Bergantiños, Gustavo and VidalPuga, Juan (2018): Oneway and twoway cost allocation in hub network problems.
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Abstract
We consider a cost allocation problem arising from a hub network problem design. Finding an optimal hub network is NPhard, so we start with a hub network that could be optimal or not. Our main objective is to divide the cost of such network among the nodes. We consider two cases. In the oneway flow case, we assume that the cost paid by a set of nodes depends only on the flow they send to other nodes (including nodes outside the set), but not on the flow they receive from nodes outside. In the twoway flow case, we assume that the cost paid by a set of nodes depends on the flow they send to other nodes(including nodes outside the set) and also on the flow they receive from nodes outside. In both cases, we study the core and the Shapley value of the corresponding cost game.
Item Type:  MPRA Paper 

Original Title:  Oneway and twoway cost allocation in hub network problems 
Language:  English 
Keywords:  game theory; hub network; cost allocation; core; Shapley value 
Subjects:  C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C71  Cooperative Games 
Item ID:  98228 
Depositing User:  Juan VidalPuga 
Date Deposited:  20 Jan 2020 15:18 
Last Modified:  20 Jan 2020 15:18 
References:  AlcaldeUnzu, J., G ́omezR ́ua, M., and Molis, E. (2015). Sharing the costs of cleaning a river: the upstream responsibility rule.Games and Economic Behavior, 90:134–150. Alumur, S. and Kara, B. Y. (2008). Network hub allocation problems: The state of the art. European Journal of Operational Research, 190:1–21. Alumur, S. A., Nickel, S., Saldanhada Gama, F., and Se ̧cerdin, Y. (2018). Multiperiod hub network design problems with modular capacities. Annals of Operations Research, 246(1):289–312. Azizi, N. (2018). Managing facility disruption in hubandspoke networks:formulations and efficient solution methods.Annals of Operations Research, Forthcoming. Azizi, N., Vidyarthi, N., and Chauhan, S. S. (2018). Modelling and analysis of hubandspoke networks under stochastic demand and congestion.Annals of Operations Research, 264(1):1–40. Bailey, J. (1997). The economics of Internet interconnection agreements. In McKnight, L. and Bailey, J., editors, Internet Economics, pages 115–168. MIT Press, Cambridge, MA. Bergantiños, G. and Kar, A. (2010). On obligation rules for minimum cost spanning tree problems. Games and Economic Behavior, 69:224–237. Bergantiños, G., GómezRúa, M., Llorca, N., Pulido, M., and SánchezSoriano, J. (2014). A new rule for source connection problems. European Journal of Operational Research, 234(3):780–788. Bogomolnaia, A. and Moulin, H. (2010). Sharing the cost of a minimal cost spanning tree: beyond the folk solution. Games and Economic Behavior,69(2):238–248. Bryan, D. and O’Kelly, M. (1999). Hubandspoke networks in air transportation: An analytical review.Journal of Regional Science, 39(2):275–295. Contreras, I., Tanash, M., and Vidyarthi, N. (2017). Exact and heuristic approaches for the cycle hub location problem. Annals of Operations Research, 258(2):655–677. Dutta, B. and Mishra, D. (2012). Minimum cost arborescences.Games andEconomic Behavior, 74(1):120–143. Farahani, R. Z., Hekmatfar, M., Arabani, A. B., and Nikbakhsh, E.(2013). Hub location problems: A review of models, classification, solution techniques, and applications. Computers & Industrial Engineering, 64(4):1096–1109. Gillies, D. (1959). Solutions to general nonzero sum games. In Tucker, A.and Luce, R., editors, Contributions to the theory of games, volume IV of Annals of Mathematics Studies, chapter 3, pages 47–85. Princeton UP, Princeton. Greenfield, D. (2000). Europe’s virtual conundrum. Network Magazine, 15:116–123. Guardiola, L. A., Meca, A., and Puerto, J. (2009). Productioninventory games: A new class of totally balanced combinatorial optimization games. Games and Economic Behavior, 65(1):205–219. Special Issue in Honor of Martin Shubik. Guden, H. (2018). New complexity results for the phub median problem. Annals of Operations Research, Forthcoming. Helme, M. and Magnanti, T. (1989). Designing satellite communication networks by zeroone quadratic programming. Networks, 19:427–450. Jankovic, O., Miskovic, S., Stanimirovic, Z., and Todosijevic, R. (2017). Novel formulations and VNSbased heuristics for single and multiple allocation phub maximal covering problems. Annals of Operations Research, 259(1):191–216. Matsubayashi, N., Umezawa, M., Masuda, Y., and Nishino, H. (2005). A cost allocation problem arising in hubspoke network systems. European Journal of Operational Research, 160:821–838. Moulin, H. (2014). Pricing traffic in a spanning network. Games and Economic Behavior, 86:475–490. Perea, F., Puerto, J., and Fernandez, F. (2009). Modeling cooperation on a class of distribution problems. European Journal of Operational Research,198:726–733. Roni, M. S., Eksioglu, S. D., Cafferty, K. G., and Jacobson, J. J. (2017). A multiobjective, hubandspoke model to design and manage biofuel supply chains. Annals of Operations Research, 249(1): 351–380. Shapley, L. S. (1953). A value for nperson games. In Kuhn, H.K.;Tucker,A., editor, Contributions to the theory of games, volume II of Annals of Mathematics Studies, pages 307–317. Princeton University Press, Princeton NJ. Sim, T., Lowe, T. J., and Thomas, B. W. (2009). The stochastichub center problem with servicelevel constraints. Computers & Operations Research, 36(12):3166–3177. SkorinKapov, D. (1998). Hub network games. Networks, 31:293–302. SkorinKapov, D. (2001). On cost allocation in hublike networks. Annals of Operations Research, 106:63–78. Trudeau, C. (2012). A new stable and more responsible cost sharing solution for mcst problems. Games and Economic Behavior, 75(1): 402–412. Trudeau, C. and VidalPuga, J. (2017). On the set of extreme core allocations for minimal cost spanning tree problems. Journal of Economic Theory, 169:425–452. Yang, T.H. (2009). Stochastic air freight hub location and flight routes planning. Applied Mathematical Modelling, 33(12): 4424–4430. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/98228 
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Oneway and twoway cost allocation in hub network problems. (deposited 05 Jan 2020 05:25)
 Oneway and twoway cost allocation in hub network problems. (deposited 20 Jan 2020 15:18) [Currently Displayed]