Mathematical Model for Bi-objective Maximal Hub Covering Problem with Periodic Variations of Parameters

Document Type : Original Article

Authors

Department of Industrial and Systems Engineering, Isfahan University of Technology, Isfahan, Iran

Abstract

The problem of maximal hub covering as a challenging problem in operation research. Transportation programming seeks to find an optimal location of a set of hubs to reach maximum flow in a network. Since the main structure's parameters of the problem such as origin-destination flows, costs and travel time, change periodically in the real world applications, new issues arise in handling it. In this paper, to deal with the periodic variations of parameters, a bi-objective mathematical model is proposed for the single allocation multi-period maximal hub covering problem. The ε-constraint approach has been applied to achieve non-dominated solutions. Given that the single-objective problem found in the ε-constraint method is computationally intractable. Benders decomposition algorithm by adding valid inequalities is developed to accelerate the solution process. Finally, the proposed method is carried out by CAB data set, and the results confirm the efficiency of it regarding optimality and running time.

Keywords

Main Subjects


1. Cont reras, I., Hub location problems, in Locat ion science, G.
Laporte, S. Nickel, and F. Saldanha da Gama, Edit ors. 2015,
Springer Int ernat ional Publishing: Cham. 311-344.
2. Campbell, J.F., "Integer programming formulations of discret e
hub locat ion problems", European Journal of Operational
Research,  Vol. 72, No. 2, (1994), 387-405.
3. Karimi, H. and Bashiri, M., "Hub covering locat ion problems
wit h different coverage t ypes", Scientia Iranica,  Vol. 18, No.
6, (2011), 1571-1578.
4. Hwang, Y.H. and Lee, Y.H., "Uncapacitat ed single allocat ion
p-hub maximal covering problem", Computers & Industrial
Engineering,  Vol. 63, No. 2, (2012), 382-389.
5. Jabalameli, M.S., Barzinpour, F., Saboury, A. and GhaffariNasab,

N., "A simulat ed annealing-based heurist ic for t he
single allocat ion maximal covering hub locat ion problem",
International Journal of Metaheuristics,  Vol. 2, No. 1,
(2012), 15-37.
6. Ebrahimi-zade, A., Sadegheih, A. and Lot fi, M.M., "A
modified nsga-ii solut ion for a new mult i-object ive hub
maximal covering problem under uncert ain shipment s",
Journal of Industrial Engineering International,  Vol. 10,
No. 4, (2014), 185-197.
7. Pasandideh, S.H.R., Niaki, S.T.A. and Sheikhi, M., "A biobject
ive hub maximal covering location problem considering
t ime-dependent reliability and t he second t ype of coverage",
International Journal of Management Science and
Engineering Management,  Vol. 11, No. 4, (2015), 195-202.
8. Bashiri, M. and Rezanezhad, M., "A reliable multi-objective phub

covering locat ion problem considering of hubs
capabilit ies", International Journal of EngineeringTransactions
B:
Applications,

Vol.
28,
No.
5,
(2015),
717-
729.
9. Karimi, H., Bashiri, M. and Nickel, S., "Capacit at ed single
allocat ion p-hub covering problem in mult i-modal net work
using t abu search", International Journal of EngineeringTransactions
C:
Aspects,

Vol.
29,
No.
6,
(2016),
797-808.

10. Ebrahimi-zade, A., Sadegheih, A. and Lot fi, M.M., "Fuzzy
mult i-object ive linear programming for a st ochast ic hub
maximal covering problem wit h uncert ain shipment s",
International Journal of Industrial and Systems Engineering,
Vol. 23, No. 4, (2016), 482-499.
11. Janković, O. and St animirović, Z., "A general variable
neighborhood search for solving t he uncapacitated r-allocat ion
p-hub maximal covering problem", Electronic Notes in
Discrete Mathematics,  Vol. 58, (2017), 23-30.
12. Janković, O., Mišković, S., St animirović, Z. and Todosijević,
R., "Novel formulations and vns-based heuristics for single and
mult iple allocation p-hub maximal covering problems", Annals
of Operations Research,  Vol. 259, No. 1-2, (2017), 191-216. 13. Madani, S.R., Shahandeh Nookabadi, A. and Hejazi, S.R., "A
bi-object ive, reliable single allocation p-hub maximal covering
locat ion problem: Mat hemat ical formulat ion and solut ion
approach", Journal of Air Transport Management,  Vol. 68,
(2018), 118-136.
14. Gelareh, S., "Hub locat ion models in public t ransport at ion
planning", Kaiserslaut ern Universit y of Technology, Ph.D,
Thesis  (2008),  
15. Ebrahimi-zade, A., Hosseini-Nasab, H., zare-mehrjerdi, Y. and
Zahmat kesh, A., "Multi-period hub set  covering problems wit h
flexible radius: A modified genet ic solut ion", Applied
Mathematical Modelling,  Vol. 40, No. 4, (2016), 2968-2982.
16. Campbell, J.F. and O'Kelly, M.E., "Twent y-five years of hub
locat ion research", Transportation Science,  Vol. 46, No. 2,
(2012), 153-169.
17. Balaman, Ş.Y., Mat opoulos, A., Wright , D.G. and Scot t , J.,
"Int egrat ed opt imizat ion of sust ainable supply chains and
t ransport at ion net works for mult i t echnology bio-based
product ion: A decision support  syst em based on fuzzy ε-
const raint method", Journal of Cleaner Production,  Vol. 172,
(2018), 2594-2617.
18. Yu, H. and Solvang, W.D., "An improved mult i-object ive
programming wit h augment ed ε-const raint  met hod for
hazardous wast e locat ion-rout ing problems", International
Journal of Environmental Research and Public Health,  Vol.
13, No. 6, (2016), DOI: 10.3390/ijerph13060548.
19. Emami, S., Moslehi, G. and Sabbagh, M., "A benders
decomposition approach for order accept ance and scheduling
problem: A robust  optimization approach", Computational and
Applied Mathematics,  Vol. 36, No. 4, (2017), 1471-1515.
20. Saharidis , K.D., Minoux , M. and Ierapet rit ou , G.,
"Accelerat ing benders met hod using covering cut  bundle
generat ion", International Transactions in Operational
Research,  Vol. 17, No. 2, (2010), 221-237.
21. O'Kelly, M.E., "A quadrat ic integer program for t he location of
int eracting hub facilit ies", European Journal of Operational
Research,  Vol. 32, No. 3, (1987), 393-404.
22. Alumur, S.A., Nickel, S., Saldanha-da-Gama, F. and Seçerdin,
Y., "Mult i-period hub net work design problems wit h modular
capacit ies", Annals of Operations Research,  Vol. 246, No. 1,
(2016), 289-312.
23. Gelareh, S., Neamat ian Monemi, R. and Nickel, S., "Mult i-
period hub locat ion problems in t ransport at ion",
Transportation Research Part E: Logistics and
Transportation Review,  Vol. 75, (2015), 67-94.
24. Silva, M.R. and Cunha, C.B., "A t abu search heurist ic for t he
uncapacit at ed single allocat ion p-hub maximal covering
problem", European Journal of Operational Research,  Vol.
262, No. 3, (2017), 954-965.