مدل سازی ریاضی دوسطحی مساله مکان‌یابی و استحکام‌سازی تسهیلات سلسله مراتبی با محدودیت ظرفیت و بودجه تحت شرایط تخریب و حل آن با الگوریتم ژنتیک

نوع مقاله : مقاله پژوهشی

نویسنده

استادیار گروه ریاضی و آمار، دانشکده علوم پایه و فنی مهندسی، دانشگاه گنبد کاووس، گلستان، ایران

چکیده

DOR : 20.1001.1.24766291.1399.5.3.3.8
اهمیت مکان یابی و استحکام سازی تسهیلات سلسله مراتبی در شرایط عملیات خرابکارانه، بسیاری از محققین را به اتخاذ تصمیمات مناسب ترغیب نموده است. در این مقاله، یک مدل برنامه ریزی دوسطحی معرفی شده که با در نظرگرفتن عملیات ممانعتی و از کارافتادگی تسهیلات سلسله مراتبی در دو سطح، استراتژی های مناسب جهت مکان‌یابی و استحکام سازی آنها انتخاب می نماید. با توجه به منابع مکان‌یابی موجود، تقاضای خدمات و بدترین سناریوی خرابی تسهیلات در هر دوسطح، تصمیمات تخصیص، مکان‌یابی و استحکام سازی تسهیلات موجود تعیین می شوند. برای نزدیکی بیشتر به واقعیت سیستم سلسله مراتبی از مفاهیم ظرفیت و بودجه استفاده شده‌است. هدف مدل کمینه سازی هزینه مکان یابی و فاصله خدمات رسانی بین نقاط تقاضا و تسهیلات در هر دو سطح است. در ادامه، چند نمونه عددی از مساله ارایه و با رویکردهای ترکیبی دوسطحی مبتنی بر الگوریتم‌های فراابتکاری ژنتیک و کوچ پرندگان برای مساله سطح اول و روش دقیق برای مساله سطح دوم ‎حل شده است.

کلیدواژه‌ها


عنوان مقاله [English]

Bi-level mathematical modeling of the location and fortification problem of hierarchical facilities with capacity and budget constraints under destruction conditions and solving it with genetic algorithm

نویسنده [English]

  • Raheleh Khanduzi
Assistant Professor-Department of Mathematics and Statistics-Applied Mathematics - Operations Research (Optimization)-Gonbad Kavous University
چکیده [English]

The importance of locating and fortifying hierarchical facilities in the face of sabotage operations has encouraged many researchers to make appropriate decisions. In this paper, a bi-level programming model has been introduced, which, considering the interdiction operations and failure of hierarchical facilities at two levels, selects appropriate strategies to locate and fortify them. Depending on available location resources, service demand, and the worst-case scenario of facility failure at both levels, the decisions as to the allocation, location, and fortification of existing facilities are determined. The concepts of capacity and budget have been used to bring the hierarchical system closer to reality. The model aims at minimizing the location cost as well as service distance between demand points and facilities at both levels. In the following, a number of numerical examples of the problem have been presented and solved with two-level combined approaches based on genetic and particle swarm algorithms for the first level and the exact method for the second level problem.

کلیدواژه‌ها [English]

  • Hierarchical network
  • Bi-level model
  • Fortification
  • Interdiction
  • Genetic algorithm
[1]    Church, R. L., Scaparra, M. P., & Middleton, R. S. (2004). Identifying critical infrastructure: the median and covering facility interdiction problems. Annals of the Association of American Geographers, 94(3), 491–502.
[2]    Narula, S. C. (1986). Minisum hierarchical location-allocation problems on a network: A survey. Annals of Operations Research, 6(8), 255-272.
[3]    Marianov, V., & Serra, D. (2001). Hierarchical location–allocation models for congested systems. European Journal of Operational Research, 135(1), 195-208.
[4]    Şahin, G., &Süral, H. (2007). A review of hierarchical facility location models. Computers & Operations Research, 34(8), 2310-2331.
[5]    Teixeira, J. C., &Antunes, A. P. (2008). A hierarchical location model for public facility planning. European Journal of Operational Research, 185(1), 92-104.
[6]    Ratick, S. J., Osleeb, J. P., &Hozumi, D. (2009). Application and extension of the Moore and ReVelle hierarchical maximal covering model. Socio-Economic Planning Sciences, 43(2), 92-101.
[7]    Şahin, G., Süral, H., &Meral, S. (2007). Locational analysis for regionalization of Turkish Red Crescent blood services. Computers & Operations Research, 34(3), 692-704.
[8]    Barros, A. I., Dekker, R., &Scholten, V. (1998). A two-level network for recycling sand: a case study. European journal of operational research, 110(2), 199-214.
[9]    Van Roy, T. J. (1989). Multi-level production and distribution planning with transportation fleet optimization. Management Science, 35(12), 1443-1453.
[10] Moore, G. C., &ReVelle, C. (1982). The hierarchical service location problem. Management science, 28(7), 775-780.
[11] Kim, J. G., &Tcha, D. W. (1992). Optimal design of a two-level hierarchical network with tree-star configuration. Computers & industrial engineering, 22(3), 273-281.
[12] Farahani, R. Z., Hassani, A., Mousavi, S. M., &Baygi, M. B. (2014). A hybrid artificial bee colony for disruption in a hierarchical maximal covering location problem. Computers & Industrial Engineering, 75, 129-141.
[13] Zarrinpoor, N., Fallahnezhad, M. S., &Pishvaee, M. S. (2017). Design of a reliable hierarchical location-allocation model under disruptions for health service networks: A two-stage robust approach. Computers & Industrial Engineering, 109, 130-150.
[14] Miyagawa, M. (2019). Optimal Number of Hierarchical Facilities with Failures. Geographical Analysis.
[15] Aliakbarian, N., Dehghanian, F., & Salari, M. (2015). A bi-level programming model for protection of hierarchical facilities under imminent attacks. Computers & operations research, 64, 210–224.
[16] Akbari-Jafarabadi, M., Tavakkoli-Moghaddam, R., Mahmoodjanloo, M., & Rahimi, Y. (2015). A three-level mathematical model for an r-interdiction hierarchical facilities location problem. Iranian Journal of Operations Research, 6(2), 58–72.
[17] Forghani, A., Dehghanian, F., Salari, M., & Ghiami, Y. (2020). A bi-level model and solution methods for partial interdiction problem on capacitated hierarchical facilities. Computers & Operations Research, 114, 104831.
[18] Forghani, A., &Dehghanian, F. (2014). An interdiction median model for hierarchical capacitated facilities. International Journal of Research In Industrial Engineering, 3(1), 1-10.
[19] Forghani, A., & Dehghanian, F. (2014). Interdiction problem as a tool to identify an effective budget allocation to quality improvement plans. Iranian Journal of Operations Research, 5(1), 52–66.
[20] Amiri, M., TaghaviFard, M. T., &Aghaei, M. (2016). Development of Three-Objective Model for the Location–Allocation of Assistance Centers in a probabilistic Condition of availability to emergency Vehicles. Modern Researches in Decision Making (Scientific Research Quarterly), 1(2), 1-27.
[21] Kazemi, A., & Sarvandi, F (2018). Mathematical Modeling of Resource-Constrained Project Scheduling Problem and Solving It by Using Metaheuristic Algorithms. Modern Researches in Decision Making (Scientific Research Quarterly), 3(4), 28-50.
[22] Olfat, L (2017).Total Tardiness Minimization in Flow Shop with Intermediate Due Dates. Modern Researches in Decision Making (Scientific Research Quarterly), 2(3), 25-47.
[23] Notash, M., Zandieh, M., &Dorri Nokorani, B. (2015). Using a Genetic Algorithm Approach for Designing Multi-objective Supply Chain Network. IQBQ.18 (4):183-203
[24] Taghavifard, S. M. T., Dehghani, M. H, & Aghaei, M. (2015). The Model for Lot Sizing Problem with Supplier Selection and Solving by NSGA-II (Case Study: Morvarid Panberiz Company). IQBQ.19 (2):65-89
[25] Holland, J. H. (1992). Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. MIT press.
[26] Kennedy, J., &Eberhart, R. (1995, November). Particle swarm optimization. In Proceedings of ICNN'95-International Conference on Neural Networks (Vol. 4, pp. 1942-1948). IEEE.