演講者：陳彥銘教授

單　位：國立高雄第一科技大學運籌管理系

日　期：2013年5月8日　PM 14:30

地　點：國立高雄大學理學院408室

講　題：Allocation Problems in Management: A Possible Structure Extension of the Fenchel Core and Fixed-Point 

　　　　Equilibrium to Matroids

摘　要：

This talk covers two types of games: production games and replenishment games. The production games, one type of cooperative games, represent a base model for many convex optimization games. We extend the classical Owen's results to another core solution in a form of Lagrange multiplier and Fenchel conjugate. This Fenchel core enjoys additional nice properties in the solution concept of cooperative games. The replenishment practice in management involves one-time and periodic operations, which have been modelled as newsvendor games and joint replenishment games, respectively.

The two non-cooperative games are of parsimonious importance and represent a base model for many applications in the scientific management field. The matroid results have been well developed for the joint replenishment games.  

Our past study has also characterized the existence and uniqueness conditions of Nash equilibriums for the Multi-newsvendor games through fixed-point theorems. 

The purpose of this study is not to develop an algorithm for the maximum value of a convex combinatorial optimization.

Based on our Fenchel core results, we show the possibility of extending the underlying structure to a more generalized Matroid. For example, we can extend R to a graph G = (N, E) or to a joint newsvendor Matroid.