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Transshipment games with identical newsvendors and cooperation costs

Transshipment games with identical newsvendors and cooperation costs
Transshipment games with identical newsvendors and cooperation costs
In a transshipment game, supply chain agents cooperate to transship surplus products. Although the game has been well studied in the OR literature, the fundamental question whether the agents can afford cooperation costs to set up and maintain the game in the first place has not been addressed thus far. This paper addresses this question for the cooperative transshipment games with identical agents having normally distributed independent demands. We provide characterization of equal allocations which are in the core of symmetric games, and prove that not all transshipment games are convex. In particular, we prove that though individual allocations grow with the coalition size, the growth diminishes according to two rules of diminishing individual allocations. These results are the basis for studying the games with cooperation costs. We model the cooperation costs by the cooperation network topology and the cooperation cost per network link. We consider two network topologies, the clique and the hub, and prove bounds for the cost per link that render coalitions stable. These bounds always limit coalition size for cliques. However, the opposite is shown for hubs, namely news vendors can afford cooperation costs only if their coalition is sufficiently large.
1432-2994
315–339
Hezarkhani, B.
ae3fc227-94dc-47bd-b52c-2fdf90277bef
Kubiak, W.
7020eb70-23e1-49f5-bc49-f743837523b4
Hezarkhani, B.
ae3fc227-94dc-47bd-b52c-2fdf90277bef
Kubiak, W.
7020eb70-23e1-49f5-bc49-f743837523b4

Hezarkhani, B. and Kubiak, W. (2013) Transshipment games with identical newsvendors and cooperation costs. Mathematical Methods of Operations Research, 78, 315–339. (doi:10.1007/s00186-013-0446-5).

Record type: Article

Abstract

In a transshipment game, supply chain agents cooperate to transship surplus products. Although the game has been well studied in the OR literature, the fundamental question whether the agents can afford cooperation costs to set up and maintain the game in the first place has not been addressed thus far. This paper addresses this question for the cooperative transshipment games with identical agents having normally distributed independent demands. We provide characterization of equal allocations which are in the core of symmetric games, and prove that not all transshipment games are convex. In particular, we prove that though individual allocations grow with the coalition size, the growth diminishes according to two rules of diminishing individual allocations. These results are the basis for studying the games with cooperation costs. We model the cooperation costs by the cooperation network topology and the cooperation cost per network link. We consider two network topologies, the clique and the hub, and prove bounds for the cost per link that render coalitions stable. These bounds always limit coalition size for cliques. However, the opposite is shown for hubs, namely news vendors can afford cooperation costs only if their coalition is sufficiently large.

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Published date: 27 July 2013

Identifiers

Local EPrints ID: 479789
URI: http://eprints.soton.ac.uk/id/eprint/479789
ISSN: 1432-2994
PURE UUID: 638bac33-1271-40bf-9a9a-344914905a2d
ORCID for B. Hezarkhani: ORCID iD orcid.org/0000-0003-3439-3474

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Date deposited: 26 Jul 2023 17:03
Last modified: 28 Jul 2023 02:05

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Contributors

Author: B. Hezarkhani ORCID iD
Author: W. Kubiak

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