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A Note to the Objective Function for Centralized Case in Netessine and Rudi's Inventory Model

Chinese Quarterly Journal of Mathematics 2008年第1期23卷 56-60页

作者：李小申王仲英高克权 Department of Applied Mathematics Dallas University of Technology Office of Education Administrator Jiyuan Vocational and Technical College Department of Mathematics and Physics Henan University of Science and Technology

Netessine and Rudi（2003） consider a consumer-driven substitution problem with an arbitrary number of products under both centralized management and competition. They obtain analytically tractable solutions, establish concavity of the objective function, i.e., the expected profit function generated by each product and uniqueness of the equilibrium for the decentralize case. For the centralized case, they indicate that the objective function, i.e., the expected profit function, might not be concave and not even quasiconcave. In this note we show, for the centralize case, that the objective function is submodular, and partially verify Netessine and Rudi＇s observation that the objective function be unimodal in each of the decision variables for some case.

关键词： operation research inventory substitution submodular

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Equivalence between Linear Tangle and Maximal Single Ideal

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Open Journal of Discrete Mathematics 2019年第1期9卷 7-10页

作者： Takaaki Fujita Koichi Yamazaki Graduate School of Science and Technology Gunma University Gunma Japan Division of Electronics and Informatics Gunma University Gunma Japan

The concept of linear tangle was introduced as an obstruction to mixed searching number. The concept of (maximal) single ideal has been introduced as an obstruction to linear-width. Moreover, it was already known that mixed search number is equivalent to linear-width. Hence, by combining those results, we obtain a proof of the equivalence between linear tangle and maximal single ideal. This short report gives an alternative proof of the equivalence.

关键词： Linear Tangle Maximal Single Ideal submodular Function

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