Abstract
The class of Construct and Charge (CC-) rules for minimum cost spanning tree (mcst) situations is considered. CC-rules are defined starting from the notion of charge systems, which specify particular allocation protocols rooted on the Kruskal algorithm for computing an mcst. These protocols can be easily implemented in practical network situations (for instance, in supply transportation networks), are flexible to changes in the network situation and meet the requirement of continuous monitoring by the agents involved. Special charge systems, that we call conservative, lead to a subclass of CC-rules that coincides with the class of obligation rules for mcst situations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bird CG (1976) On cost allocation for a spanning tree: a game theoretic approach. Networks 6: 335–350
Branzei R, Moretti S, Norde H, Tijs S (2004) The P-value for cost sharing in minimum cost spanning tree situations. Theory and Decis 56: 47–61
Dutta B, Kar A (2004) Cost monotonicity, consistency and minimum cost spanning tree games. Games Econ Behav 48: 223–248
Feltkamp V, Tijs S, Muto S (1994a) Minimum cost spanning extension problems: the proportional rule and the decentralized rule. CentER DP 1994 nr.96, Tilburg University, The Netherlands
Feltkamp V, Tijs S, Muto S (1994b) On the irreducible core and the equal remaining obligations rule of minimum cost spanning extension problems. CentER DP 1994 nr.106, Tilburg University, The Netherlands
Kruskal JB (1956) On the shortest spanning subtree of a graph and the traveling salesman problem. Proc Am Math Soc 7: 48–50
Norde H, Moretti S, Tijs S (2004) Minimum cost spanning tree games and population monotonic allocation schemes. Eur J Oper Res 154: 84–97
Prim RC (1957) Shortest connection networks and some generalizations. Bell Syst Tech J 36: 1389–1401
Sharkey WW (1995) Network models in economics. In: Ball MO, Magnanti TL, Monma CL, Nemhauser GL(eds) Network routing. North-Holland, Amsterdam, pp 713–765
Tijs S, Branzei R, Moretti S, Norde H (2006a) Obligation rules for minimum cost spanning tree situations and their monotonicity properties. Eur J Oper Res 175: 121–
Tijs S, Moretti S, Branzei R, Norde H (2006b) The Bird core for minimum cost spanning tree problems revisited: monotonicity and additivity aspects. In: (eds) Lectures Notes in Economics and Mathematical Systems, vol 563. Springer, Berlin, pp 305–322
Voß S, Schneidereit G (2002) Interdependencies between supply contracts and transaction costs. In: Seuring S, Goldbach M(eds) Cost management in supply chains. Springer, Berlin, pp 255–274
Author information
Authors and Affiliations
Corresponding author
Additional information
The authors thank two anonymous referees both for detailed remarks and for interesting general comments on a previous version of the paper.
Stef Tijs and Rodica Branzei are indebted to Daniel Granot for useful discussions on the topics treated in this paper and his hospitality during our research visit at British Columbia University at Vancouver in July–August 2003.
Rights and permissions
About this article
Cite this article
Moretti, S., Tijs, S., Branzei, R. et al. Cost allocation protocols for supply contract design in network situations. Math Meth Oper Res 69, 181–202 (2009). https://doi.org/10.1007/s00186-008-0226-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00186-008-0226-9