Theoretical Extension and Application of Focus Theory of Choice

2023 Fiscal Year Final Research Report

• Project/Area Number: 20K04982
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 25010:Social systems engineering-related
• Research Institution: Yokohama National University
• Principal Investigator: Kaku (Guo) Masatoshi (Peijun) (郭沛俊) 横浜国立大学, 大学院国際社会科学研究院, 教授 (60325313)
• Project Period (FY): 2020-04-01 – 2024-03-31
• Keywords: 焦点決定理論 / 焦点計画法 / 動的焦点計画法 / 2 レベル数理計画問題 / 生産計画問題 / 新聞売れ子問題

Outline of Final Research Achievements

Static stochastic optimization problems are formulated with the focus theory of choice where the optimal solution is determined as per which solution's focus (the most salient realization of a random vector) is the most preferred. The new formulation that we call the focus programming is a bi‐level programming approach in which the lower‐level program is used to choose the focus of each feasible solution and the upper‐level program is to determine the optimal solution.
A new approach to sequential decision problems under uncertainty named dynamic focus programming is proposed with the focus theory of choice. Different from stochastic dynamic programming that is based on the expected utility theory, dynamic focus programming determines the optimal decision rule according to which initial decision's focus path is the most preferred.
The proposed approaches have been applied for a production planning problem, a real bidding decision-making problem and a newsvendor problem.

Free Research Field

社会工学

Academic Significance and Societal Importance of the Research Achievements

提案した焦点計画法と動的焦点計画法は、ビジネス、経済学、社会システムによくある確率最適化問題の更なる研究のための新しい理論的基盤を提供している。提案した焦点計画法モデルは特別な2 レベル数理計画問題（BLPP）で、上位レベルと下位レベル最適化問題は非平滑、場合によって非凸である。既存の最適化アプローチが適用できない。本研究では、従来解決できなかった最適化問題を解く方法を提案しており、最適化理論において、重要な貢献である。