nKjo kufizim i fundit do t\u00eb thot\u00eb q\u00eb ne nuk mund t'i transferojm\u00eb mallrat n\u00eb nj\u00eb kontejner q\u00eb nuk e kemi zgjedhur, pra nuk kemi \"mbajtur kostot\" p\u00ebr zgjedhjen e tij. Gjithashtu, ky kufizim do t\u00eb thot\u00eb se sasia e mallrave q\u00eb transferohen nga qelit\u00eb n\u00eb kontejner nuk duhet t\u00eb tejkaloj\u00eb kapacitetin e kontejnerit. Ne do ta kuptojm\u00eb zgjidhjen e problemit si nj\u00eb grup kontejner\u00ebsh <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/db0f987f2d388ad1394d21404e183c93.jpeg\" style=\"display:block;margin: 0 auto;\" \/> dhe m\u00ebnyrat e lidhjes s\u00eb qelive-donator me kontejner\u00ebt.<\/p>\n<p>Kjo formulim e problemit t\u00eb optimizimit nuk \u00ebsht\u00eb e re dhe \u00ebsht\u00eb studiuar nga shum\u00eb matematicien\u00eb q\u00eb nga fillimi i viteve '80 t\u00eb shekullit t\u00eb kaluar. N\u00eb literatur\u00ebn e huaj ka 2 probleme optimizimi me nj\u00eb model matematikor t\u00eb p\u00ebrshtatsh\u00ebm: <noindex><a rel=\"nofollow\" href=\"http:\/\/www.math.nsc.ru\/AP\/benchmarks\/CFLP\/cflp.html\">Problem i Pozicionimit t\u00eb Leht\u00ebsis\u00eb s\u00eb Kufizuar nga Burimi i Vet\u00ebm<\/a><\/noindex> dhe <noindex><a rel=\"nofollow\" href=\"https:\/\/waset.org\/publications\/10002290\/a-survey-of-discrete-facility-location-problems\">Problem i Pozicionimit t\u00eb Leht\u00ebsis\u00eb s\u00eb Kufizuar nga Burime t\u00eb Shumta<\/a><\/noindex> (do t\u00eb flasim m\u00eb von\u00eb p\u00ebr ndryshimet e detyrave). \u00cbsht\u00eb e r\u00ebnd\u00ebsishme t\u00eb themi se n\u00eb literatur\u00ebn matematike, formulimi i k\u00ebtyre dy problemeve t\u00eb optimizimit formulohet n\u00eb terma t\u00eb pozicionimit t\u00eb nd\u00ebrmarrjeve n\u00eb territor, nga k\u00ebtu dhe emri \"Pozita e Nd\u00ebrmarrjeve\". Kryesisht, kjo \u00ebsht\u00eb nj\u00eb trash\u00ebgimi tradicionale, pasi nevoja p\u00ebr zgjidhjen e k\u00ebtyre problemeve kombinatorike u shfaq fillimisht n\u00eb sfer\u00ebn e logjistik\u00ebs, kryesisht n\u00eb industrin\u00eb ushtarake n\u00eb vitet 50-t\u00eb t\u00eb shekullit t\u00eb kaluar. N\u00eb terma t\u00eb pozicionimit t\u00eb nd\u00ebrmarrjeve, k\u00ebto probleme formulohet si: <\/p>\n<ul>\n<li>Ka nj\u00eb num\u00ebr t\u00eb kufizuar qytetesh, ku potencialisht \u00ebsht\u00eb e mundur t\u00eb vendosen nd\u00ebrmarrjet prodhuese (k\u00ebtu qytetet-prodhues). P\u00ebr \u00e7do qytet-prodhues jan\u00eb caktuar kostot p\u00ebr hapjen e nj\u00eb nd\u00ebrmarrjeje n\u00eb t\u00eb, si dhe kufizimi n\u00eb kapacitetet prodhuese t\u00eb nd\u00ebrmarrjes q\u00eb hapet n\u00eb t\u00eb.<\/li>\n<li>Ka nj\u00eb num\u00ebr t\u00eb kufizuar qytetesh, ku realisht ndodhen klient\u00ebt (k\u00ebtu qytetet-klient). P\u00ebr \u00e7do qytet-klient t\u00eb till\u00eb \u00ebsht\u00eb caktuar v\u00ebllimi i k\u00ebrkes\u00ebs p\u00ebr produktin. P\u00ebr thjesht\u00ebsi, do t\u00eb supozojm\u00eb se produkti q\u00eb prodhojn\u00eb nd\u00ebrmarrjet dhe konsumojn\u00eb klient\u00ebt \u00ebsht\u00eb i nj\u00ebjt\u00eb.<\/li>\n<li>P\u00ebr \u00e7do \u00e7ift qytet-prodhues dhe qytet-klient \u00ebsht\u00eb caktuar madh\u00ebsia e kostove t\u00eb transportit p\u00ebr d\u00ebrgimin e v\u00ebllimit t\u00eb nevojsh\u00ebm t\u00eb produktit nga prodhuesi te klienti.<\/li>\n<\/ul>\n<p>\nK\u00ebrkohet t\u00eb p\u00ebrcaktohet n\u00eb cilat qytete t\u00eb hapen nd\u00ebrmarrjet dhe si t\u00eb lidhin klient\u00ebt me k\u00ebto nd\u00ebrmarrje, n\u00eb m\u00ebnyr\u00eb q\u00eb:<\/p>\n<ul>\n<li>Kostot p\u00ebr hapjen e nd\u00ebrmarrjeve dhe kostot e transportit t\u00eb jen\u00eb minimale;<\/li>\n<li>V\u00ebllimi i k\u00ebrkes\u00ebs s\u00eb klient\u00ebve, t\u00eb lidhur me ndonj\u00eb nd\u00ebrmarrje t\u00eb hapur, t\u00eb mos tejkaloj\u00eb kapacitetet prodhuese t\u00eb k\u00ebsaj nd\u00ebrmarrjeje.<\/li>\n<\/ul>\n<p>\nTani \u00ebsht\u00eb e r\u00ebnd\u00ebsishme t\u00eb p\u00ebrmendet vet\u00ebm nj\u00eb ndryshim n\u00eb k\u00ebto dy probleme klasike:<\/p>\n<ul>\n<li>Problemi i Pozit\u00ebs s\u00eb Nd\u00ebrmarrjeve Kapaciteti nj\u00eb Burimi \u2013 klienti furnizohet vet\u00ebm nga nj\u00eb nd\u00ebrmarrje e hapur;<\/li>\n<li>Problemi i Pozit\u00ebs s\u00eb Nd\u00ebrmarrjeve Kapaciteti Shum\u00eb Burimesh \u2013 klienti mund t\u00eb furnizohet nga disa nd\u00ebrmarrje t\u00eb hapura n\u00eb t\u00eb nj\u00ebjt\u00ebn koh\u00eb.<\/li>\n<\/ul>\n<p>\nKy ndryshim midis dy problemeve n\u00eb shikim t\u00eb par\u00eb duket i par\u00ebnd\u00ebsish\u00ebm, por n\u00eb t\u00eb v\u00ebrtet\u00eb, \u00e7on n\u00eb nj\u00eb struktur\u00eb t\u00eb ndryshme kombinatorike t\u00eb k\u00ebtyre problemeve dhe, si pasoj\u00eb, n\u00eb algoritma t\u00eb ndrysh\u00ebm p\u00ebr zgjidhjen e tyre. Diferenca midis problemeve e demonstrohet n\u00eb figur\u00ebn m\u00eb posht\u00eb.<\/p>\n<p><img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/77962906c7de2fced174d4a2b7785cc2.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>Fig.3. a) Problemi i Pozit\u00ebs s\u00eb Nd\u00ebrmarrjeve Kapaciteti Shum\u00eb Burimesh<\/i><\/p>\n<p><img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/0242437e488a1aea0f00ce9ede02886d.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>Fig.3. b) Problemi i Pozit\u00ebs s\u00eb Nd\u00ebrmarrjeve Kapaciteti nj\u00eb Burimi<\/i><\/p>\n<p>T\u00eb dy problemet <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/b16678811fceca32d18c94e71cfaa603.jpeg\" style=\"display:block;margin: 0 auto;\" \/>-t\u00eb v\u00ebshtir\u00eb, pra nuk ekziston nj\u00eb algoritem i sakt\u00eb q\u00eb do t\u00eb zgjidhte k\u00ebt\u00eb detyr\u00eb p\u00ebr koh\u00eb polinomiale p\u00ebr madh\u00ebsin\u00eb e t\u00eb dh\u00ebnave hyr\u00ebse. Me fjal\u00eb m\u00eb t\u00eb thjeshta, t\u00eb gjith\u00eb algoritm\u00ebt e sakt\u00eb p\u00ebr zgjidhjen e detyr\u00ebs do t\u00eb funksionojn\u00eb p\u00ebr nj\u00eb koh\u00eb eksponenciale, megjithat\u00eb, ndoshta, m\u00eb shpejt se kontrollimi i plot\u00eb i mund\u00ebsive nga nisma. Q\u00ebllimi \u00ebsht\u00eb <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/09f42b4b905d9bdc3f00f21098f84ad7.jpeg\" style=\"display:block;margin: 0 auto;\" \/>-t\u00eb v\u00ebshtira, k\u00ebshtu q\u00eb do t\u00eb shqyrtojm\u00eb vet\u00ebm heuristik\u00eb t\u00eb af\u00ebrt, dometh\u00ebn\u00eb algoritme q\u00eb do t\u00eb llogarisin vazhdimisht zgjidhje shum\u00eb af\u00ebr optimale dhe do t\u00eb punojn\u00eb mjaft shpejt. N\u00ebse ka interes p\u00ebr k\u00ebto detyra, k\u00ebtu mund t\u00eb gjeni nj\u00eb pasqyr\u00eb t\u00eb mir\u00eb n\u00eb rusisht.<\/p>\n<p>N\u00ebse i referohemi terminologjis\u00eb t\u00eb detyr\u00ebs son\u00eb p\u00ebr kompresionin optimal t\u00eb mallrave n\u00eb seksione, at\u00ebher\u00eb:<\/p>\n<ul>\n<li>city-clients \u2013 jan\u00eb seksione-dhuruese <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/e6db70dbb85d1c7249f4c30e97e2942e.jpeg\" style=\"display:block;margin: 0 auto;\" \/> me mbetjet e mallrave, <\/li>\n<li>city-producers \u2013 jan\u00eb seksione-kontejner\u00eb <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/5ef31fe0483d2bc9a0c18b5dc25e9867.jpeg\" style=\"display:block;margin: 0 auto;\" \/>, n\u00eb t\u00eb cilat parashikohet t\u00eb vendosen mbetjet nga seksione t\u00eb tjer\u00eb,<\/li>\n<li>kostot e transportit \u2013 jan\u00eb kostot e koh\u00ebs <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/afac567e9057a46de6e0f3d29df9315a.jpeg\" style=\"display:block;margin: 0 auto;\" \/> t\u00eb magazinierit p\u00ebr l\u00ebvizjen e v\u00ebllimit t\u00eb mallrave nga seksioni-dhuruese <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/829df82255e40cb99024d7c8dd408d41.jpeg\" style=\"display:block;margin: 0 auto;\" \/> n\u00eb seksionin-kontejner <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/b87c9d9260adb26ce623dbe80b4f22c2.jpeg\" style=\"display:block;margin: 0 auto;\" \/>; <\/li>\n<li>kostot e hapjes s\u00eb nd\u00ebrmarrjes \u2013 jan\u00eb kostot p\u00ebr zgjedhjen e konteinerit <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/db4d21fc2067a23b5af5bb01c412323a.jpeg\" style=\"display:block;margin: 0 auto;\" \/>, t\u00eb barabarta me v\u00ebllimin e seksionit-konteiner <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/b631a01a65f1ffd3348cbcaeeab11f0d.jpeg\" style=\"display:block;margin: 0 auto;\" \/>, t\u00eb shum\u00ebzuara me nj\u00eb koeficient t\u00eb caktuar t\u00eb kursimit t\u00eb hap\u00ebsirave t\u00eb lira (vlera e koeficientit gjithmon\u00eb &gt; 1) (shih seksionin p\u00ebrgatitja e t\u00eb dh\u00ebnave hyr\u00ebse).<\/li>\n<\/ul>\n<p>\nPas krijimit t\u00eb analogjis\u00eb me detyrat klasike t\u00eb njohura, \u00ebsht\u00eb e nevojshme t\u00eb p\u00ebrgjigjemi n\u00eb nj\u00eb pyetje t\u00eb r\u00ebnd\u00ebsishme, nga e cila varet zgjedhja e arkitektur\u00ebs s\u00eb algoritmit t\u00eb zgjidhjes: transferimi i mbetjeve nga seksioni-dhuruese \u00ebsht\u00eb i mundsh\u00ebm vet\u00ebm n\u00eb nj\u00eb dhe vet\u00ebm nj\u00eb konteiner (Single-Source), ose \u00ebsht\u00eb e mundur t\u00eb transferohen mbetje n\u00eb disa seksione-kontejner\u00eb (Multi-Source)?<\/p>\n<p>\u00cbsht\u00eb e r\u00ebnd\u00ebsishme t\u00eb theksohet se n\u00eb praktik\u00eb, t\u00eb dy format e detyr\u00ebs ekzistojn\u00eb. Do t\u00eb paraqesim t\u00eb gjitha 'p\u00ebr' dhe 'kund\u00ebr' p\u00ebr \u00e7do format t\u00eb till\u00eb m\u00eb posht\u00eb:<\/p>\n<table>\n<tr>\n<th>Varianti i detyr\u00ebs<\/th>\n<th>Pikat e forta t\u00eb variantit<\/th>\n<th>Dob\u00ebsit\u00eb e variantit<\/th>\n<\/tr>\n<tr>\n<td>Single-Source<\/td>\n<td>Operacionet e transferimit t\u00eb mallrave, t\u00eb llogaritura sipas k\u00ebtij varianti t\u00eb detyr\u00ebs:<\/p>\n<ul>\n<li>k\u00ebrkojn\u00eb m\u00eb pak kontroll nga ana e magazinierit (mori T\u00cb GJITHA nga nj\u00eb seksion, vendosi T\u00cb GJITHA n\u00eb nj\u00eb seksion-kontejner), \u00e7ka eliminon rreziqet: gabimeve gjat\u00eb num\u00ebrimit t\u00eb sasis\u00eb s\u00eb mallrave gjat\u00eb operacioneve 'Vij n\u00eb seksion'; gabimeve gjat\u00eb hyrjes s\u00eb sasive t\u00eb num\u00ebruara n\u00eb TSD;<\/li>\n<li>Nuk\u00eb k\u00ebrkohet koh\u00eb p\u00ebr t\u00eb rinum\u00ebruar sasin\u00eb e produkteve gjat\u00eb operacioneve \"Vendos n\u00eb qeli\" dhe p\u00ebr t'i futur ato n\u00eb TSD.<\/li>\n<\/ul>\n<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Burim shum\u00ebfishe<\/td>\n<td>Kompresimi i llogaritur sipas k\u00ebtij varianti t\u00eb problemit, zakonisht \u00ebsht\u00eb m\u00eb kompakt me 10-15% krahasuar me comprimin e llogaritur sipas variantit \"Burim i vet\u00ebm\". Por gjithashtu v\u00ebrejm\u00eb se sa m\u00eb e vog\u00ebl t\u00eb jet\u00eb sasia e mbetur n\u00eb qelit\u00eb donatore, aq m\u00eb i vog\u00ebl \u00ebsht\u00eb ky ndryshim n\u00eb kompakt\u00ebsi.<\/td>\n<td>Operacionet e transferimit t\u00eb mallrave, t\u00eb llogaritura sipas k\u00ebtij varianti t\u00eb detyr\u00ebs:<\/p>\n<ul>\n<li>k\u00ebrkojn\u00eb m\u00eb shum\u00eb kontroll nga ana e magazinierit (duhet t\u00eb rinum\u00ebroj sasin\u00eb e produktit q\u00eb po transferohet n\u00eb secil\u00ebn nga qelit\u00eb-container t\u00eb planifikuara), duke eliminuar k\u00ebshtu rrezikun e gabimit gjat\u00eb rinum\u00ebrimit t\u00eb sasis\u00eb s\u00eb produktit dhe futjes s\u00eb t\u00eb dh\u00ebnave n\u00eb TSD gjat\u00eb operacioneve \"Vendos n\u00eb qeli\".<\/li>\n<li>K\u00ebrkohet koh\u00eb p\u00ebr t\u00eb rinum\u00ebruar sasin\u00eb e produkteve gjat\u00eb operacioneve \"Vendos n\u00eb qeli\".<\/li>\n<li>K\u00ebrkohet koh\u00eb p\u00ebr \"shpenzimet e mbulimit\" (ndaloni, shkoni te paleta, skanoni kodin barkod t\u00eb qelis\u00eb-container) gjat\u00eb operacioneve \"Vendos n\u00eb qeli\".<\/li>\n<li>Ndonj\u00ebher\u00eb algoritmi mund t\u00eb \"shk\u00ebput\u00eb\" sasin\u00eb e nj\u00eb palete pothuajse t\u00eb plot\u00eb midis nj\u00eb numri t\u00eb madh qelish-container, ku ka tashm\u00eb nj\u00eb produkt t\u00eb p\u00ebrshtatsh\u00ebm, q\u00eb p\u00ebr klientin kishte qen\u00eb e papranueshme.<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<\/table>\n<p><i>Tabela 1. Avantazhet dhe disavantazhet e varianteve Burim i vet\u00ebm dhe Burim shum\u00ebfishe.<\/i><\/p>\n<p>Duke marr\u00eb parasysh se numri i avantazheve t\u00eb variantit Burim i vet\u00ebm \u00ebsht\u00eb m\u00eb i madh, dhe gjithashtu duke marr\u00eb parasysh faktin se sa m\u00eb e vog\u00ebl t\u00eb jet\u00eb sasia e mbetur n\u00eb qelit\u00eb donatore, aq m\u00eb i vog\u00ebl \u00ebsht\u00eb ndryshimi n\u00eb shkall\u00eb t\u00eb kompakt\u00ebsis\u00eb s\u00eb kompresimit t\u00eb llogaritur sipas t\u00eb dy varianteve t\u00eb problemit, zgjedhja jon\u00eb ra n\u00eb variantin Burim i vet\u00ebm.<\/p>\n<p>Duhet th\u00ebn\u00eb se zgjidhja e variantit Burim shum\u00ebfishe gjithashtu ka vendin e saj. Ekzistojn\u00eb nj\u00eb num\u00ebr t\u00eb madh algoritmesh efikas p\u00ebr ta zgjidhur at\u00eb, shumica prej t\u00eb cil\u00ebve reduktohen n\u00eb zgjidhjen e disa problemeve t\u00eb transportit. Gjithashtu ka jo vet\u00ebm algoritme efikase, por edhe elegante, p\u00ebr shembull,<noindex><a rel=\"nofollow\" href=\"http:\/\/www.mathnet.ru\/php\/archive.phtml?wshow=paper&amp;jrnid=da&amp;paperid=791&amp;option_lang=rus\"> k\u00ebtu.<\/a><\/noindex><\/p>\n<h4>P\u00ebrgatitja e t\u00eb dh\u00ebnave hyr\u00ebse<\/h4>\n<p>\nPara se t\u00eb filloni me analiz\u00ebn dhe zhvillimin e algoritmit p\u00ebr zgjidhjen e problemit, \u00ebsht\u00eb e nevojshme t\u00eb p\u00ebrcaktoni se cilat t\u00eb dh\u00ebna dhe n\u00eb \u00e7far\u00eb forme do t'i japim atij n\u00eb hyrje. Me sasi t\u00eb mbetjeve t\u00eb produkteve n\u00eb qelit\u00eb donatore dhe kapacitetin e qelive-container, nuk ka probleme, pasi kjo \u00ebsht\u00eb triviale \u2013 k\u00ebto sasi do t\u00eb maten n\u00eb m3, por me kostot p\u00ebr p\u00ebrdorimin e qelis\u00eb-container dhe matric\u00ebn e kostove p\u00ebr l\u00ebvizjen, nuk \u00ebsht\u00eb gjith\u00e7ka kaq e thjesht\u00eb!<\/p>\n<p>Fillimisht le t\u00eb shqyrtojm\u00eb llogaritjen <b>kostos p\u00ebr l\u00ebvizjen e mallrave<\/b> nga qelia-dhuruese n\u00eb qelin\u00eb-kontejner. E para duhet t\u00eb p\u00ebrcaktojm\u00eb se n\u00eb cilat nj\u00ebsi matjeje do t\u00eb llogarisim kostot e l\u00ebvizjes. Dy opsionet m\u00eb t\u00eb dukshme jan\u00eb metrat dhe sekondat. N\u00eb \"metra\" t\u00eb past\u00ebr, llogaritja e kostove t\u00eb l\u00ebvizjes nuk ka kuptim. Do ta ilustruar k\u00ebt\u00eb me nj\u00eb shembull. Le t\u00eb themi se qelia <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/990a5fae8988ddf41395483263de2bcc.jpeg\" style=\"display:block;margin: 0 auto;\" \/> \u00ebsht\u00eb e vendosur n\u00eb katin e par\u00eb, qelia <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/9d17b98e807444f431d01f2e77fc96f7.jpeg\" style=\"display:block;margin: 0 auto;\" \/> \u00ebsht\u00eb n\u00eb nj\u00eb distanc\u00eb prej 30 metrash dhe ndodhet n\u00eb katin e dyt\u00eb:<\/p>\n<ul>\n<li>L\u00ebvizja nga <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/3188fd9853d5cda2834a5083539ac11d.jpeg\" style=\"display:block;margin: 0 auto;\" \/> n\u00eb <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/e212a0be19ea687b1017c3aacec3df19.jpeg\" style=\"display:block;margin: 0 auto;\" \/> \u00ebsht\u00eb m\u00eb e shtrenjt\u00eb se l\u00ebvizja nga <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/d65e60dec37fb3b83c83ca1c566f1ee9.jpeg\" style=\"display:block;margin: 0 auto;\" \/> n\u00eb <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/4168198a4c90bdd3dd4b7f0c904b06e0.jpeg\" style=\"display:block;margin: 0 auto;\" \/>, pasi q\u00eb zbritja nga kati i dyt\u00eb (1,5-2 metra nga toka) \u00ebsht\u00eb m\u00eb e leht\u00eb se ngritja n\u00eb t\u00eb dytin, edhe pse distanca do t\u00eb jet\u00eb e nj\u00ebjt\u00eb;<\/li>\n<li>T\u00eb zhvendos\u00ebsh 1 cop\u00eb mall nga qelia <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/039864ccd0a2bd14a99a83494f056fa3.jpeg\" style=\"display:block;margin: 0 auto;\" \/> n\u00eb <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/9f9bc7a256119b110f47760b145e174b.jpeg\" style=\"display:block;margin: 0 auto;\" \/> do t\u00eb jet\u00eb m\u00eb e leht\u00eb se sa t\u00eb zhvendos\u00ebsh 10 cop\u00eb t\u00eb s\u00eb nj\u00ebjt\u00ebs mall, edhe pse distanca do t\u00eb jet\u00eb e nj\u00ebjt\u00eb.<\/li>\n<\/ul>\n<p>\nKostot p\u00ebr l\u00ebvizje \u00ebsht\u00eb m\u00eb mir\u00eb t\u00eb llogariten n\u00eb sekonda, pasi kjo lejon t\u00eb merret parasysh ndryshimi n\u00eb katet dhe ndryshimi n\u00eb sasin\u00eb e mallrave q\u00eb po l\u00ebvizin. P\u00ebr t\u00eb llogaritur kostot e l\u00ebvizjes n\u00eb sekonda, ne duhet t\u00eb ndajm\u00eb operacionin e l\u00ebvizjes n\u00eb p\u00ebrb\u00ebr\u00ebs elementar\u00eb dhe t\u00eb masim koh\u00ebn e realizimit t\u00eb secilit p\u00ebrb\u00ebr\u00ebs elementar.<\/p>\n<p>Le t\u00eb themi se nga qelia <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/538c4304e37f340a5a5a8e47e0ee2865.jpeg\" style=\"display:block;margin: 0 auto;\" \/> po l\u00ebvizet <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/6c7e32728f4771726f8ef9b2d78111d6.jpeg\" style=\"display:block;margin: 0 auto;\" \/> cop\u00eb mall n\u00eb konteiner <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/fc2ad051b500eae5884404f4b9419841.jpeg\" style=\"display:block;margin: 0 auto;\" \/>. Le t'i themi <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/6733192a31618a03e51e8e3133cb96ee.jpeg\" style=\"display:block;margin: 0 auto;\" \/> \u2013 shpejt\u00ebsia mesatare e l\u00ebvizjes s\u00eb punonj\u00ebsit n\u00eb depo, e matur n\u00eb m\/sec. Le t'i themi <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/97f7e9c65c2196fa586f957618d1c8a2.jpeg\" style=\"display:block;margin: 0 auto;\" \/> dhe <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/bbe48d987f180e2f9ccec6e090e6f942.jpeg\" style=\"display:block;margin: 0 auto;\" \/> \u2013 shpejt\u00ebsit\u00eb mesatare p\u00ebr realizimin e operacioneve t\u00eb marrjes dhe vendosjes p\u00ebrkat\u00ebsisht p\u00ebr nj\u00eb v\u00ebllim t\u00eb mallrave q\u00eb \u00ebsht\u00eb 4 dm3 (v\u00ebllimi mesatar q\u00eb merr nj\u00eb punonj\u00ebs n\u00eb depot kur kryen operacionet). Le t'i themi <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/267d74648f49d5a2d063b1377c6d2fe6.jpeg\" style=\"display:block;margin: 0 auto;\" \/> dhe <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/fefdd606d5a81ba4e2ce57b107dfe1e6.jpeg\" style=\"display:block;margin: 0 auto;\" \/> lart\u00ebsit\u00eb e qelive nga t\u00eb cilat realizohen operacionet e marrjes dhe vendosjes p\u00ebrkat\u00ebsisht. P\u00ebr shembull, lart\u00ebsia mesatare e katit t\u00eb par\u00eb (toka) \u00ebsht\u00eb 1 m, kati i dyt\u00eb 2 m etj. At\u00ebher\u00eb formula p\u00ebr llogaritjen e koh\u00ebs totale p\u00ebr realizimin e operacionit t\u00eb l\u00ebvizjes <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/a48ae3c2e9dc8f2c3108cb2be1f96c40.jpeg\" style=\"display:block;margin: 0 auto;\" \/> \u00ebsht\u00eb si vijon:<\/p>\n<p><img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/55afb96b1141bb5656351bdaeba31ae4.jpeg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>N\u00eb tabel\u00ebn 2 jepet statistika e koh\u00ebs s\u00eb realizimit t\u00eb \u00e7do operacioni elementar, e mbledhur nga punonj\u00ebsit e depot duke marr\u00eb parasysh specifik\u00ebn e mallrave t\u00eb ruajtura.<\/p>\n<table>\n<tr>\n<th>Emri i operacionit<\/th>\n<th>Simboli<\/th>\n<th>Vlera mesatare<\/th>\n<\/tr>\n<tr>\n<td>Shpejt\u00ebsia mesatare e l\u00ebvizjes s\u00eb punonj\u00ebsit n\u00eb depo<\/td>\n<td><img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/dadbfb13d2b84b95ab2c5d653a21668b.jpeg\" style=\"display:block;margin: 0 auto;\" \/><\/td>\n<td>1,5 m\/sec<\/td>\n<\/tr>\n<tr>\n<td>Shpejt\u00ebsia mesatare p\u00ebr realizimin e nj\u00eb operacioni vendosje (p\u00ebr v\u00ebllimin e mallrave 4 dm3)<\/td>\n<td><img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/aa619b43a70a7cf646ad35d5c8883329.jpeg\" style=\"display:block;margin: 0 auto;\" \/><\/td>\n<td>2,4 sekond\u00eb<\/td>\n<\/tr>\n<\/table>\n<p><i>Tabela 2. Koha mesatare p\u00ebr realizimin e operacioneve n\u00eb depo<\/i><\/p>\n<p>Kemi vendosur p\u00ebr metod\u00ebn e llogaritjes s\u00eb kostove t\u00eb l\u00ebvizjes. Tani \u00ebsht\u00eb e nevojshme t\u00eb kuptojm\u00eb si t\u00eb llogarisim <b>kostot p\u00ebr zgjedhjen e qelis\u00eb-kontejner<\/b>K\u00ebtu \u00ebsht\u00eb shum\u00eb m\u00eb e komplikuar se sa kostot e zhvendosjes, pasi: <\/p>\n<ul>\n<li>s\u00eb pari, kostot duhet t\u00eb jen\u00eb n\u00eb var\u00ebsi t\u00eb drejtp\u00ebrdrejt\u00eb nga volumi i qelizave \u2013 t\u00eb nj\u00ebjtin volum t\u00eb mbetjeve, q\u00eb zhvendosen nga qelizat-donore, \u00ebsht\u00eb m\u00eb mir\u00eb ta vendosni n\u00eb nj\u00eb kontejner m\u00eb t\u00eb vog\u00ebl sesa n\u00eb nj\u00eb kontejner t\u00eb madh, me kusht q\u00eb ky volum t\u00eb futet plot\u00ebsisht n\u00eb t\u00eb dy kontejner\u00ebt. K\u00ebshtu, duke minimizuar kostot totale p\u00ebr zgjedhjen e kontejner\u00ebve, ne k\u00ebrkojm\u00eb t\u00eb kursim fuqit\u00eb e depozitimit \"me deficit\" n\u00eb zon\u00ebn e ndarjes, p\u00ebr t\u00eb realizuar operacione t\u00eb m\u00ebtejshme t\u00eb vendosjes s\u00eb mallrave n\u00eb qeliza. N\u00eb figur\u00ebn 4 demonstrohen variantet e zhvendosjes s\u00eb mbetjeve n\u00eb kontejner\u00eb t\u00eb m\u00ebdhenj dhe t\u00eb vegj\u00ebl dhe pasojat e k\u00ebtyre varianteve t\u00eb zhvendosjes gjat\u00eb realizimit t\u00eb operacioneve t\u00eb m\u00ebtejshme n\u00eb depo.<\/li>\n<li>s\u00eb dyti, pasi n\u00eb zgjidhjen e detyr\u00ebs fillestare na nevojitet t\u00eb minimizojm\u00eb pik\u00ebrisht kostot totale, q\u00eb \u00ebsht\u00eb shuma e kostove t\u00eb zhvendosjes dhe kostove p\u00ebr zgjedhjen e kontejner\u00ebve, volumi i qelizave n\u00eb metra kub duhet t\u00eb lidhet ndonj\u00ebher\u00eb me sekondat, gj\u00eb q\u00eb nuk \u00ebsht\u00eb aspak e thjesht\u00eb.<\/li>\n<\/ul>\n<p>\n<img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/2c906f9e80b32fcb111fcba7000ea2ba.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>Fig. 4. Variantet e zhvendosjes s\u00eb mbetjeve n\u00eb kontejner\u00eb me kapacitet t\u00eb ndrysh\u00ebm.<\/i><\/p>\n<p>N\u00eb figur\u00ebn 4, n\u00eb ngjyr\u00eb t\u00eb kuqe \u00ebsht\u00eb paraqitur volumi i mbetjeve q\u00eb nuk p\u00ebrputhet m\u00eb n\u00eb kontejner n\u00eb faz\u00ebn e dyt\u00eb t\u00eb vendosjes s\u00eb mallrave t\u00eb m\u00ebtejshme. <\/p>\n<p>Do t\u00eb ndihmoj\u00eb t\u00eb lidhim metrat kub t\u00eb kostove p\u00ebr zgjedhjen e kontejnerit me sekondat e kostove p\u00ebr zhvendosje k\u00ebrkesat e m\u00ebposhtme p\u00ebr zgjidhjet e llogaritura t\u00eb detyr\u00ebs:<\/p>\n<ul>\n<li>\u00cbsht\u00eb e nevojshme q\u00eb mbetjet nga qeliza-donore t\u00eb zhvendosen n\u00eb qeliza-kontejner gjithmon\u00eb, n\u00ebse kjo zvog\u00eblon numrin total t\u00eb qelizave-kontejner ku ndodhen produktet.<\/li>\n<li>Duhet t\u00eb respektohet balanca midis volumin e kontejner\u00ebve dhe kostot e koh\u00ebs p\u00ebr zhvendosje: p\u00ebr shembull, n\u00ebse n\u00eb variantin e ri t\u00eb zgjidhjes s\u00eb detyr\u00ebs krahasuar me variantin e m\u00ebparsh\u00ebm, fitimi n\u00eb volum \u00ebsht\u00eb i madh, nd\u00ebrsa humbja n\u00eb kostot e koh\u00ebs \u00ebsht\u00eb e vog\u00ebl, at\u00ebher\u00eb duhet t\u00eb zgjidhet varianti i ri.<\/li>\n<\/ul>\n<p>\nLe t\u00eb fillojm\u00eb me k\u00ebrkes\u00ebn e fundit. P\u00ebr t\u00eb p\u00ebrcaktuar fjal\u00ebn shum\u00ebkuptimshm\u00ebria \"balanc\u00eb\" ne kryem nj\u00eb pyetje p\u00ebr punonj\u00ebsit e depot me q\u00ebllim t\u00eb zbulojm\u00eb si vijon. Le t\u00eb kemi nj\u00eb qeli-kontejner me volum <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/2b831b12448ccaee33c528ac622b7ee3.jpeg\" style=\"display:block;margin: 0 auto;\" \/>, n\u00eb t\u00eb cil\u00ebn \u00ebsht\u00eb caktuar zhvendosja e mbetjeve t\u00eb mallrave nga qelizat-donore dhe koha totale e k\u00ebtij zhvendosjeje \u00ebsht\u00eb e barabart\u00eb me <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/8050f4b02464164d334048bda86b3923.jpeg\" style=\"display:block;margin: 0 auto;\" \/>. Le t\u00eb ket\u00eb disa varianta alternative p\u00ebr vendosjen e t\u00eb nj\u00ebjtit num\u00ebr produktesh nga t\u00eb nj\u00ebjtat qeliza donatore n\u00eb kontejner\u00eb t\u00eb tjer\u00eb, ku \u00e7do vendosje ka vler\u00ebsimet e saj. <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/76f11cd5ab85f9092c8f458d01ac347b.jpeg\" style=\"display:block;margin: 0 auto;\" \/>index <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/9e735d8a9c4cff3c69fd926eac8c85aa.jpeg\" style=\"display:block;margin: 0 auto;\" \/>&lt;<img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/d963e193a263a1505467c19e874f0aab.jpeg\" style=\"display:block;margin: 0 auto;\" \/> dhe <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/ff5d990cf5a1752d7bb45da9fd58cd7a.jpeg\" style=\"display:block;margin: 0 auto;\" \/>index <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/485f34b3e720011c38740712cdb8edd9.jpeg\" style=\"display:block;margin: 0 auto;\" \/>&gt;<img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/c66b20d93fd1791e9f186f707b1517bb.jpeg\" style=\"display:block;margin: 0 auto;\" \/>. <\/p>\n<p>Shqet\u00ebsimi \u00ebsht\u00eb: \u00e7far\u00eb \u00ebsht\u00eb fitimi minimal n\u00eb volum <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/86861ad2236d827efdc683d759d4c120.jpeg\" style=\"display:block;margin: 0 auto;\" \/> q\u00eb pranohet, p\u00ebr nj\u00eb humbje t\u00eb caktuar n\u00eb koh\u00eb. <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/3d49171042fd83244c054dfd84e5c6bb.jpeg\" style=\"display:block;margin: 0 auto;\" \/>? \u041f\u043e\u044f\u0441\u043d\u0438\u043c \u043d\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u0435. \u0418\u0437\u043d\u0430\u0447\u0430\u043b\u044c\u043d\u043e \u043e\u0441\u0442\u0430\u0442\u043a\u0438 \u043f\u043e\u043b\u0430\u0433\u0430\u043b\u043e\u0441\u044c \u0440\u0430\u0437\u043c\u0435\u0449\u0430\u0442\u044c \u0432 \u043a\u043e\u043d\u0442\u0435\u0439\u043d\u0435\u0440 \u043e\u0431\u044a\u0435\u043c\u0430 1000 \u0434\u043c3 (1 \u043c3) \u0438 \u0432\u0440\u0435\u043c\u044f \u043d\u0430 \u043f\u0435\u0440\u0435\u043c\u0435\u0449\u0435\u043d\u0438\u0435 \u0441\u043e\u0441\u0442\u0430\u0432\u0438\u043b\u043e 70 \u0441\u0435\u043a\u0443\u043d\u0434. \u0415\u0441\u0442\u044c \u0432\u0430\u0440\u0438\u0430\u043d\u0442 \u0440\u0430\u0437\u043c\u0435\u0449\u0435\u043d\u0438\u044f \u043e\u0441\u0442\u0430\u0442\u043a\u043e\u0432 \u0432 \u0434\u0440\u0443\u0433\u043e\u0439 \u043a\u043e\u043d\u0442\u0435\u0439\u043d\u0435\u0440 \u043e\u0431\u044a\u0435\u043c\u0430 500 \u0434\u043c3 \u0438 \u0432\u0440\u0435\u043c\u0435\u043d\u0435\u043c 130 \u0441\u0435\u043a\u0443\u043d\u0434. \u0412\u043e\u043f\u0440\u043e\u0441: \u0433\u043e\u0442\u043e\u0432\u044b \u043b\u0438 \u043c\u044b \u0442\u0440\u0430\u0442\u0438\u0442\u044c \u0435\u0449\u0435 \u0434\u043e\u043f\u043e\u043b\u043d\u0438\u0442\u0435\u043b\u044c\u043d\u044b\u0435 60 \u0441\u0435\u043a\u0443\u043d\u0434 \u0432\u0440\u0435\u043c\u0435\u043d\u0438 \u043a\u043b\u0430\u0434\u043e\u0432\u0449\u0438\u043a\u0430 \u043d\u0430 \u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u0438\u0435 \u043f\u0435\u0440\u0435\u043c\u0435\u0449\u0435\u043d\u0438\u044f \u0434\u043b\u044f \u0442\u043e\u0433\u043e, \u0447\u0442\u043e\u0431\u044b \u0441\u044d\u043a\u043e\u043d\u043e\u043c\u0438\u0442\u044c 500 \u0434\u043c3 \u0441\u0432\u043e\u0431\u043e\u0434\u043d\u043e\u0433\u043e \u043e\u0431\u044a\u0435\u043c\u0430? \u041f\u043e \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0430\u043c \u043e\u043f\u0440\u043e\u0441\u0430 \u0441\u043e\u0442\u0440\u0443\u0434\u043d\u0438\u043a\u043e\u0432 \u0441\u043a\u043b\u0430\u0434\u0430 \u0431\u044b\u043b\u0430 \u0441\u043e\u0441\u0442\u0430\u0432\u043b\u0435\u043d\u0430 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0430\u044f \u0434\u0438\u0430\u0433\u0440\u0430\u043c\u043c\u0430.<\/p>\n<p><img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/283289c63fe1232e95b73d1dffdaa030.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>Fig. 5. Diagrami i varshm\u00ebris\u00eb s\u00eb kursimit minimal t\u00eb pranuesh\u00ebm t\u00eb volumit nga rritja e diferenc\u00ebs n\u00eb koh\u00ebn e realizimit t\u00eb operacionit.<\/i><\/p>\n<p>Pra, n\u00ebse kostot shtes\u00eb n\u00eb koh\u00eb jan\u00eb 40 sekonda, ne jemi t\u00eb gatsh\u00ebm t'i shpenzojm\u00eb ato vet\u00ebm kur fitimi n\u00eb volum \u00ebsht\u00eb t\u00eb pakt\u00ebn 500 dm\u00b3. Megjith\u00ebse ka nj\u00eb jo-linearitet t\u00eb vog\u00ebl n\u00eb varshm\u00ebri, p\u00ebr thjesht\u00ebsi n\u00eb llogaritjet e m\u00ebtejshme, do t\u00eb supozojm\u00eb se varshm\u00ebria midis vlerave \u00ebsht\u00eb lineare dhe p\u00ebrshkruhet nga nj\u00eb pabarazi.<\/p>\n<p><img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/666802648033d918a1119e58963feffe.jpeg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>N\u00eb figur\u00ebn m\u00eb posht\u00eb do t\u00eb shqyrtojm\u00eb m\u00ebnyrat e ndryshme t\u00eb vendosjes s\u00eb produkteve n\u00eb kontejner\u00eb.<\/p>\n<p><img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/a1cb3a5bce4c369f63b3ebeebb738911.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>Fig. 6. Opsioni (a): 2 kontejner\u00eb, volume totale 400 dm\u00b3, kohe totale 150 sekonda.<\/i><br \/>\n<img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/a13f35b0e2a188e9a8cbf27bcfbf0292.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>Fig. 6. Opsioni (b): 2 kontejner\u00eb, volume totale 600 dm\u00b3, kohe totale 190 sekonda.<\/i><br \/>\n<img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/35699c8bd00546c9828dbe50d4b53c46.jpeg\" style=\"display:block;margin: 0 auto;\" \/><br \/>\n<i>Fig. 6. Opsioni (c): 1 kontejner, volume totale 400 dm\u00b3, kohe totale 200 sekonda.<\/i><\/p>\n<p>Opsioni (a) p\u00ebrzgjedhjeje t\u00eb kontejner\u00ebve \u00ebsht\u00eb m\u00eb i preferuesh\u00ebm se opsioni origjinal, pasi p\u00ebrmbush pabarazin\u00eb: (800-400)\/10 &gt;= 150-120, nga e cila ndiqet 40 &gt;= 30. Opsioni (b) \u00ebsht\u00eb m\u00eb pak i preferuesh\u00ebm se opsioni origjinal, pasi pabarazia nuk p\u00ebrmbushet: (800-600)\/10 &gt;= 190-150, nga e cila ndiqet 20 &gt;= 40. Por opsioni (c) nuk p\u00ebrputhet me k\u00ebt\u00eb logjik\u00eb! Le ta shqyrtojm\u00eb k\u00ebt\u00eb opsion m\u00eb n\u00eb detaje. Nga nj\u00ebra an\u00eb, pabarazia (800-400)\/10 &gt;= 200-120, k\u00ebshtu q\u00eb pabarazia 40 &gt;= 80 nuk p\u00ebrmbushet, q\u00eb tregon se fitimi n\u00eb volum nuk vlejn\u00eb nj\u00eb humbje kaq t\u00eb madhe n\u00eb koh\u00eb. <\/p>\n<p>Por nga ana tjet\u00ebr, n\u00eb k\u00ebt\u00eb variant (c) ne jo vet\u00ebm se reduktojm\u00eb volumet totale t\u00eb z\u00ebnie, por gjithashtu zvog\u00eblojm\u00eb numrin e qelizave t\u00eb z\u00ebna, q\u00eb \u00ebsht\u00eb k\u00ebrkesa e par\u00eb nga dy k\u00ebrkesat e r\u00ebnd\u00ebsishme p\u00ebr zgjidhjet e llogaritura t\u00eb problemeve t\u00eb p\u00ebrmendura m\u00eb sip\u00ebr. Sigurisht, p\u00ebr t\u00eb filluar p\u00ebrmbushjen e k\u00ebtij k\u00ebrkese, \u00ebsht\u00eb e nevojshme t\u00eb shtojm\u00eb nj\u00eb konstant\u00eb pozitive n\u00eb an\u00ebn e majt\u00eb t\u00eb pabarazis\u00eb. <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/61d6b2cb21474a2f4512d6a130a15a0a.jpeg\" style=\"display:block;margin: 0 auto;\" \/>, e cila duhet t\u00eb shtohet vet\u00ebm kur numri i kontejner\u00ebve zvog\u00eblohet. Kujtojm\u00eb se <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/d80d33679896035041d0ca9a78e8177a.jpeg\" style=\"display:block;margin: 0 auto;\" \/> \u2014 \u00ebsht\u00eb nj\u00eb variab\u00ebl, i barabart\u00eb me 1, kur kontejneri <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/a83cd6273e544b63099939e6845740fb.jpeg\" style=\"display:block;margin: 0 auto;\" \/> \u00ebsht\u00eb zgjedhur, dhe 0 kur kontejneri <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/bc94d9e952782e630125a6e8919ba5ad.jpeg\" style=\"display:block;margin: 0 auto;\" \/> nuk \u00ebsht\u00eb zgjedhur. Do ta sh\u00ebnojm\u00eb, <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/1e3fb5d7013e60f67c56a56899630852.jpeg\" style=\"display:block;margin: 0 auto;\" \/> \u2013 nj\u00eb num\u00ebr kontejner\u00ebsh n\u00eb zgjidhjen fillestare dhe <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/26ac9732af37e865cea1bb10a343175c.jpeg\" style=\"display:block;margin: 0 auto;\" \/> \u2013 nj\u00eb num\u00ebr kontejner\u00ebsh n\u00eb zgjidhjen e re. N\u00eb formatin e p\u00ebrgjithsh\u00ebm, pabarazia e re do t\u00eb duket k\u00ebshtu:<\/p>\n<p><img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/1237914e5fdafcc6013203e2624009d0.jpeg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Duke e transformuar pabarazin\u00eb m\u00eb lart, marrim <\/p>\n<p><img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/80b039f9ef44301c3b624ada42c28db8.jpeg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Duke u bazuar n\u00eb k\u00ebt\u00eb, kemi formul\u00ebn p\u00ebr llogaritjen e kostos totale <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/cb5bce584fee0156b23adbab83f66b33.jpeg\" style=\"display:block;margin: 0 auto;\" \/> t\u00eb nj\u00eb varianti t\u00eb caktuar t\u00eb zgjidhjes s\u00eb problemit:<\/p>\n<p><img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/34f382d40368a980674914916c65b4ec.jpeg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p><b>Por tani lind pyetja<\/b>: \u00e7far\u00eb vlere duhet t\u00eb ket\u00eb nj\u00eb konstante e till\u00eb <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/e4754f88bcddfba85b3c785512bee697.jpeg\" style=\"display:block;margin: 0 auto;\" \/>? \u041e\u0447\u0435\u0432\u0438\u0434\u043d\u043e, \u0447\u0442\u043e \u0435\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u0434\u043e\u043b\u0436\u043d\u043e \u0431\u044b\u0442\u044c \u0434\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u043e \u0431\u043e\u043b\u044c\u0448\u0438\u043c, \u0434\u043b\u044f \u0442\u043e\u0433\u043e, \u0447\u0442\u043e\u0431\u044b \u0432\u0441\u0435\u0433\u0434\u0430 \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u043b\u043e\u0441\u044c \u043f\u0435\u0440\u0432\u043e\u0435 \u0442\u0440\u0435\u0431\u043e\u0432\u0430\u043d\u0438\u0435 \u043a \u0440\u0435\u0448\u0435\u043d\u0438\u044f\u043c \u0437\u0430\u0434\u0430\u0447\u0438. \u041c\u043e\u0436\u043d\u043e \u043a\u043e\u043d\u0435\u0447\u043d\u043e \u0432\u0437\u044f\u0442\u044c \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b \u0440\u0430\u0432\u043d\u043e\u0435 103 \u0438\u043b\u0438 106, \u043d\u043e \u0445\u043e\u0442\u0435\u043b\u043e\u0441\u044c \u0431\u044b \u0438\u0437\u0431\u0435\u0436\u0430\u0442\u044c \u0442\u0430\u043a\u0438\u0445 \u00abmagic numbers\u00bb. \u0415\u0441\u043b\u0438 \u0431\u0443\u0434\u0435\u043c \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u0442\u044c \u0441\u043f\u0435\u0446\u0438\u0444\u0438\u043a\u0443 \u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u0438\u044f \u0441\u043a\u043b\u0430\u0434\u0441\u043a\u0438\u0445 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0439, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0432\u043f\u043e\u043b\u043d\u0435 \u043e\u0431\u043e\u0441\u043d\u043e\u0432\u0430\u043d\u043d\u044b\u0445 \u0447\u0438\u0441\u043b\u043e\u0432\u044b\u0445 \u043e\u0446\u0435\u043d\u043e\u043a \u0432\u0435\u043b\u0438\u0447\u0438\u043d\u044b \u0442\u0430\u043a\u043e\u0439 \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u044b.<\/p>\n<p>Le t\u00eb themi <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/50deefe99bf1d5f948a49591904a8bfe.jpeg\" style=\"display:block;margin: 0 auto;\" \/> \u2013 distanca maksimale midis qelizave t\u00eb depozit\u00ebs n\u00eb nj\u00eb zon\u00eb ABC, e barabart\u00eb n\u00eb rastin ton\u00eb me 100 m. Le t\u00eb themi <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/466892dd75279d08b4835a42e62444d4.jpeg\" style=\"display:block;margin: 0 auto;\" \/> \u2013 v\u00ebllimi maksimale i qeliz\u00ebs-kontejner n\u00eb depo, e barabart\u00eb n\u00eb rastin ton\u00eb me 1000 dm3.<\/p>\n<p><b>Metoda e par\u00eb p\u00ebr llogaritjen e madh\u00ebsis\u00eb<\/b> <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/29b94b534da709020cbef206cb0d7dac.jpeg\" style=\"display:block;margin: 0 auto;\" \/>. Le t\u00eb shqyrtojm\u00eb situat\u00ebn ku ka 2 kontejner\u00eb n\u00eb katin e par\u00eb, n\u00eb t\u00eb cil\u00ebt tashm\u00eb ndodhet fizikisht mall, pra ato vet\u00eb jan\u00eb qeliza-dhurues, dhe shpenzimet p\u00ebr zhvendosjen e mallrave n\u00eb k\u00ebto qeliza, natyrisht q\u00eb jan\u00eb 0. Duhet t\u00eb gjejm\u00eb nj\u00eb vler\u00eb t\u00eb till\u00eb konstante <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/5cf81db57dd2a18cc0ec29bb7ca3da62.jpeg\" style=\"display:block;margin: 0 auto;\" \/>, p\u00ebr t\u00eb cil\u00ebn do t\u00eb ishte e leverdishme gjithmon\u00eb t\u00eb zhvendos\u00ebsh mbetjet nga kontejneri 1 n\u00eb kontejnerin 2. Duke futur vlerat <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/20bbd09e167edc3eb1ed49d8078ecf19.jpeg\" style=\"display:block;margin: 0 auto;\" \/> dhe <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/605017af48e7b3ca4a323642db4227cd.jpeg\" style=\"display:block;margin: 0 auto;\" \/> n\u00eb pabarazin\u00eb e p\u00ebrmendur m\u00eb lart, marrim:<\/p>\n<p><img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/2794955b8f9f3d64ffe4e2b449547555.jpeg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>nga e cila pason<\/p>\n<p><img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/292a6e80c646c7eed80e888c8805990c.jpeg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Duke futur vlerat e koh\u00ebs mesatare t\u00eb realizimit t\u00eb operacioneve elementare n\u00eb formul\u00ebn m\u00eb lart marrim<\/p>\n<p><img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/1f56bf1f98c1a3bbd65a4cea99da7efb.jpeg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p><b>Metoda e dyt\u00eb p\u00ebr llogaritjen e madh\u00ebsis\u00eb<\/b> <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/78e3dff7183b15136d9e03f4a5724479.jpeg\" style=\"display:block;margin: 0 auto;\" \/>. Le t\u00eb shqyrtojm\u00eb situat\u00ebn ku ka <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/02daff1eff70a2963ab8eaa067f15584.jpeg\" style=\"display:block;margin: 0 auto;\" \/> qeliza-dhuruese nga t\u00eb cilat planifikohet t\u00eb zhvendosen mallrat n\u00eb kontejnerin 1. Le t\u00eb sh\u00ebnojm\u00eb <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/df20c3f27815f2060aae20d260210893.jpeg\" style=\"display:block;margin: 0 auto;\" \/> \u2013 distanca nga qeliza-dhuruese <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/a29ace66656cf1680c9e00258a9ff597.jpeg\" style=\"display:block;margin: 0 auto;\" \/> n\u00eb kontejnerin 1. Ka gjithashtu nj\u00eb kontejner 2, n\u00eb t\u00eb cilin tashm\u00eb ka mallra, dhe v\u00ebllimi i t\u00eb cilit lejon t\u00eb akomodoj\u00eb mbetjet nga t\u00eb gjitha <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/e25f0828e7d794f8d804528395f6dc7e.jpeg\" style=\"display:block;margin: 0 auto;\" \/> qelizat. P\u00ebr leht\u00ebsi, le t\u00eb supozojm\u00eb se v\u00ebllimi i mallrave t\u00eb zhvendosura nga qelizat-dhuruese n\u00eb kontejner\u00eb \u00ebsht\u00eb i nj\u00ebjt\u00eb dhe i barabart\u00eb me <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/35c3392a83fc3b7eef928ddb5e93961a.jpeg\" style=\"display:block;margin: 0 auto;\" \/>. Duhet t\u00eb gjejm\u00eb nj\u00eb vler\u00eb t\u00eb till\u00eb konstante <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/c9bc10aade46cc3c63628c0ba100b364.jpeg\" style=\"display:block;margin: 0 auto;\" \/>, p\u00ebr t\u00eb cil\u00ebn vendosja e t\u00eb gjitha mbetjeve nga <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/e610d9981da2857a541f028a217f2306.jpeg\" style=\"display:block;margin: 0 auto;\" \/> qelizat n\u00eb kontejnerin 2 do t\u00eb ishte gjithmon\u00eb m\u00eb e leverdisshme se sa vendosja e tyre n\u00eb kontejner\u00eb t\u00eb ndrysh\u00ebm:<\/p>\n<p><img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/27f4f99a920799fba9725f30a04c8ebc.jpeg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Duke transformuar pabarazin\u00eb marrim<\/p>\n<p><img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/56abddb4fc3e54eeb1fe466c68e5d8d7.jpeg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>P\u00ebr t\u00eb \"forcuar\" vler\u00ebn e madh\u00ebsis\u00eb <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/d77359ea816f9d45a8910cb26649f717.jpeg\" style=\"display:block;margin: 0 auto;\" \/>, pranojm\u00eb se <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/9edf13fb4e34b5da26957e451300046f.jpeg\" style=\"display:block;margin: 0 auto;\" \/> = 0. Numri mesatar i qelizave q\u00eb zakonisht p\u00ebrfshihen n\u00eb procedur\u00ebn e kompresimit t\u00eb mbetjeve n\u00eb depo \u00ebsht\u00eb 10. Duke futur vlerat e njohura, kemi m\u00ebnyr\u00ebn e m\u00ebposhtme t\u00eb konstantes<\/p>\n<p><img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/40323791fd8cd2be3f29a2becf78e175.jpeg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Marrim vler\u00ebn m\u00eb t\u00eb madhe, e llogaritur p\u00ebr \u00e7do variant, kjo do t\u00eb jet\u00eb vlera e madh\u00ebsis\u00eb <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/fd018460792c79b8a7953c06b839711d.jpeg\" style=\"display:block;margin: 0 auto;\" \/> p\u00ebr parametrat e caktuar t\u00eb depozit\u00ebs. Tani, p\u00ebr p\u00ebrfundim, le t\u00eb shkruajm\u00eb formul\u00ebn p\u00ebr llogaritjen e kostove totale <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/d4cb2c81bcc788380f1f0c1123b0eeda.jpeg\" style=\"display:block;margin: 0 auto;\" \/> p\u00ebr nj\u00eb zgjidhje t\u00eb pranueshme <img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/052e710199e9417aaea94b16dbed47d3.jpeg\" style=\"display:block;margin: 0 auto;\" \/>:<\/p>\n<p><img decoding=\"async\" alt=\"Matematika diskrete p\u00ebr WMS: algoritmi i kompresimit t\u00eb mallrave n\u00eb qeliza (pjesa 1)\" src=\"\/wp-content\/uploads\/2019\/08\/8dd672c7b91639fe1872ef50dca7a220.jpeg\" style=\"display:block;margin: 0 auto;\" \/><\/p>\n<p>Tani tani, pas t\u00eb gjitha <b>p\u00ebrpjekjeve titanike<\/b> p\u00ebr transformimin e t\u00eb dh\u00ebnave hyr\u00ebse, tani mund t\u00eb themi se t\u00eb gjitha t\u00eb dh\u00ebnat jan\u00eb p\u00ebrpunuar n\u00eb formatin e nevojsh\u00ebm dhe jan\u00eb t\u00eb gatshme p\u00ebr t'u p\u00ebrdorur n\u00eb algoritmin e optimizimit.<\/p>\n<h4>P\u00ebrfundim<\/h4>\n<p>\nSi\u00e7 tregon praktika, puna dhe r\u00ebnd\u00ebsia e faz\u00ebs s\u00eb p\u00ebrgatitjes dhe transformimit t\u00eb t\u00eb dh\u00ebnave hyr\u00ebse p\u00ebr algoritmin shpesh n\u00ebnvler\u00ebsohet. N\u00eb k\u00ebt\u00eb artikull, ne i kushtuam shum\u00eb v\u00ebmendje k\u00ebsaj faze, p\u00ebr t\u00eb treguar se vet\u00ebm t\u00eb dh\u00ebnat hyr\u00ebse t\u00eb p\u00ebrgatitura me cil\u00ebsi dhe arsyesh\u00ebm mund t\u00eb b\u00ebjn\u00eb vendimet, t\u00eb llogaritura nga algoritmi, t\u00eb jen\u00eb v\u00ebrtet t\u00eb vlefshme p\u00ebr klientin. Po, kishte shum\u00eb p\u00ebrfundime formulash, por ju paralajm\u00ebruam q\u00eb m\u00eb par\u00eb \ud83d\ude42<\/p>\n<p>N\u00eb artikullin e ardhsh\u00ebm, ne p\u00ebrfundimisht do t\u00eb arrijm\u00eb n\u00eb at\u00eb q\u00eb ishte q\u00ebllimi i dy publikimeve t\u00eb m\u00ebparshme \u2013 algoritmin e optimizimit diskret.<\/p>\n<p><i>Artikulli \u00ebsht\u00eb p\u00ebrgatitur nga<br \/>\nRoman Shangin, programues n\u00eb departamentin e projekteve,<br \/>\nkompania Parimi Bit, qyteti \u00c7eljabinsk<\/i><br \/>\n<br \/>Burimi: <a content=\"nofollow\" rel=\"nofollow\" href=\"https:\/\/habr.com\/ru\/post\/463481\/\">habr.com<\/a><\/p>","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"<p>\u0412 \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u044b \u0440\u0430\u0441\u0441\u043a\u0430\u0436\u0435\u043c, \u043a\u0430\u043a \u0440\u0435\u0448\u0430\u043b\u0438 \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u0443 \u043d\u0435\u0445\u0432\u0430\u0442\u043a\u0438 \u0441\u0432\u043e\u0431\u043e\u0434\u043d\u044b\u0445 \u044f\u0447\u0435\u0435\u043a \u043d\u0430 \u0441\u043a\u043b\u0430\u0434\u0435 \u0438 \u043e \u0440\u0430\u0437\u0440\u0430\u0431\u043e\u0442\u043a\u0435 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0430 \u0434\u0438\u0441\u043a\u0440\u0435\u0442\u043d\u043e\u0439 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438 \u0434\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0442\u0430\u043a\u043e\u0439 \u0437\u0430\u0434\u0430\u0447\u0438. \u0420\u0430\u0441\u0441\u043a\u0430\u0436\u0435\u043c \u043e \u0442\u043e\u043c, \u043a\u0430\u043a \u043c\u044b \u00ab\u0441\u0442\u0440\u043e\u0438\u043b\u0438\u00bb \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0443\u044e \u043c\u043e\u0434\u0435\u043b\u044c \u0437\u0430\u0434\u0430\u0447\u0438 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438, \u0438 \u043e \u0442\u043e\u043c \u0441 \u043a\u0430\u043a\u0438\u043c\u0438 \u0442\u0440\u0443\u0434\u043d\u043e\u0441\u0442\u044f\u043c\u0438 \u043c\u044b \u043d\u0435\u043e\u0436\u0438\u0434\u0430\u043d\u043d\u043e \u0441\u0442\u043e\u043b\u043a\u043d\u0443\u043b\u0438\u0441\u044c \u043f\u0440\u0438 \u043e\u0431\u0440\u0430\u0431\u043e\u0442\u043a\u0435 \u0432\u0445\u043e\u0434\u043d\u044b\u0445 \u0434\u0430\u043d\u043d\u044b\u0445 \u0434\u043b\u044f \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0430. \u0415\u0441\u043b\u0438 \u0432\u0430\u043c \u0438\u043d\u0442\u0435\u0440\u0435\u0441\u043d\u044b \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u044f \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438 \u0432 \u0431\u0438\u0437\u043d\u0435\u0441\u0435 \u0438 [&hellip;]<\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":1,"featured_media":27819,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[702],"tags":[],"class_list":["post-37108","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-news"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.2.1 - aioseo.com -->\n\t<meta name=\"description\" content=\"\u0412 \u0441\u0442\u0430\u0442\u044c\u0435 \u043c\u044b.\" \/>\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<meta name=\"author\" content=\"Yuri Gagarin\"\/>\n\t<link rel=\"canonical\" href=\"https:\/\/prohoster.info\/sq\/blog\/news\/diskretnaya-matematika-dlya-wms-algoritm-szhatiya-tovarov-v-yachejkah-chast-1\" \/>\n\t<meta name=\"generator\" content=\"All in One SEO (AIOSEO) 5.0.2.1\" \/>\n\t\t<meta property=\"og:locale\" content=\"sq_AL\" 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