یک مدل برنامه ریزی ریاضی احتمالی برای مکان‌یابی هاب‌های مجازی در شبکه حمل و نقل خطوط هوایی تحت یک مدل صف M/M/C/K

شیری پور, صابر

doi:10.22119/jte.2021.274657.2516

یک مدل برنامه ریزی ریاضی احتمالی برای مکان‌یابی هاب‌های مجازی در شبکه حمل و نقل خطوط هوایی تحت یک مدل صف M/M/C/K

نوع مقاله : علمی - پژوهشی

نویسنده

صابر شیری پور

استادیار، دانشکده فنی و مهندسی گرمسار، دانشگاه گرمسار، گرمسار، ایران

10.22119/jte.2021.274657.2516

چکیده

در این مقاله، یک مدل برنامه ریزی ریاضی احتمالی برای مکانیابی هاب های مجازی در یک شبکه حمل و نقل خطوط هوایی در یک محیط پویا و با در نظر گرفتن محدودیت های ظرفیتی هاب های اصلی و مجازی بررسی میشود. هدف، تعیین مکان های بهینه برای استقرار هاب های مجازی از میان مکان های نامزد و طراحی یک شبکه هاب مجازی بهینه برای تخصیص جریان تقاضای بین گره ها به هر هاب در طول افق برنامه ریزی میباشد بطوریکه مجموع هزینه های حمل و نقل در مسیرهای متفاوت و هزینه های مکانیابی هاب های مجازی در طول افق برنامه ریزی کمینه گردد. در اینجا، محدودیت های ظرفیتی با استفاده از یک مدل صف M/M/C/K در مدل اعمال شده اند. همچنین، مقدار تقاضای گره های متقاضی بصورت نامعین و سناریو محور در نظر گرفته شده اند. مساله پیشنهادی به صورت یک مدل برنامه ریزی ریاضی بهینه سازی استوار غیرخطی فرمول بندی و با استفاده از نرم افزار بهینه سازی LINGO حل شده است. اثر بخشی مدل پیشنهادی و حساسیت آن نسبت به پارامترهای مختلف با استفاده از یک مجموعه اطلاعات شناخته شدهCAB بررسی شده است.

کلیدواژه‌ها

20.1001.1.20086598.1401.13.3.13.5

عنوان مقاله [English]

A Probabilistic Mathematical Programming model for Locating Virtual Hubs in Airline Transportation Network under a M/M/C/K Queuing Model

نویسنده [English]

Saber Shiripour

Faculty of Engineering, University of Garmsar, Garmsar, Iran

چکیده [English]

In this study, a probabilistic mathematical programming model for locating virtual hubs in an airline transportation network in a dynamic environment and taking into account the capacity constraints for the original and virtual hubs is considered. The aim is to determine the optimal locations for establishment of the virtual hubs from among the candidate locations and design an optimal virtual hub network for allocation of the demand flow between the nodes to each hub along the planning horizon, so that the sum of transportation costs on different routes and the virtual hub location costs, along the planning horizon is minimized. In here, capacity constraints are applied to the model using an M/M/C/K queue model. Also, the demand at the relevant nodes are considered nondeterministic and scenario-based. The proposed problem is formulated as a nonlinear robust optimization mathematical programming model and solved by the LINGO optimization software. The effectiveness of the proposed model and its sensitivity to various parameters are investigated using a well-known CAB data set.

کلیدواژه‌ها [English]

Dynamic virtual hub location problem
airline transportation network
robust optimization model
scenario-based demand
M/M/C/K queuing model

مراجع

- زاهدی اناکی، امیرحسین، خیرخواه، امیرسامان و جعفری اسکندری، میثم (1399) "یک رویکرد دو هدفه برای مکانیابی پیوسته هاب ها تحت هزینه احداث وابسته به مختصات پیوسته شهری" ، فصلنامه علمی پژوهشی مهندسی حمل و نقل، سال دوازدهم، شماره 2، زمستان 1399، ص 307-329.

- Abbasi-Parizi, S., Aminnayeri, M. and Bashiri, M. (2018) “Robust solution for a minimax regret hub location problem in a fuzzy-stochastic environment”, Journal of Industrial & Management Optimization, Vol. 14, No. 3, pp. 1271.

- Alumur, S. A., Kara, B. Y., and Karasan, O. E. (2009) “The design of single allocation incomplete hub networks”, Transportation Research Part B: Methodological, Vol. 43, No. 10, pp. 936-951.

- Ardalan, Z. and Karimi, S. (2020) “A variable service rate queue model for hub median problem” arXiv preprint arXiv:2002.11908.

- Bashiri, M., Mirzaei, M. and Randall, M. (2013) “Modeling fuzzy capacitated p-hub center problem and a genetic algorithm solution”, Applied Mathematical Modelling, Vol. 37, No. 5, pp. 3513-3525.

- Ben-Tal, A. and Nemirovski, A. (2000) “Robust solutions of linear programming problems contaminated with uncertain data”, Mathematical programming, Vol. 88, No. 3, pp. 411-424.

- Campbell, J. F. (1994) “Integer programming formulations of discrete hub location problems”, European Journal of Operational Research, Vol. 72, No. 2, pp. 387-405.

- Ebery, J. (2001) “Solving large single allocation p-hub problems with two or three hubs”, European Journal of Operational Research, Vol. 128, No. 2, pp. 447-458.

- Ernst, A. T. and Krishnamoorthy, M. (1999) “Solution algorithms for the capacitated single allocation hub location problem”, Annals of operations Research, Vol. 86, pp. 141-159.

- Goldman, A. J. (1969) “Optimal locations for centers in a network”, Transportation Science, Vol. 3, No. 4, pp. 352-360.

- Hasanzadeh, H., Bashiri, M. and Amiri, A. (2018) “A new approach to optimize a hub covering location problem with a queue estimation component using genetic programming”, Soft Computing, Vol. 22, No. 3, pp. 949-961.

- Hou, Y. T., Huo, J. Z. and Chu, F. (2019) “An Integrated Problem of-Hub Location and Revenue Management with Multiple Capacity Levels under Disruptions”, Journal of Advanced Transportation, 2019.

- HUANG, J. and Qingyun, W. A. N. G. (2009) “Robust optimization of hub-and-spoke airline network design based on multi-objective genetic algorithm”, Journal of Transportation Systems Engineering and Information Technology, Vol. 9, No. 3, pp. 86-92.

- Karow, M. J. (2003) “Virtual hubs: An airline schedule recovery concept and model”, (Doctoral dissertation, Massachusetts Institute of Technology).

- Kazemian, I. and Aref, S. (2017) “Hub location under uncertainty: a minimax regret model for the capacitated problem with multiple allocations”, International Journal of Supply Chain and Inventory Management, Vol. 2, No. 1, pp. 1-19.

- Khodemani-Yazdi, M., Tavakkoli-Moghaddam, R., Bashiri, M. and Rahimi, Y. (2019) “Solving a new bi-objective hierarchical hub location problem with an M∕ M∕ c queuing framework”, Engineering Applications of Artificial Intelligence, Vol. 78, pp. 53-70.

- Makui, A., Rostami, M., Jahani, E. and Nikui, A. (2002) “A multi-objective robust optimization model for the capacitated P-hub location problem under uncertainty”, Management Science Letters, Vol. 2, No. 2, pp. 525-534.

- Marianov, V. and Serra, D. (2003) “Location models for airline hubs behaving as M/D/c queues”, Computers & Operations Research, Vol. 30, No. 7, pp. 983-1003.

- Mohammadi, M., Jolai, F. and Rostami, H. (2011) “An M/M/c queue model for hub covering location problem”, Mathematical and Computer Modelling, Vol. 54, No. 11-12, pp. 2623-2638.

- Mohammadi, M., Jula, P. and Tavakkoli-Moghaddam, R. (2019) “Reliable single-allocation hub location problem with disruptions”, Transportation Research Part E: Logistics and Transportation Review, Vol. 123, pp. 90-120.

- Mulvey, J. M., Vanderbei, R. J. and Zenios, S. A. (1995) “Robust optimization of large-scale systems”, Operations research, Vol. 43, No. 2, pp. 264-281.

- Niakan, F., Vahdani, B. and Mohammadi, M. (2015) “A multi-objective optimization model for hub network design under uncertainty: An inexact rough-interval fuzzy approach”, Engineering Optimization, Vol. 47, No. 12, pp. 1670-1688.

- Nickel, S., Schöbel, A. and Sonneborn, T. (2001) “Hub location problems in urban traffic networks”, In Mathematical methods on optimization in transportation systems (pp. 95-107). Springer, Boston, MA.

- Nourzadeh, F., Ebrahimnejad, S., Khalili-Damghani, K. and Hafezalkotob, A. (2020) “Development of a Model for Locating Hubs in a Competitive Environment under Uncertainty: A Robust Optimization Approach”, International Journal of Engineering, Vol. 33, No. 1, pp. 124-133.

- O'kelly, M. E. (1986) “The location of interacting hub facilities” Transportation science, Vol. 20, No. 2, pp. 92-106.

- O'kelly, M. E. (1987) “A quadratic integer program for the location of interacting hub facilities”, European journal of operational research, Vol. 32, No. 3, pp. 393-404.

- O'Kelly, M. E. (1992) “Hub facility location with fixed costs”, Papers in Regional Science, Vol. 71, No. 3, pp. 293-306.

- Pasandideh, S. H. R., Niaki, S. T. A. and Sheikhi, M. (2016) “A bi-objective hub maximal covering location problem considering time-dependent reliability and the second type of coverage”, International Journal of Management Science and Engineering Management, Vol. 11, No. 4, pp. 195-202.

- Rahimi, Y., Tavakkoli-Moghaddam, R., Mohammadi, M. and Sadeghi, M. (2016) “Multi-objective hub network design under uncertainty considering congestion: An M/M/c/K queue system”, Applied Mathematical Modelling, Vol. 40, No. 5-6, pp. 4179-4198.

- Rahmati, R. and Bashiri, M. (2018) “Robust hub location problem with uncertain inter hub flow discount factor”, Proceedings of the International Conference on Industrial Engineering and Operations Management Paris, France, July 26-27.

- Roghanian, E. and Haghdoost, M. (2018) “Mathematical model for P-hub location problem under simultaneous disruption”, Journal of Industrial and Systems Engineering, Vol. 12, No. 1, pp. 83-94.

- Seifbarghy, M., Hemmati, M. and Soltan Karimi, S. (2018) “Hub Covering Location Problem Considering Queuing and Capacity Constraints”, Journal of Optimization in Industrial Engineering, Vol. 11, No. 1, pp. 143-156.

- Skorin-Kapov, D., Skorin-Kapov, J. and O'Kelly, M. (1997) “Tight linear programming relaxation of uncapacitated p-hub median problems”, Location Science, Vol, 1, No. 5, pp. 68-69.

- Soyster, A. L. (1973) “Convex programming with set-inclusive constraints and applications to inexact linear programming”, Operations research, Vol. 21, No. 5, pp. 1154-1157.

- Taghipourian, F., Mahdavi, I., Mahdavi-Amiri, N. and Makui, A. (2012) “A fuzzy programming approach for dynamic virtual hub location problem”, Applied Mathematical Modelling, Vol. 36, No. 7, pp. 3257-3270.

- Vahdani, B., Behzadi, S. S., Mousavi, S. M. and Shahriari, M. R. (2016) “A dynamic virtual air hub location problem with balancing requirements via robust optimization: Mathematical modeling and solution methods”, Journal of Intelligent & Fuzzy Systems, Vol. 31, No. 3, pp. 1521-1534.

- Vasconcelos, A. D., Nassi, C. D. and Lopes, L. A. (2011) “The uncapacitated hub location problem in networks under decentralized management”, Computers & Operations Research, Vol. 38, No. 12, pp. 1656-1666.