Robust sustainable multi-period hub location considering uncertain time-dependent demand

Khaleghi, Amir; Eydi, Alireza

doi:10.1051/ro/2021155

Khaleghi, Amir ; Eydi, Alireza

RAIRO. Operations Research, Tome 55 (2021) no. 6, pp. 3541-3574

Résumé

This paper presents a mathematical programming model for designing a sustainable continuous-time multi-period hub network considering time-dependent demand. The present model can be used in situations where the distribution of parameters related to the demand function is unknown, and we only can determine the range of changes of these parameters. To model these conditions, we consider interval uncertainty for the demand function parameters. The proposed model is a nonlinear multi-objective model. The objectives of the model cover economic, environmental, and social aspects of sustainability. These objectives include minimizing total costs, minimizing emissions, and maximizing fixed and variable job opportunities. We linearize the model by using some linearization techniques, and then, with the help of Bertsimas and Sim’s method, we construct a robust counterpart of the model. We also present some valid inequalities to strengthen the formulation. To solve the proposed model, we use Torabi and Hassini method. From solving the proposed model, network design decisions and the best time to implement decisions during the planning horizon are determined. To validate the model, we solve a sample problem based on the Turkish dataset and compare the designed network in two cases: in the first case, the demand function parameters take nominal values, and in the second case, the value of these parameters can change up to 20% of their nominal values. The results show that in the second case, the total capacity selected for hubs and hub links is greater than the first case. To investigate changes in objective functions to parameters level of conservatism and probability of constraints violation, we perform sensitivity analysis on these parameters in both single-objective and multi-objective optimization cases and report the results.

MR

DOI : 10.1051/ro/2021155

Classification : 90B06
Keywords: Transportation, multi-period hub location, time-dependent demand, sustainability, robust optimization

@article{RO_2021__55_6_3541_0,
     author = {Khaleghi, Amir and Eydi, Alireza},
     title = {Robust sustainable multi-period hub location considering uncertain time-dependent demand},
     journal = {RAIRO. Operations Research},
     pages = {3541--3574},
     year = {2021},
     publisher = {EDP-Sciences},
     volume = {55},
     number = {6},
     doi = {10.1051/ro/2021155},
     mrnumber = {4344866},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ro/2021155/}
}

TY  - JOUR
AU  - Khaleghi, Amir
AU  - Eydi, Alireza
TI  - Robust sustainable multi-period hub location considering uncertain time-dependent demand
JO  - RAIRO. Operations Research
PY  - 2021
SP  - 3541
EP  - 3574
VL  - 55
IS  - 6
PB  - EDP-Sciences
UR  - https://www.numdam.org/articles/10.1051/ro/2021155/
DO  - 10.1051/ro/2021155
LA  - en
ID  - RO_2021__55_6_3541_0
ER  -

%0 Journal Article
%A Khaleghi, Amir
%A Eydi, Alireza
%T Robust sustainable multi-period hub location considering uncertain time-dependent demand
%J RAIRO. Operations Research
%D 2021
%P 3541-3574
%V 55
%N 6
%I EDP-Sciences
%U https://www.numdam.org/articles/10.1051/ro/2021155/
%R 10.1051/ro/2021155
%G en
%F RO_2021__55_6_3541_0

Khaleghi, Amir; Eydi, Alireza. Robust sustainable multi-period hub location considering uncertain time-dependent demand. RAIRO. Operations Research, Tome 55 (2021) no. 6, pp. 3541-3574. doi: 10.1051/ro/2021155

Bibliographie
Cité par

[1] S. Alumur and B. Y. Kara, Network hub location problems: the state of the art. Eur. J. Oper. Res. 190 (2008) 1–21. | MR | Zbl | DOI

[2] S. A. Alumur, S. Nickel and F. Saldanha-Da-Gama, Hub location under uncertainty. Transp. Res. Part B Methodol. 46 (2012) 529–543. | DOI

[3] S. A. Alumur, H. Yaman and B. Y. Kara, Hierarchical multimodal hub location problem with time-definite deliveries. Transp. Res. Part E Logist. Transp. Rev. 48 (2012) 1107–1120. | DOI

[4] S. A. Alumur, S. Nickel, F. Saldanha-Da-Gama and Y. Seçerdin, Multi-period hub network design problems with modular capacities. Ann. Oper. Res. 246 (2016) 289–312. | MR | DOI

[5] A. B. Arabani and R. Z. Farahani, Facility location dynamics: an overview of classifications and applications. Comput. Ind. Eng. 62 (2012) 408–420. | DOI

[6] T. Aykin, Lagrangian relaxation based approaches to capacitated hub-and-spoke network design problem. Eur. J. Oper. Res. 79 (1994) 501–523. | Zbl | DOI

[7] T. Aykin, Networking policies for hub-and-spoke systems with application to the air transportation system. Transp. Sci. 29 (1995) 201–221. | Zbl | DOI

[8] M. Barth and K. Boriboonsomsin, Energy and emissions impacts of a freeway-based dynamic eco-driving system. Transp. Res. Part D Transp. Environ. 14 (2009) 400–410. | DOI

[9] M. Barth, T. Younglove and G. Scora, Development of a Heavy-duty Diesel Modal Emissions and Fuel Consumption Model. Calif. Partners Adv. Transit Highw., Institute of Transportation Studies. University of California at Berkeley (2005).

[10] M. Bashiri, M. Rezanezhad and R. Tavakkoli-Moghaddam, H. Hasanzadeh, Mathematical modeling for a $p$ -mobile hub location problem in a dynamic environment by a genetic algorithm. Appl. Math. Model. 54 (2018) 151–169. | MR | DOI

[11] J. E. Beasley, OR-library: hub location http//people.brunel.ac.uk/mastjjb/jeb/orlib/phubinfo.html (Accessed 01.05. 15) (1990).

[12] T. Bektaş and G. Laporte, The pollution-routing problem. Transp. Res. Part B Methodol. 45 (2011) 1232–1250. | DOI

[13] D. Bertsimas and M. Sim, Robust discrete optimization and network flows 1 introduction. Oper. Res. 71 (2002) 1–26.

[14] D. Bertsimas and M. Sim, Robust discrete optimization and network flows. Math. Program. 98 (2003) 49–71. | MR | Zbl | DOI

[15] F. H. Boukani, B. F. Moghaddam and M. S. Pishvaee, Robust optimization approach to capacitated single and multiple allocation hub location problems. Comput. Appl. Math. 35 (2016) 45–60. | MR | DOI

[16] J. F. Campbell, Locating transportation terminals to serve an expanding demand. Transp. Res. Part B Methodol. 24 (1990) 173–192. | DOI

[17] J. F. Campbell, Integer programming formulations of discrete hub location problems. Eur. J. Oper. Res. 72 (1994) 387–405. | Zbl | DOI

[18] J. F. Campbell, Hub location and the $p$ -hub median problem. Oper. Res. 44 (1996) 923–935. | MR | Zbl | DOI

[19] J. F. Campbell and M. E. O’Kelly, Twenty-five years of hub location research. Transp. Sci. 46 (2012) 153–169. | DOI

[20] M. Campbell, J. Ernst and A. Krishnamoorthy, Hub location problems. In: Facility Location: Application and Theory. Springer, Berlin (2002). | MR | Zbl | DOI

[21] I. Contreras, J.-F. Cordeau and G. Laporte, The dynamic uncapacitated hub location problem. Transp. Sci. 45 (2011) 18–32. | DOI

[22] I. Correia, S. Nickel and F. Saldanha-Da-Gama, A stochastic multi-period capacitated multiple allocation hub location problem: formulation and inequalities. Omega 74 (2018) 122–134. | DOI

[23] E. M. De Sá, R. Morabito and R. S. De Camargo, Benders decomposition applied to a robust multiple allocation incomplete hub location problem. Comput. Oper. Res. 89 (2018) 31–50. | MR | DOI

[24] Z. Drezner and G. O. Wesolowsky, Facility location when demand is time dependent. Nav. Res. Logist. 38 (1991) 763–777. | MR | Zbl | DOI

[25] O. Dukkanci, M. Peker and B. Y. Kara, Green hub location problem. Transp. Res. Part E Logist. Transp. Rev. 125 (2019) 116–139. | DOI

[26] A. Ebrahimi-Zade, H. Hosseini-Nasab and ;A. Zahmatkesh, Multi-period hub set covering problems with flexible radius: a modified genetic solution. Appl. Math. Model. 40 (2016) 2968–2982. | DOI

[27] R. Z. Farahani, Z. Drezner and N. Asgari, Single facility location and relocation problem with time dependent weights and discrete planning horizon. Ann. Oper. Res. 167 (2009) 353–368. | MR | Zbl | DOI

[28] R. Z. Farahani, M. Hekmatfar, A. B. Arabani and E. Nikbakhsh, Hub location problems: a review of models, classification, solution techniques, and applications. Comput. Ind. Eng. 64 (2013) 1096–1109. | DOI

[29] P. Fattahi and Z. Shakeri Kebria, A bi objective dynamic reliable hub location problem with congestion effects. Int. J. Ind. Eng. Prod. Res. 31 (2020) 63–74.

[30] F. Fotuhi and N. Huynh, A reliable multi-period intermodal freight network expansion problem. Comput. Ind. Eng. 115 (2018) 138–150. | DOI

[31] S. Gelareh, Hub location models in public transport planning. Ph.D. disseration. Universitätsbibliothek (2008).

[32] S. Gelareh, R. N. Monemi and S. Nickel, Multi-period hub location problems in transportation. Transp. Res. Part E Logist. Transp. Rev. 75 (2015) 67–94. | DOI

[33] N. Ghaffari-Nasab, M. Ghazanfari and E. Teimoury, Robust optimization approach to the design of hub-and-spoke networks. Int. J. Adv. Manuf. Technol. 76 (2015) 1091–1110. | DOI

[34] A. Ghodratnama, R. Tavakkoli-Moghaddam and A. Azaron, A fuzzy possibilistic bi-objective hub covering problem considering production facilities, time horizons and transporter vehicles. Int. J. Adv. Manuf. Technol. 66 (2013) 187–206. | DOI

[35] S. L. Hakimi, Optimum locations of switching centers and the absolute centers and medians of a graph. Oper. Res. 12 (1964) 450–459. | Zbl | DOI

[36] E. Holden, K. Linnerud and D. Banister, Sustainable development: our common future revisited. Glob. Environ. Chang. 26 (2014) 130–139. | DOI

[37] E. S. Jafar Bagherinejad, M. Bashiri and Z. Abedpour, Dynamic single allocation hub location problem considering life cycle and reconstruction hubs. Prod. Oper. Manag. 11 (2020) 71–87.

[38] B. Y. Kara and M. R. Taner, Hub location problems: the location of interacting facilities. In: Foundations of Location Analysis. Springer (2011) 273–288. | DOI

[39] Y. Khosravian, A. Shahandeh Nookabadi and G. Moslehi, Mathematical model for bi-objective maximal hub covering problem with periodic variations of parameters. Int. J. Eng. 32 (2019) 964–975.

[40] J. G. Klincewicz, Heuristics for the $p$ -hub location problem. Eur. J. Oper. Res. 53 (1991) 25–37. | Zbl | DOI

[41] J. G. Klincewicz, Avoiding local optima in the $p$ -hub location problem using tabu search and GRASP. Ann. Oper. Res. 40 (1992) 283–302. | MR | Zbl | DOI

[42] A. Lozkins, M. Krasilnikov and V. Bure, Robust uncapacitated multiple allocation hub location problem under demand uncertainty: minimization of cost deviations. J. Ind. Eng. Int. 15 (2019) 199–207. | DOI

[43] A. Makui, M. Rostami, E. Jahani and A. Nikui, A multi-objective robust optimization model for the capacitated P-hub location problem under uncertainty. Manag. Sci. Lett. 2 (2002) 525–534. | DOI

[44] M. Merakl and H. Yaman, Robust intermodal hub location under polyhedral demand uncertainty. Transp. Res. Part B Methodol. 86 (2016) 66–85. | DOI

[45] M. Merakl and H. Yaman, A capacitated hub location problem under hose demand uncertainty. Comput. Oper. Res. 88 (2017) 58–70. | MR | DOI

[46] M. Mohammadi, R. Tavakkoli-Moghaddam and R. Rostami, A multi-objective imperialist competitive algorithm for a capacitated hub covering location problem. Int. J. Ind. Eng. Comput. 2 (2011) 671–688.

[47] M. Mohammadi, F. Jolai and R. Tavakkoli-Moghaddam, Solving a new stochastic multi-mode $p$ -hub covering location problem considering risk by a novel multi-objective algorithm. Appl. Math. Model. 37 (2013) 10053–10073. | MR | DOI

[48] M. Mohammadi, S. A. Torabi and R. Tavakkoli-Moghaddam, Sustainable hub location under mixed uncertainty. Transp. Res. Part E Logist. Transp. Rev. 62 (2014) 89–115. | DOI

[49] F. Niakan, B. Vahdani and M. Mohammadi, A multi-objective optimization model for hub network design under uncertainty: an inexact rough-interval fuzzy approach. Eng. Optim. 47 (2015) 1670–1688. | MR | DOI

[50] S. Nickel and F. Saldanha-Da-Gama, Multi-period facility location. In: Location Science. Springer (2019) 303–326. | MR | DOI

[51] M. E. O’Kelly, A quadratic integer program for the location of interacting hub facilities. Eur. J. Oper. Res. 32 (1987) 393–404. | MR | Zbl | DOI

[52] M. E. O’Kelly, Hub facility location with fixed costs. Pap. Reg. Sci. 71 (1992) 293–306. | DOI

[53] Y. Rahimi, R. Tavakkoli-Moghaddam, M. Mohammadi and M. Sadeghi, Multi-objective hub network design under uncertainty considering congestion: an $M / M / c / K$ queue system. Appl. Math. Model. 40 (2016) 4179–4198. | MR | Zbl | DOI

[54] J. Razmi and R. Tavakkoli-Moghaddam, Multi-objective invasive weed optimization for stochastic green hub location routing problem with simultaneous pick-ups and deliveries. Econ. Comput. Econ. Cybern. Stud. Res. 47 (2013) 247–266.

[55] S. Sedehzadeh, R. Tavakkoli-Moghaddam, M. Mohammadi and F. Jolai, Solving a new priority M/M/C Queue model for a multi-mode hub covering location problem by multi-objective parallel simulated annealing. Econ. Comput. Econ. Cybern. Stud. Res. 48 (2014) 299–318.

[56] M. Shahabi and A. Unnikrishnan, Robust hub network design problem. Transp. Res. Part E Logist. Transp. Rev. 70 (2014) 356–373. | DOI

[57] H. D. Sherali, On mixed-integer zero-one representations for separable lower-semicontinuous piecewise-linear functions. Oper. Res. Lett. 28 (2001) 155–160. | MR | Zbl | DOI

[58] F. Taghipourian, I. Mahdavi, N. Mahdavi-Amiri and A. Makui, A fuzzy programming approach for dynamic virtual hub location problem. Appl. Math. Model. 36 (2012) 3257–3270. | MR | Zbl | DOI

[59] E.-G. Talbi and R. Todosijević, The robust uncapacitated multiple allocation p-hub median problem. Comput. Ind. Eng. 110 (2017) 322–332. | DOI

[60] R. S. Toh and R. G. Higgins, The impact of hub and spoke network centralization and route monopoly on domestic airline profitability. Transp. J. 24 (1985) 16–27.

[61] S. A. Torabi and E. Hassini, An interactive possibilistic programming approach for multiple objective supply chain master planning. Fuzzy Sets Syst. 159 (2008) 193–214. | MR | Zbl | DOI

[62] S. S. Torkestani, S. M. Seyedhosseini, A. Makui and K. Shahanaghi, The reliable design of a hierarchical multi-modes transportation hub location problems (HMMTHLP) under dynamic network disruption (DND). Comput. Ind. Eng. 122 (2018) 39–86. | DOI

[63] F. Yin, Y. Chen, F. Song and Y. Liu, A new distributionally robust $p$ -hub median problem with uncertain carbon emissions and its tractable approximation method. Appl. Math. Model. 74 (2019) 668–693. | MR | Zbl | DOI

[64] R. Zanjirani Farahani, W. Y. Szeto and S. Ghadimi, The single facility location problem with time-dependent weights and relocation cost over a continuous time horizon. J. Oper. Res. Soc. 66 (2015) 265–277. | DOI

[65] C. A. Zetina, I. Contreras, J.-F. Cordeau and E. Nikbakhsh, Robust uncapacitated hub location. Transp. Res. Part B Methodol. 106 (2017) 393–410. | DOI

[66] M. Zhalechian, R. Tavakkoli-Moghaddam, Y. Rahimi and F. Jolai, An interactive possibilistic programming approach for a multi-objective hub location problem: economic and environmental design. Appl. Soft Comput. 52 (2017) 699–713. | DOI

[67] M. Zhalechian, R. Tavakkoli-Moghaddam and Y. Rahimi, A self-adaptive evolutionary algorithm for a fuzzy multi-objective hub location problem: an integration of responsiveness and social responsibility. Eng. Appl. Artif. Intell. 62 (2017) 1–16. | DOI

Cité par Sources :