Shafin Farko

Operations Research


Gabatarwa

Wannan fanni da ake kira "Operations Research" a rubutun Amurka ko "Operational Research" a rubutun Ingila, sabon fannin karatu ne wanda yake karantar da dabaru da matakan da ake amfani da su wajen binciko matsalar da ke adabbar wata hukuma, masana'anta, ko kamfani ta fuskacin aiki kamar yadda sunan yake (Operations), ko kuma inganta yanayin aikin, ko kuma samun riba mai gwaɓi, ko rage hasara, da kuma samar da mafita a kan hakan. Ƙari a kan wannan binciken yana ma iya zamowa sabunta hanyar yin aikin, ko kuma sauƙaƙa wahalar da ake ci wajen yin aikin, da sauran dangoginsu. Ana iya rubuta wannan sunan darasi da "Operations Research" ko "Operational Research".

Ana karantar da wannan darai ga ɗaliban da ke nazartar kwamfuta a matakai daban-daban a manyan makaratu kamawa daga masu karatun difiloma, NCE, digiri, da sauransu.

Menene "Operations Research"?

Wannan kalma ta "Operations Research" wacce ake taƙaita ta da OR kuma cikin manyan baƙaƙe, ana iya bata fassara ta "Bincike ko Nazarin yin aiki". Abin nufi a nan shi ne bincike kan yadda ake aiwatar da aiki wanda ka iya zama kowane irin aiki ne. Kamar yadda bayanai za su zo dalla-dalla a muhallinsu.

Ta fuskacin ma'ana kuwa, yana da mabambantan ma'anoni da yawa waɗanda masana suka samar gwargwadon fahimta. Duba da yanayi, muna iya cewa shi OR, fannin gamin-gambiza ne da aka samar daga fagagen lissafi, kimiyya, da duk abin da ya samu.

Wato a taƙaice shi OR darasi ne da aka haɗa shi ta hanyar tsakure daga wasu darrusan. Misali, wani abin nasa daga lissafi (mathematics) aka ciro, wani kuma daga kimiyya (science), wani kuma daga saikoloji (psychology), wani kuma daga tsimi (economics), da sauransu, a haka aka harhaɗa shi, don ya samar da mafita ta kankat ko kusa da hakan ga wata matsala mai sarƙaƙiya.

Gudunmawarsa

Wannan darasi yana da matuƙar amfani a rayuwar ma'aikatu da ma'aikata, masana'antu da kuma kamfaninka, kai harma da rayuwarmu ta ɗaiɗaiku. Babban tinƙahon wannan fanni shi ne haɓɓakawa (Maximizing) wanda ta ƙare a kan riba. Abin nufi a nan shi ne haɓɓaka riba (Miximization of profit), da kuma rage hasara (minimizing lost) wacce maƙurarta ta ƙare a kan hasara. Kaɗan daga cikin irin gudunmawar da wannan fanni yake bayarwa akwai:

  1. Yanke hukunci mai inganci (Effective Decision Making): Wannan fanni yana taimakawa manajoji wajen saurin ɗaukar ingantacce kuma nagartaccen mataki a lokaci da kuma muhallin da ya dace. Yana basu damammaki da yawa wajen tantancewa tare da zaɓar matakin da ya fi dacewa.
  2. Gudanar da Sana'a (Business Operations): OR yana bada cikakkiyar dama ta kula da abubuwan da suka shafi adana bayanan kayayyaki (inventory Control) a fannin ma'aikatu, tsarin rarraba aiki (schedule of jobs), kula da hatsari da sauransu a ma'aikatu da masana'antu.
  3. Kyakkyawar Sada Tsakani (Better Coordination); OR yana baiwa ma'aikatu da ma'aikata damar sada tsakanin sassa. Misali, cikin sauƙi yakan samar da damar sada tsakanin fannin samar da kayayyaki (Production department) da kuma fannin tallace-tallace (marketing department)
  4. Taimako ta Fannin Sarrafawa (Facilitate Control): OR yana taimakawa manajoji wajen sarrafa kamfani. Wannan kan faru ta hanyar rarraba aiki. Shi manaja ya ɗauki muhimman ayyuka sauran kuma ya rarraba su ga mataimakansa su riƙa saka masa ido suna bashi bahasi.
  5. Yana Haɓɓaka Hazaƙa (Improves Productivity): Wannan fanni na OR, yana haɓɓaka hazaƙar kamfani. Yana taimakawa wajen zaɓin muhallin gudanar da sana'a ko kafa masana'anta, yana taimakwa wajen zaɓin irin kayan da za a sarrafa, da sauransu.

Fannonin Akin OR

Kusan muna iya cewa babu wani fanni na rayuwa wanda ba za a iya amfani da OR ba, kamawa tun daga rayuwarmu ta ɗaiɗaiku har zuwa yadda muke gudanar da kasuwancinmu manya da ƙanana, hukumomin gwamnati da sauran makamantansu. Misali, 'yan kasuwa masu sayar da ɗanyun kaya wanda muka fi sani da kasuwar gwari kamar irin su tumatir da dangoginsu, za su iya amfani da OR wajen rage yawan hasara da kuma ƙara yawan ribarsu. Sau da yawa wasu idan suka je kasuwa suka taras kaya ya yi yawa sai su bar shi har ya ruɓe wanda ruɓewar hasara ce baki ɗaya. A nan suna iya rage yawan hasara ta ɗaya daga cikin hanyaroyi biyu, ko dai su karya farashi ko kuma su busar da kayan idan wanda za a busar ɗin ne.

Ɗabi'un OR

Wannan fanni na OR yana da wasu ɗabi'un da ake iya gane shi da su don a bambance shi daga dukkan wani fannin da ba shi ba. Muhimmai daga ciki su ne:

  1. Yanke Hukunci ko Ɗaukar Mataki (Decision Making): Abin da ake nufi da yanke hukunci shi ne ɗaukar matakin ƙarshe kan wata matsala. Wannan fanni na OR yana da ɗabi'a ta yanke hukunci. Abin nufi a nan yana taimaka wa jami'an gudanarwa (Executives) na ma'aikata, kamfani ko masana'anta da dabaru, hikimomi da matakan ɗaukar ingantaccen mataki a kan wata matsala.
  2. Halayyar Kimiyya (Scientific Approach): Halayya a nan tana nufin fuskantar abu. Sanannen abu ne cewa a kimiyyance ana warware matsala ne ta hanyar gudanar da gwaje-gwaje da kuma ɗaukar matakai na hankali ta hanyar bincike da nazari. Wannan fanni na OR yakan yi amfani da matakai (methods), gwaje-gwajen (Tests), da kuma kayan aikin kimiyya (sciencetific tools) wajen samar da mafita ga wasu matsaloli, wanda idan ka kalla kai kace ma kimiyyarce. Saboda haka wannan halayya ta kimiyya shima OR yana da ita. A wannan fage babu shaci-faɗi wajen yanke hukunci, a'a, dole a yi aiki da hankali a bincika a gano, ko kuma a yi gwaji a gurin da ake buƙatar hakan.
  3. Halayyar Aikin-Gayya (Inter-Disciplinary Team Approach): A nan, ana nufin gangamin ƙwararru daga fannoni daban-daban don samar da mafita ga wata matsala. Kasancewar hukumomi da ma'aikatu da masana'antu gurare ne na hannu-da-yawa wanda ya tattara mutane daga mabanbantan fannoni, akwai buƙatar tuntuɓar juna don musayar gogayya da nufin samar da mafita ga wata matsala. Wato OR kan tunkari matsala ta hanyar tattara ƙwararru daga fannoni daban-daban don tattara shawarwarin ƙwararru sannan a samar da mafita ga wata matsala da nufin wannan mafita ta zama ta kankat ko kusa da haka.
  4. Halayyar Sistam (system Approach): Abin nufi da system a nan shi ne haɗakar sassa ko ɓangarori da ke ayyuka mabambanta tare da juna don samar da sakamako guda ɗaya. Misali, jini yana gudana a jikin mutum, wannan tsarin gudanar jini shi masana kimiyyar halittu suka kira Tsarin Gudanar Jini (Blood Circulatory Systm); a cikin wannan tsari akwai sassa mabambanta da kowane ke yin aikinsa daban don ya zama jini ya gudana a jikin mutum. Misali akwai huhu wanda ke harba iskar da ke tunkuɗa jini, akwai jijiya da ke a matsayin makwararar jini d.s. idan kowane sashe ya yi aiki, jini sai ya gudana. To wannan fanni yana da halayyar fuskantar matsala ta irin wannan hanyar.

    A nan, wannan fanni na OR yakan bi diddigin tayin (proposal) da aka yi wajen samar da mafita, ya duba irin tasiri da amfanin da kowane ɓangare ko mataki yake da shi a wannan tsari (system). Sannan ya tantance dangataka ko sarƙaƙiyar da ke tsakanin waɗannan ɓangarori ta hanyar dabarun lissafi (Mathematical models) don a samu karɓaɓɓiyar mafita guda.

  5. Aiki da Kwamfuta (Use of computer): Babban makamin da wannan fanni na OR ya fi amfani da shi, shi ne salo ko dabarun lissafi (mathematical models) masu sarƙaƙiya, don yin kyakkyawan amfani da wannan salo na lissafi, akwai bukatar amfani da kwamfuta wajen aiwatar da wannan lissafi wanda hakan kan taimaka matuƙa gaya wajen gudanar da ayyuka. Saboda haka wannan ya zama hali na wannan fanni, wato amfani da kwamfuta.

Matakan Gudanar da Bincike a Fannin OR (Phases for OR Study)

Shi wannan fanni na OR kacokaf ɗinsa, tafarki ne tsararre na gudanar da bincike ta hanyar samar da dalilai na hankali don yanke hukunci. Saboda haka, matakan OR na yanke hukunci (decision making), matakai ne daki-daki na hikima da kuma hankali waɗanda ke sarƙafe da juna kuma suna taimakon junansu. Gagga-gagga daga cikinsu su ne:

  1. Duban Matsala (Problem Observation): Matakin farko na gudanar da bincike a fannin OR shi ne duba matsala. Duban matsala a nan na nufin ɗaukar matakan da suka dace don a tabbatar da samuwar matsalar. Babban abin yi a nan shi ne a nazarci muhallin da ake zaton matsalar tana faruwa. Abubuwan da za a yi don cimma hakan su ne:
    • Ziyarar Gani-da-Ido (Visit): A nan, ƙwararru za su tashi su je muhallin da matsalar take don ganewa idanuwansu abubuwan da ke faruwa, sannan su aiwatar da abubuwa kamar haka:
    • Zaman tattaunawa: bayan sun je sun ga abin da ke faruwa sai kuma su yi zaman tattaunawa. Ana aiwatar da shi wannan zama a matakai daban-daban. Na farko shi ne su ƙwararrun su fara zama su tattauna kan abin da suka gano don su tabbatar da cewa matsalar ce koma ba ita bace. Sannan kuma sai su zauna da shugabannin guri ko kuma waɗanda abin ya shafa, haka-haka har aiki ya kammala. Kenan ana gudanar da wannan zama na tattaunawa a matakai daban-daban tun daga farkon farawa har zuwa mataki na ƙarshe wanda shi ne aiwatarwa.
  2. Nazari: bayan tattaunawa kuma sai a shiga fagen nazarin matsalar don a gane kalarta da abubuwan da suka haifar da ita, da sauransu: Tabbas, wannan mataki na farko mataki ne mai muhimmanci, saboda haka akwai bukatar a bi shi sannu a hankali. Matuƙar aka yi gaggawa a wannan mataki, to fa ba lallai ne a samu biyan buƙata yadda ya kamata ba.
  3. Tantance Matsala (Analysis of the Problem): Wannan mataki shi ne matakin da ake tantance matsala a ƙalailaice ta, a tabbatar da cewa lallai wannan matsala akwai ta kuma kala kaza ce. Sannan kuma a danganta ta da manufa ko manufofin (objectives) gudanar da wannan bincike da ma hurumominsa (limitations). Misali, idan ana gudanar da bincike a kan rashin karɓuwar wani kaya a kasuwa, to a nan rashin karɓuwar ita ce matsalar. Sannan samun karɓuwarsa kuma ita ce manufar (objective) a halin gudanar da binciken. Haka nan tabbatar da ya samu karɓuwar kuma ita ce hurumin (limitation) binciken. Da za a kai ga batun riba to an tsallake iyakar kenan.
  4. Samar da Samfuri (Model Development): Samar da samfuri a nan na nufin samar da wakilci na zahiri ko na gaibi. Samfuri a fannin OR yawanci yakan zama dabarun lissafi (mathematical models) ne, waɗanda ke wakiltar tsarurruka (systems), matakai (process) ko kuma muhalli (environment), a tsakanin ikwashin (equation), dangantaka ko kuma tsarurruka.

    Ayyukan da ake yi a wannan mataki sun haɗa da bayyana dangantakar da ke tsakanin bariyabuls (variables) a bayyane filla-filla; su kuma bariyabuls ɗin a nan ka iya zama abin binciken, wato abinda ake aiwatar da binciken a kansa misali, kaya da kuma matsalar. Da kuma tsara ikwashin ta hanyar amfani da sanannanun samfuran OR (OR Models), ko kuma lalubo wasu nagartattun hanyoyin na daban. Sannan a gwada samfurin da ake sa ran amfani da shi dan ya zama bai wuce gona da iri ba, ko kuma ya gaza.

  5. Zaɓin Bayanan da za a Shigar (Data Selection for Input): Abin nufi da wannan shi ne cewa a tattace bayanan da aka tattaro a zaɓi ingantattu daga cikinsu a yi amfani da su wajen yanke hukunci. Sanannen abu ne cewa a wannan fanni na gudanar da binciken OR, bayanan gaskiya kuma nagartattu su ne kaɗai za su iya haifar da ingantaccen sakamako kuma abin dogaro. Ayyukan da za a yi don samun dacewa a wannan mataki sun haɗa da:
    • Tantance bayanan da aka samo na cikin gida dana waje.
    • Sauraron Ra'ayuyyuka: Wannan ita ce hanyar samun bayanan da za a tantance. A nan ƙwararru za su fita waje su nemi bayanai daga hannun da ya dace. Misali, idan ana son warware matsalar da ta hana kaya karɓuwa a kasuwa kamar yadda muka ambata, sai a je a tattauna da waɗanda ke yin kayan, sannan a tuntuɓi masu kai kayan kasuwa, sannan a fita kasuwar a tuntuɓi masu sayar da kayan, sannan kuma a ƙarshe a tuntuɓi masu amfani da kayan. Sai a haɗa waɗannan bayanai waje guda sannan a tantance me ke faruwa.
    • Binciken Adanannun Bayanai: A wannan mataki kuma sai a waiwaici wasu bayanai da aka adana a kwamfuta a kan wata matsala irin wannan don a nazarce ta kuma a sake samun wani guzurin a cikinsu. Kamar hanyoyin da aka bi aka warware matsalar.
  6. Samar da Mafita da Kuma Gwaji (Solution and Testing): Ya zuwa wannan mataki an gama tattara bayanai kuma ma har an fara tunanin samar da mafita koma an samar. To a wannan matakin sai a gwada wannan mafita da ake tunanin ɗauka ta hanyar amfani da wancan samufuri (model) da aka samar. Idan buƙata ta biya, to sai a wuce mataki na gaba, idan kuma an ga cewa, kwalliya ba za ta biya kuɗin sabulu ba, to sai a sake nazartar wancan samfuri ko kuma a sake waiwaitar waɗancan matakai a ga ina matsalar ta faru sannan a gyarata ko a faɗaɗa samfurin koma a sake wani kaco-kaf.
  7. Aiwatarwa (Implementation): Wannan shi ne matakin ƙarshe na gudanar da bincike a fannin OR. Wannan mataki, mataki ne da yake buƙatar samun kyakkyawar fahimtar juna tsakanin ɓangarori biyu; ɓangaren ma'aikata, masana'anta ko kamfani da ya ƙunshi jami'an gudanar da aikin da kuma masu duba su. Sannan kuma a ɗayan ɓangare akwai jami'an da suka gudanar da binciken kafin a zartar da hukuncin da aka ɗauka. Rashin yin hakan zai iya haifar da babban giɓi. Sannan kuma fahimtar juna za ta haifar da ɗa-mai-ido ta hanyar haɓɓaka tsarin gudanarwar muhallin da abin ya shafa, dama samun karɓuwa a wajen shugabanni.

    Babban abin da ake nema a nan shi ne cuɗe-ni-in-cuɗe-ka. Wato kowa ya bayar da gudunmawar da ta kamace shi don cimma mafita. Sannan ana samun wannan natija ne kawai ta hanyar tattaunawa da kuma tuntuɓar juna kamar yadda aka zayyan tun farko cewa tattaunawa aba ce da ake yinta tun daga farko har zuwa ƙarshen bincike. To wannan ita ce gaɓar.

Dabaru ko Kayan Aikin da Ake Amfani da su

A nan ana nufin abubuwan da OR ke amfani da su wajen gano matsaloli da kuma warware su. Daga cikinsu akwai:

  1. Tsari ko Dabarar Rabon Arziƙi (Linear Programming): Wato idan za mu kalli Turancin mu bashi fassara za mu fara da ɗaukar kalmar (Linear) ɗin wacce ke da ma'ana ta: dangantakar da za a iya bayyana ta ta hanyar miƙaƙƙen layi. Ita kuma kalmar (Programming) a nan ta ɗauki ma'ana ta kyakkyawan rabon arziƙi, arziƙin kuma a nan yana nufin (resources). Saboda haka babbar damuwar Linear Programming a nan ita ce samar da hanya ko dabarar rarraba arziƙi don a kai maƙura wajen cin moriyarsa. Ana kuma yin wannan ne ta hanyar lissafi. Misali, idan akwai matsalar rabon arziƙi a masana'anta kamar a ce sinadarin aiki (raw materials) sun yi ƙaɗan, to ana iya amfani da Linear Programming a kasafta su yadda ya dace.
  2. Nazariyyar Yanke Hukunci (Decision Theory): Wannan kuma wata hanya ce da ake amfani da ita a wannan fanni dan ɗaukar matakin da ya dace a kan wata matsala. Wannan dabara ita ce ta fito da halayya ta farko (Decision Making) da kuma ta uku (Inter-disciplinary team approach) ta wannan fanni.

    Wannan dabara ita ce take haɗa ƙwararru daga fannoni daban-daban su yi aiki tare don cimma manufa guda ɗaya. Misali, idan za a gudanar da bincike kan abin da ya shafi siyasa da kuma masu dangwala ƙuri'a, to sai a samu masanin kimiyyar siyasa (Political Science) ya nazarci dokoki da ƙa'idojin zaɓe don yanke hukunci. Sai kuma a samu masanin halayyar ɗan'adam (psychologist), ya nazarci halayen ɗaiɗaikun mutane dangane da yanke hukunci. Masanin falsafa (Philosophy) kuma ya nazarci abubuwan buƙata don yin tunanin hankali wajen yanke hukunci, da sauransu sai a haɗa baki ɗaya a yanke hukuncin haɗaka. Ka ga a nan halayyar wannan fanni na OR ta aikin gayya ta bayyana a fili.

Dabarun Rage Raɗaɗin Hasara da kuma Ƙara Yawan Riba (Maximin da Minimax Strategies)

Waɗannan kuma dabaru ne da ake amfani da su wajen rage yawan hasara ko ƙara yawan riba kamar yadda aka bada misali da masu sana'ar sayar da ɗanyun kaya kamar irinsu tumatir a baya. Wannan dabara daga fannin tsimi (economic) aka ɗauko ta. Wato kenan wannan dabara ta bayyana mana halayar wannan fanni ta (system Approach da Inter-Disciplinary).

Dabarun Gudanar da Aiki (Network Analysis):

Network Analysis a nan suna ne da aka bai wa wasu dabaru na musamman da ake mafani da su wajen tsarawa (planning), sarrafawa (management) da kuma ƙa'idance (controlling) wani aiki (project). Wannan dabara ita za ta baka dama ka shirya aiki sannan ka kula da gudanawarsa. Daga cikin hikimomin da ake amfani da su akwai tafarki mai sarƙaƙiya (Ciritical Path). Ta wannan dabara za ka iya tsara cewa zan yi aiki kaza daga lokaci kaza zuwa lokaci kaza. Zan fara takan kaza sannan sai kaza. Wannan dabara ta fito mana da halayyar wannan fanni ta (system Approach). Saboda ta wannan hanya ce ake iya nazartar kowane mataki na aiki sannan a san irin tasirin da yake da shi a cikin tsarin da sauransu.

Matsalar Sufuri (Transportation Problem):

Wannan wata dabara ce da ake amfani da ita wajen warware matsalar da ta shafi ɗaukar kayan da kamfani ya samar daga masana'anta zuwa kasuwanni daidai da buƙatar masu saye. Misali, farkon fari akan fara duba yawan abin da ake buƙata da kuma yawan abin da aka samar. Idan akwai daidaito sai kuma a duba hanyar da za a bi a taƙaita yawan kuɗaɗen da za a kashe wajen kai kayan zuwa kasuwa. Wannan dabara ce ta bamu amsar wane guri za a fara kai kayan kafin wancan? Wanne irin abin sufuri ya kamata a yi amfani da shi? D.s. Wannan dabara lissafi ne mai sarƙaƙiya wanda yake bukatar amfani da kwamfuta. Halayyar wannan fanni ta amfani da kwamfuta ta fito a nan.

Manazarta:


Hansson S.O. (2005). Decision Theory A Brief Introduction. Department of Philosophy and the History of Technology Royal Institute of Technology (KTH), Stockholm.

Sottinen T. (2009). Operations Research with GNU Linear Programming Kit. An ciro a shekarar 2016, daga shafin: www.uwasa.fi/tsottine/orms1020

Wang J.Y. (2008). Operation Research I. College of Management, NCTU.