Abstract
We consider telecommunication network design in which each pair of nodes can communicate via a direct link and the communication flow can be delivered through any path in the network. The cost of flow through each link is discounted if and only if the amount of flow exceeds a certain threshold. This exploitation of economies of scale encourages the concentration of flows and use of relatively small number of links. We will call such networks hub-like networks. The cost of services delivered through a hub-like network is distributed among its users who may be individuals or organizations with possibly conflicting interests. The cooperation of these users is essential for the exploitation of economies of scale. Consequently, there is a need to find a fair distribution of the cost of providing the service among users of such network. In order to describe this cost allocation problem we formulate the associated cooperative game, to be referred to as the hub-like game. Special attention is paid to users' contribution to economies of scale. We then demonstrate that certain cost allocation solutions (the core and the nucleolus of the hub-like game), which provide users with the incentive to cooperate, can be efficiently characterized.
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References
J.F. Campbell, A survey of network hub location, Studies in Locational Analysis 6 (1994) 31–49.
A.T. Ernst and M. Krishnamoorthy, Efficient algorithms for the uncapacited single allocation p–hub median problem, Location Science 4 (1996) 139–154.
D. Granot and F. Granot, On some network flow games, Mathematics of Operations Research 17(4) (1992) 792–841.
D. Granot and M. Hojati, On the cost allocation in telecommunication networks, Networks 20 (1990) 209–229.
D. Granot and G. Huberman, Minimum cost spanning tree games, Mathematical Programming 21 (1981) 1–18.
M.E. O'Kelly, A quadratic integer program for the location of interacting hub facilities, European Journal of Operational Research 32 (1987) 393–404.
M. O'Kelly, D. Skorin–Kapov and J. Skorin–Kapov, Lower bounds for the hub location problem, Management Science 41(4) (1995) 713–728.
J.G. Klincewicz, Hub location in backbone/tributary network design: A review, Location Science 6 (1998) 307–335.
M. Maschler, B. Peleg and L.S. Shapley, Geometric properties of the kernel, nucleolus and related solution concepts, Mathematics of Operations Research 4 (1979) 303–338.
H. Podnar, J. Skorin–Kapov and D. Skorin–Kapov, Network cost minimization using threshold based discounting, Technical Paper, SUNY at Stony Brook, Applied Mathematics and Statistics (October 1999).
J.A.M. Potters, I.J. Curiel and S.H. Tijs, Traveling salesman games, Mathematical Programming 53 (1987) 199–211.
D. Schmeidler, The nucleolus of a characteristic function game, SIAM Journal of Applied Mathematics 17 (1969) 1163–1170.
W.W. Sharkey, Networks models in economics, in: Handbooks in OR & MS, Vol. 8, eds. M.O. Ball et al. (Elsevier, 1995) chapter 9.
D. Skorin–Kapov, On a cost allocation problem arising from a capacitated concentrator covering problem, Operations Research Letters 13(5) (1993) 315–323.
D. Skorin–Kapov, On the core of the minimum Steiner tree game in networks, Annals of Operations Research 57 (1995) 233–249.
D. Skorin–Kapov, Hub network games, Networks 31 (1998) 293–302.
D. Skorin–Kapov and H.F. Beltran, An efficient characterization of cost allocation solutions associated with capacitated network design problems, Telecommunication Systems 3(1) (1994) 91–107.
D. Skorin–Kapov and J. Skorin–Kapov, On tabu search for the location of interacting hub facilities, European Journal of Operational Research 73 (1994) 502–509.
D. Skorin–Kapov, J. Skorin–Kapov and M. O'Kelly, Tight linear programming relaxations of uncapacitated p–hub median problems, European Journal of Operational Research 94 (1996) 582–593.
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Skorin-Kapov, D. On Cost Allocation in Hub-Like Networks. Annals of Operations Research 106, 63–78 (2001). https://doi.org/10.1023/A:1014505607701
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DOI: https://doi.org/10.1023/A:1014505607701