Abstract
Ostrovsky generalized the stable marriage model of Gale and Shapley to a model on an acyclic directed graph, and showed the existence of a chain stable allocation under the conditions called same-side substitutability and cross-side complementarity. In this paper, we extend Ostrovsky's model and the concepts of same-side substitutability and cross-side complementarity by using value functions which are defined on integral vectors and allow indifference. We give a characterization of chain stability under the extended versions of same-side substitutability and cross-side complementarity, and develop an algorithm which always finds a chain stable allocation. We also verify that twisted M♮-concave functions, which are variants of M♮-concave functions central to discrete convex analysis, satisfy these extended conditions. For twisted M♮-concave value functions of the agents, we analyze the time-complexity of our algorithm.
| Original language | English |
|---|---|
| Pages (from-to) | 271-290 |
| Number of pages | 20 |
| Journal | Journal of the Operations Research Society of Japan |
| Volume | 58 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2015 Jul 1 |
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Keywords
- Acyclic networks
- Discrete convex analysis
- Economics
- Stability
ASJC Scopus subject areas
- Decision Sciences(all)
- Management Science and Operations Research
Cite this
Stability in supply chain networks : An approach by discrete convex analysis. / Ikebe, Yoshiko T.; Tamura, Akihisa.
In: Journal of the Operations Research Society of Japan, Vol. 58, No. 3, 01.07.2015, p. 271-290.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Stability in supply chain networks
T2 - An approach by discrete convex analysis
AU - Ikebe, Yoshiko T.
AU - Tamura, Akihisa
PY - 2015/7/1
Y1 - 2015/7/1
N2 - Ostrovsky generalized the stable marriage model of Gale and Shapley to a model on an acyclic directed graph, and showed the existence of a chain stable allocation under the conditions called same-side substitutability and cross-side complementarity. In this paper, we extend Ostrovsky's model and the concepts of same-side substitutability and cross-side complementarity by using value functions which are defined on integral vectors and allow indifference. We give a characterization of chain stability under the extended versions of same-side substitutability and cross-side complementarity, and develop an algorithm which always finds a chain stable allocation. We also verify that twisted M♮-concave functions, which are variants of M♮-concave functions central to discrete convex analysis, satisfy these extended conditions. For twisted M♮-concave value functions of the agents, we analyze the time-complexity of our algorithm.
AB - Ostrovsky generalized the stable marriage model of Gale and Shapley to a model on an acyclic directed graph, and showed the existence of a chain stable allocation under the conditions called same-side substitutability and cross-side complementarity. In this paper, we extend Ostrovsky's model and the concepts of same-side substitutability and cross-side complementarity by using value functions which are defined on integral vectors and allow indifference. We give a characterization of chain stability under the extended versions of same-side substitutability and cross-side complementarity, and develop an algorithm which always finds a chain stable allocation. We also verify that twisted M♮-concave functions, which are variants of M♮-concave functions central to discrete convex analysis, satisfy these extended conditions. For twisted M♮-concave value functions of the agents, we analyze the time-complexity of our algorithm.
KW - Acyclic networks
KW - Discrete convex analysis
KW - Economics
KW - Stability
UR - http://www.scopus.com/inward/record.url?scp=84991044080&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84991044080&partnerID=8YFLogxK
U2 - 10.15807/jorsj.58.271
DO - 10.15807/jorsj.58.271
M3 - Article
VL - 58
SP - 271
EP - 290
JO - Journal of the Operations Research Society of Japan
JF - Journal of the Operations Research Society of Japan
SN - 0453-4514
IS - 3
ER -