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A novel activity time planning methodology for resource constrained projects by a new mathematical model and a hybrid metaheuristic: A case study

Yıl 2022, Cilt: 37 Sayı: 3, 1169 - 1184, 28.02.2022
https://doi.org/10.17341/gazimmfd.913666

Öz

Projects are set of processes which aim to serve a unique product or a service in a time-bounded period. In the real life, every project has budget, time, scope and quality constraints. It is required to use all the resources efficiently, comply with the time and budget constraints, and satisfy all the project shareholders, especially the customer in order to complete the project successively. However, it is getting more difficult to reach a successful project due to the aggressive competitive requirements in almost all the sectors. Especially, pressure in terms of accelerating the time to market of the unique product or service which is the output of the project has become the reality in every organization. Thus, the companies need to search for new methodologies in order to make activity time planning of their resource constrained projects effectively. This paper presents a new mathematical model to complete activities of resource constrained projects in accordance with their logical relationships. Optimal solution of this complex model cannot be found in case of a high number of activities. Therefore, a new hybrid metaheuristic approach is proposed to find efficient solutions for the mathematical model. Moreover, the proposed mathematical model and hybrid metaheuristic are applied to plan the activities of projects in an information technology company in Turkey. It is observed that proposed model and solution approach provide efficient solutions with a small number of delayed projects and activities, high success ratio, and reliable plans.

Kaynakça

  • [1] PMI, A Guide to the Project Management Body of Knowledge. (PMBOK® Guide), Newtown Square, Pennsylvania, U.S.A., 2007.
  • [2] Wateridge J., How can IS/IT projects be measured for success?, International Journal of project Management, 16 (1), 59- 63, 1998.
  • [3] Atkinson R., Project management: cost, time and quality, two best guesses and a phenomenon, its time to accept other success criteria, International Journal of Project Management, 17, 337-342, 1999.
  • [4] Blaskovics B., The impact of project manager on project success—The case of ICT sector, Society and Economy, 38 (2), 261-281, 2016.
  • [5] Knoepfel H., Cost and quality control in the project cycle, International Journal of Project Management, 7 (4), 229-235, 1989.
  • [6] Aaron L., The Engineer’s Cost Handbook: Tools for Managing Project Costs.” Marcel Decker Pub., New York, U.S.A, 1997.
  • [7] Arkes H., Overconfidence in judgmental forecasting, In: Armstrong J.S. (eds) Principles of Forecasting. International Series in Operations Research & Management Science, vol 30. Springer, New York, U.S.A, 2001.
  • [8] Lin S.W., Bier V.M., A study of expert overconfidence, Reliability Engineering & System Safety, 93, 711-721, 2008.
  • [9] Kerzner H., Project Management: A Systems Approach to Planning, Scheduling and Controlling, John Wiley & Sons, 12, Canada, 2017.
  • [10] Malcolm D.G., Roseboom J.H., Clark C.E., Fazar W., Application of a technique for a research and development program evaluation, In: Operations Research, 7, 646–669, 1959.
  • [11] Badruzzaman F.H., Fajar M.Y., Rohaeni, O., Gunawan G., Harahap, E., CPM and PERT technique efficiency model for child veil production, International Journal of Scientific & Technology Research, 9 (4), 2020.
  • [12] Azaron A., Perkgoz C., Sakawa M., A genetic algorithm approach for the time-cost trade-off in PERT networks, Applied Mathematics and Computation, 168, 1317– 1339, 2005.
  • [13] Hendradewai A.P., Schedule risk analysis by different phases of construction project using CPM-PERT and Monte-Carlo simulation, IOP Conference Series: Materials Science and Engineering, Volume 528, 11th International Seminar on Industrial Engineering & Management, Technology and Innovation Challenges Towards Industry 4.0 Era, Makasar, South Sulawesi, Indonesia, 2018.
  • [14] Kholil M., Alfa B.N., Hariadi M., Scheduling of house development projects with CPM and PERT method for time efficiency (Case Study: House Type 36), IOP Conference Series: Earth and Environmental Science, 4th International Conference on Civil and Environmental Engineering for Sustainability, Langkawi, Malaysia, 2017.
  • [15] Kotiah T.C.T., Wallace N.D., Another look at the PERT asssumptions, In: Management Science, 20 (3-4), 44-49, 1973.
  • [16] Johnson D., The triangular distribution as a proxy for the beta distribution in risk analysis, In: Journal of the Royal Statistical Society: Series D (The Statistician), 46, 387–398, 1997.
  • [17] Mohan S., Gopalakrishnan M., Balasubramanian H., Chandrashekar A., A lognormal approximation of activity duration in PERT using two time estimates, Journal of the Operational Research Society, 58, 827–831. 2007.
  • [18] Hahn E.D., Mixture densities for project management activity times: A robust approach to PERT, European Journal of Operational Research, 188, 450–459, 2008.
  • [19] Trietsch D., Mazmanyan L., Gevorgyan L., Baker K.R., Modeling activity times by the Parkinson distribution with a lognormal core: Theory and validation, European Journal of Operations Research Volume 216 (2), 386-396, 2012.
  • [20] Williams T., The contribution of mathematical modelling to the practice of project management, Journal of Management Mathematics, 4 (1), 3-30, 2003.
  • [21] Dantzig G., Fulkerson R., Johnson S., Solution of a large-scale travelling salesman problem. Journal of the Operational Research Society, 2, 393-410, 1954.
  • [22] Gomory R., An algorithm for integer solutions to linear programs, In: Recent Advances in Mathematical Programming, 269-302, Eds. Graves, R.L. ve Wolfe, P., McGraw-Hill, New York, U.S.A, 1963.
  • [23] Bellman R.E., Dynamic Programming, Princeton University Press, New Jersey, U.S.A., 1957.
  • [24] Geoffrion A.M., Lagrangian relaxation and its uses in integer programming, Mathematical Programming Study, 2, 82-114, 1974.
  • [25] Glover F., Heuristics for integer programming using surrogate constraints, Decision Sciences, 8, 156-166., 1977.
  • [26] Arıkan M., A tabu search algorithm for the simple assembly line balancing problem of type-2 with workload balancing objective, Journal of the Faculty of Engineering and Architecture of Gazi University, 32 (4), 1169 – 1180, 2017.
  • [27] Başar A., Kabak Ö., Topçu Y.İ., A tabu search algorithm for a multi-period bank branch location problem: A case study in a Turkish bank, Scientica Iranica, 26 (6), 3728-3746, 2019.
  • [28] Baar T., Brucker P., Knust S., Tabu-search algorithms for the resource constrained project scheduling problem, Technical Report, Osnabrück, 1997.
  • [29] Pan N.H., Hsaio P.W., Chen K.Y., A study of project scheduling optimization using Tabu Search algorithm, ngineering Applications of Artificial Intelligence, 21 (7), 1101- 1112, 2008.
  • [30] Holland J., Adaption in natural and artificial systems, University of Michigan Press, Michigan, U.S.A., 1975.
  • [31] Goldberg D.E, Genetic algorithms in search, optimization and machine learning, Addisson-Wesley, Massachusetts, U.S.A, 1989.
  • [32] Uçaner M.E., Özdemir O.N., Optimization of booster chlorination in water distribution networks with genetic algorithm, Journal of the Faculty of Engineering and Architecture of Gazi University, 17(4), 1169 – 1180, 2002.
  • [33] Hosseinabadi A.A.R., Vahidi J., Saemi B. et al, Extended Genetic Algorithm for solving open-shop scheduling problem, Soft Computing, 23, 5099–5116, 2019.
  • [34] Leu S.S., Chen A.T., Yang C.H., A GA-based fuzzy optimal model for construction time-cost trade-off, International Journal of Project Management, 19, 47–58, 2001.
  • [35] Demirel N., Gokcen H., Akcayol M.A., Demirel E., A hybrid genetic algorithm for multistage integrated logistics network optimization problem, Journal of the Faculty Engineering and Architecture of Gazi University, 26 (4), 929-936, 2011.
  • [36] Kumar N.S., Kumar R.R., Study on application of genetic algorithm in construction resource levelling, International Journal of Innovative Research in Science, Engineering and Technology, 3 (2), 78-83, 2014.
  • [37] Hussain W., Trivedi M.K., Kansal R., Optimization of construction resource allocation and levelling using genetic algorithm, International Journal of Innovative Research in Science, Engineering and Technology, 4 (6), 2015.
  • [38] Calp M.H., Akcayol M.A., Optimization of project scheduling activities in dynamic CPM and PERT networks using genetic algorithms, Süleyman Demirel University, Journal of Natural and Applied Sciences, 22 (2), 615-627, 2018.
  • [39] Cerny V., A thermo dynamical approach to the travelling salesman problem: An efficient simulation algorithm. Journal of Optimization Theory and Applications, 45, 41–51, 1985.
  • [40] Şahin R., A simulated annealing heuristic for the dynamic facility layout problem, Journal of the Faculty of Engineering and Architecture of Gazi University, 23 (4), 863 – 870, 2008.
  • [41] Abdel-Basset M., Ding W., El-Shahat D., A hybrid Harris Hawks optimization algorithm with simulated annealing for feature selection. Artificial Intelligence Review, 54, 593–637, 2021.
  • [42] Dorigo M., Maniezzo V., Colorni A., The ant system: An autocatalytic optimizing process. Technical Report, Politecnico di Milano, Italy, 1991.
  • [43] Keskintürk T., Söyler H., Global Ant Colony Optimization, Journal of the Faculty of Engineering and Architecture of Gazi University, 21 (4), 2006.
  • [44] Deng W., Xu J., Song Y., Zhao H., An effective improved co-evolution ant colony optimisation algorithm with multi-strategies and its application, International Journal of Bio-Inspired Computation, 16(3), 158–170, 2020.
  • [45] Kennedy J., Eberhart R.C., Particle swarm optimization. Proceedings of IEEE International Conference on Neural Networks, 4, Perth, Austraila, 1942–1948, 1995.
  • [46] Turan Ö., Oruç R., Baklacıoğlu T., Optimization of an afterburning turbofan engine with multi objective particle swarm method, Journal of the Faculty of Engineering and Architecture of Gazi University 35(4): 1997 – 2012, 2020.
  • [47] Lei H., Lei T., Yuenian T., Sports image detection based on particle swarm optimization algorithm, https://doi.org/10.1016/j.micpro.2020.103345, 2021.
  • [48] Zwikael O., Chih Y., Meredith J.R., Project benefit management: setting effective target benefits, International Journal of Project Management, 36 (4), 650 – 658, 2018.
  • [49] Başar A., A novel methodology for time planning of resource-constrained software projects with hesitant fuzzy durations: A case study. International Journal of Industrial Engineering: Theory, Applications and Practice, 26 (4), 471-485, 2019.
  • [50] Silberholz J., Golden B., Comparison of Metaheuristics. In: Gendreau M., Potvin JY. (eds) Handbook of Metaheuristics. International Series in Operations Research & Management Science, 146. Springer, Boston, U.S.A, 2010.

Yeni bir matematiksel model ve hibrit meta sezgisel ile kaynak kısıtlı projelerin çizelgelenmesi: Bir vaka çalışması

Yıl 2022, Cilt: 37 Sayı: 3, 1169 - 1184, 28.02.2022
https://doi.org/10.17341/gazimmfd.913666

Öz

Projeler, başlangıç ve bitiş tarihi belli olacak şekilde belirlenmiş bir zaman diliminde özgün çıktıların sunulmasının hedeflendiği çalışmalardır. Gerçek hayatta her projenin bütçe, zaman, kapsam ve kalite kısıtları vardır. Projelerin başarıyla sonuçlanabilmesi için bu kısıtlar dâhilinde tüm kaynakların etkin kullanımı, zaman ve bütçe kısıtlarına uyulması ve başta müşteri olmak üzere bütün paydaşların memnun edilmesi şarttır. Her alanda gittikçe zorlaşan rekabet koşulları nedeniyle projelerin başarılı bir şekilde tamamlanması her geçen gün zorlaşmaktadır. Özellikle proje çıktısı olan yeni ürün veya servisin pazara çıkış süresini hızlandırmak amacıyla zaman baskısı artık her işletmede rastlanan bir durumdur. Bunun için işletmeler, kaynak kısıtlı projelerin aktivite zamanını doğru planlamak için yeni yöntem arayışına girmek durumundadır. Bu çalışmada, kaynak kısıtlı projelerin aktivitelerinin zaman planına uygun olarak tamamlanabilmesi için aktiviteler arasındaki mantıksal ilişkileri dikkate alacak şekilde yeni bir matematiksel model önerilmiştir. İşletmelerdeki projelerin aktivite sayısının fazla olduğu durumlarda karmaşık yapıya sahip bu modelin en iyi çözümü bulunamamaktadır. Bu nedenle önerilen hibrit metasezgisel sayesinde kaynak kısıtlı projelerin aktivitelerinin zamanında tamamlanması probleminin çözülmesi hedeflenmiştir. Geliştirilen model ve metasezgisel yöntem, Türkiye’de hizmet vermekte olan bir bilgi teknolojileri şirketinin proje aktivite zaman planlaması için uygulanmıştır. Bu yaklaşım ile geciken proje ve aktivite sayısının çok az olduğu, yöntemlerin başarı yüzdesinin yüksek olduğu ve planların gerçekçi olduğu görülmüştür.

Kaynakça

  • [1] PMI, A Guide to the Project Management Body of Knowledge. (PMBOK® Guide), Newtown Square, Pennsylvania, U.S.A., 2007.
  • [2] Wateridge J., How can IS/IT projects be measured for success?, International Journal of project Management, 16 (1), 59- 63, 1998.
  • [3] Atkinson R., Project management: cost, time and quality, two best guesses and a phenomenon, its time to accept other success criteria, International Journal of Project Management, 17, 337-342, 1999.
  • [4] Blaskovics B., The impact of project manager on project success—The case of ICT sector, Society and Economy, 38 (2), 261-281, 2016.
  • [5] Knoepfel H., Cost and quality control in the project cycle, International Journal of Project Management, 7 (4), 229-235, 1989.
  • [6] Aaron L., The Engineer’s Cost Handbook: Tools for Managing Project Costs.” Marcel Decker Pub., New York, U.S.A, 1997.
  • [7] Arkes H., Overconfidence in judgmental forecasting, In: Armstrong J.S. (eds) Principles of Forecasting. International Series in Operations Research & Management Science, vol 30. Springer, New York, U.S.A, 2001.
  • [8] Lin S.W., Bier V.M., A study of expert overconfidence, Reliability Engineering & System Safety, 93, 711-721, 2008.
  • [9] Kerzner H., Project Management: A Systems Approach to Planning, Scheduling and Controlling, John Wiley & Sons, 12, Canada, 2017.
  • [10] Malcolm D.G., Roseboom J.H., Clark C.E., Fazar W., Application of a technique for a research and development program evaluation, In: Operations Research, 7, 646–669, 1959.
  • [11] Badruzzaman F.H., Fajar M.Y., Rohaeni, O., Gunawan G., Harahap, E., CPM and PERT technique efficiency model for child veil production, International Journal of Scientific & Technology Research, 9 (4), 2020.
  • [12] Azaron A., Perkgoz C., Sakawa M., A genetic algorithm approach for the time-cost trade-off in PERT networks, Applied Mathematics and Computation, 168, 1317– 1339, 2005.
  • [13] Hendradewai A.P., Schedule risk analysis by different phases of construction project using CPM-PERT and Monte-Carlo simulation, IOP Conference Series: Materials Science and Engineering, Volume 528, 11th International Seminar on Industrial Engineering & Management, Technology and Innovation Challenges Towards Industry 4.0 Era, Makasar, South Sulawesi, Indonesia, 2018.
  • [14] Kholil M., Alfa B.N., Hariadi M., Scheduling of house development projects with CPM and PERT method for time efficiency (Case Study: House Type 36), IOP Conference Series: Earth and Environmental Science, 4th International Conference on Civil and Environmental Engineering for Sustainability, Langkawi, Malaysia, 2017.
  • [15] Kotiah T.C.T., Wallace N.D., Another look at the PERT asssumptions, In: Management Science, 20 (3-4), 44-49, 1973.
  • [16] Johnson D., The triangular distribution as a proxy for the beta distribution in risk analysis, In: Journal of the Royal Statistical Society: Series D (The Statistician), 46, 387–398, 1997.
  • [17] Mohan S., Gopalakrishnan M., Balasubramanian H., Chandrashekar A., A lognormal approximation of activity duration in PERT using two time estimates, Journal of the Operational Research Society, 58, 827–831. 2007.
  • [18] Hahn E.D., Mixture densities for project management activity times: A robust approach to PERT, European Journal of Operational Research, 188, 450–459, 2008.
  • [19] Trietsch D., Mazmanyan L., Gevorgyan L., Baker K.R., Modeling activity times by the Parkinson distribution with a lognormal core: Theory and validation, European Journal of Operations Research Volume 216 (2), 386-396, 2012.
  • [20] Williams T., The contribution of mathematical modelling to the practice of project management, Journal of Management Mathematics, 4 (1), 3-30, 2003.
  • [21] Dantzig G., Fulkerson R., Johnson S., Solution of a large-scale travelling salesman problem. Journal of the Operational Research Society, 2, 393-410, 1954.
  • [22] Gomory R., An algorithm for integer solutions to linear programs, In: Recent Advances in Mathematical Programming, 269-302, Eds. Graves, R.L. ve Wolfe, P., McGraw-Hill, New York, U.S.A, 1963.
  • [23] Bellman R.E., Dynamic Programming, Princeton University Press, New Jersey, U.S.A., 1957.
  • [24] Geoffrion A.M., Lagrangian relaxation and its uses in integer programming, Mathematical Programming Study, 2, 82-114, 1974.
  • [25] Glover F., Heuristics for integer programming using surrogate constraints, Decision Sciences, 8, 156-166., 1977.
  • [26] Arıkan M., A tabu search algorithm for the simple assembly line balancing problem of type-2 with workload balancing objective, Journal of the Faculty of Engineering and Architecture of Gazi University, 32 (4), 1169 – 1180, 2017.
  • [27] Başar A., Kabak Ö., Topçu Y.İ., A tabu search algorithm for a multi-period bank branch location problem: A case study in a Turkish bank, Scientica Iranica, 26 (6), 3728-3746, 2019.
  • [28] Baar T., Brucker P., Knust S., Tabu-search algorithms for the resource constrained project scheduling problem, Technical Report, Osnabrück, 1997.
  • [29] Pan N.H., Hsaio P.W., Chen K.Y., A study of project scheduling optimization using Tabu Search algorithm, ngineering Applications of Artificial Intelligence, 21 (7), 1101- 1112, 2008.
  • [30] Holland J., Adaption in natural and artificial systems, University of Michigan Press, Michigan, U.S.A., 1975.
  • [31] Goldberg D.E, Genetic algorithms in search, optimization and machine learning, Addisson-Wesley, Massachusetts, U.S.A, 1989.
  • [32] Uçaner M.E., Özdemir O.N., Optimization of booster chlorination in water distribution networks with genetic algorithm, Journal of the Faculty of Engineering and Architecture of Gazi University, 17(4), 1169 – 1180, 2002.
  • [33] Hosseinabadi A.A.R., Vahidi J., Saemi B. et al, Extended Genetic Algorithm for solving open-shop scheduling problem, Soft Computing, 23, 5099–5116, 2019.
  • [34] Leu S.S., Chen A.T., Yang C.H., A GA-based fuzzy optimal model for construction time-cost trade-off, International Journal of Project Management, 19, 47–58, 2001.
  • [35] Demirel N., Gokcen H., Akcayol M.A., Demirel E., A hybrid genetic algorithm for multistage integrated logistics network optimization problem, Journal of the Faculty Engineering and Architecture of Gazi University, 26 (4), 929-936, 2011.
  • [36] Kumar N.S., Kumar R.R., Study on application of genetic algorithm in construction resource levelling, International Journal of Innovative Research in Science, Engineering and Technology, 3 (2), 78-83, 2014.
  • [37] Hussain W., Trivedi M.K., Kansal R., Optimization of construction resource allocation and levelling using genetic algorithm, International Journal of Innovative Research in Science, Engineering and Technology, 4 (6), 2015.
  • [38] Calp M.H., Akcayol M.A., Optimization of project scheduling activities in dynamic CPM and PERT networks using genetic algorithms, Süleyman Demirel University, Journal of Natural and Applied Sciences, 22 (2), 615-627, 2018.
  • [39] Cerny V., A thermo dynamical approach to the travelling salesman problem: An efficient simulation algorithm. Journal of Optimization Theory and Applications, 45, 41–51, 1985.
  • [40] Şahin R., A simulated annealing heuristic for the dynamic facility layout problem, Journal of the Faculty of Engineering and Architecture of Gazi University, 23 (4), 863 – 870, 2008.
  • [41] Abdel-Basset M., Ding W., El-Shahat D., A hybrid Harris Hawks optimization algorithm with simulated annealing for feature selection. Artificial Intelligence Review, 54, 593–637, 2021.
  • [42] Dorigo M., Maniezzo V., Colorni A., The ant system: An autocatalytic optimizing process. Technical Report, Politecnico di Milano, Italy, 1991.
  • [43] Keskintürk T., Söyler H., Global Ant Colony Optimization, Journal of the Faculty of Engineering and Architecture of Gazi University, 21 (4), 2006.
  • [44] Deng W., Xu J., Song Y., Zhao H., An effective improved co-evolution ant colony optimisation algorithm with multi-strategies and its application, International Journal of Bio-Inspired Computation, 16(3), 158–170, 2020.
  • [45] Kennedy J., Eberhart R.C., Particle swarm optimization. Proceedings of IEEE International Conference on Neural Networks, 4, Perth, Austraila, 1942–1948, 1995.
  • [46] Turan Ö., Oruç R., Baklacıoğlu T., Optimization of an afterburning turbofan engine with multi objective particle swarm method, Journal of the Faculty of Engineering and Architecture of Gazi University 35(4): 1997 – 2012, 2020.
  • [47] Lei H., Lei T., Yuenian T., Sports image detection based on particle swarm optimization algorithm, https://doi.org/10.1016/j.micpro.2020.103345, 2021.
  • [48] Zwikael O., Chih Y., Meredith J.R., Project benefit management: setting effective target benefits, International Journal of Project Management, 36 (4), 650 – 658, 2018.
  • [49] Başar A., A novel methodology for time planning of resource-constrained software projects with hesitant fuzzy durations: A case study. International Journal of Industrial Engineering: Theory, Applications and Practice, 26 (4), 471-485, 2019.
  • [50] Silberholz J., Golden B., Comparison of Metaheuristics. In: Gendreau M., Potvin JY. (eds) Handbook of Metaheuristics. International Series in Operations Research & Management Science, 146. Springer, Boston, U.S.A, 2010.
Toplam 50 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Ayfer Başar 0000-0002-3648-2158

Yayımlanma Tarihi 28 Şubat 2022
Gönderilme Tarihi 12 Nisan 2021
Kabul Tarihi 12 Eylül 2021
Yayımlandığı Sayı Yıl 2022 Cilt: 37 Sayı: 3

Kaynak Göster

APA Başar, A. (2022). Yeni bir matematiksel model ve hibrit meta sezgisel ile kaynak kısıtlı projelerin çizelgelenmesi: Bir vaka çalışması. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, 37(3), 1169-1184. https://doi.org/10.17341/gazimmfd.913666
AMA Başar A. Yeni bir matematiksel model ve hibrit meta sezgisel ile kaynak kısıtlı projelerin çizelgelenmesi: Bir vaka çalışması. GUMMFD. Şubat 2022;37(3):1169-1184. doi:10.17341/gazimmfd.913666
Chicago Başar, Ayfer. “Yeni Bir Matematiksel Model Ve Hibrit Meta Sezgisel Ile Kaynak kısıtlı Projelerin çizelgelenmesi: Bir Vaka çalışması”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 37, sy. 3 (Şubat 2022): 1169-84. https://doi.org/10.17341/gazimmfd.913666.
EndNote Başar A (01 Şubat 2022) Yeni bir matematiksel model ve hibrit meta sezgisel ile kaynak kısıtlı projelerin çizelgelenmesi: Bir vaka çalışması. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 37 3 1169–1184.
IEEE A. Başar, “Yeni bir matematiksel model ve hibrit meta sezgisel ile kaynak kısıtlı projelerin çizelgelenmesi: Bir vaka çalışması”, GUMMFD, c. 37, sy. 3, ss. 1169–1184, 2022, doi: 10.17341/gazimmfd.913666.
ISNAD Başar, Ayfer. “Yeni Bir Matematiksel Model Ve Hibrit Meta Sezgisel Ile Kaynak kısıtlı Projelerin çizelgelenmesi: Bir Vaka çalışması”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi 37/3 (Şubat 2022), 1169-1184. https://doi.org/10.17341/gazimmfd.913666.
JAMA Başar A. Yeni bir matematiksel model ve hibrit meta sezgisel ile kaynak kısıtlı projelerin çizelgelenmesi: Bir vaka çalışması. GUMMFD. 2022;37:1169–1184.
MLA Başar, Ayfer. “Yeni Bir Matematiksel Model Ve Hibrit Meta Sezgisel Ile Kaynak kısıtlı Projelerin çizelgelenmesi: Bir Vaka çalışması”. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, c. 37, sy. 3, 2022, ss. 1169-84, doi:10.17341/gazimmfd.913666.
Vancouver Başar A. Yeni bir matematiksel model ve hibrit meta sezgisel ile kaynak kısıtlı projelerin çizelgelenmesi: Bir vaka çalışması. GUMMFD. 2022;37(3):1169-84.