Research projects

アマゾンが「置き配」を取り入れたように，当然と考えられてきたサービス目標をあえて緩和させることで事業を成功させるという逆転の発想による成功事例は十分に論議されていない．本研究は，完璧を目指していた従来のサービス観とは異なる，多様な目標の間のバランスを取ることを重視する新たなサービス観の理論的体系化を目的とする．サービス失敗の許容範囲と補償制度を主要要素とするサービス運用の理論モデルを構築し，サービス企業，従業員，顧客の全てが便益を与えられる新しい解決策の実務への提案を行う．さらに，労働者不足などのサービス業の問題を解決し，働き甲斐も経済成長も両立できる持続可能なサービス観を社会に発信する．

最適化問題はいろいろな分野で扱われる重要な問題であり、無制約最適化問題と制約付き最適化問題とに分けられる。最適化問題を効率よく解くための数値解法の研究は近年ますます活発に行われている。本研究では、非線形最適化問題の数値計算アルゴリズムの研究に焦点をあてる。提案した数値計算アルゴリズムの収束性を証明して理論的な裏づけをするとともに、数値実験を通してその有効性・実用性を検証する。さらに、実社会で発生する具体的な最適化問題を解く際の実用化を目指して、提案する数値計算アルゴリズムのソフトウェアも開発していく。したがって、本研究は社会的に大きな意義を持つ。

Supply Chain Management (hereafter referred to as SCM) is a central research topic in the current field of management science. Mathematical models aiming for overall optimization in Supply Chain Networks (hereafter referred to as SCN) have been studied for a long time, but research on competitive SCNs has not advanced as much as its importance would suggest. In this study, we focus on formulating competitive situations in SCNs as equilibrium problems, particularly addressing "equilibrium problems in SCNs with uncertainties," "equilibrium problems in SCNs considering service," and "equilibrium problems in SCNs with complex structures and constraints".

We studied a proximal Newton-type method to solve the minimization of a composite function that is the sum of a smooth nonconvex function and a nonsmooth convex function. We proposed an inexact proximal memoryless quasi-Newton method based on the Broyden family and showed its global convergence. We considered the case where the nonsmooth function was given as a DC function. In addition, we dealt with the smooth function whose Hessian has a special structure. We also combined the active set strategy with the memoryless quasi-Newton method for solving bound constrained minimization problems. We considered memoryless quasi-Newton methods for optimization problems on Riemannian manifolds. We also proposed a primal-dual interior point trust-region method for nonlinear semidefinite programming problems, and a trust-region SQP method in which negative-curvature directions were used to obtain the global convergence to a second-order critical point for constrained optimization problems.

Speculating possible strategy and organization to utilize bigdata and SNS technology is quite urgent issue for business organization and academics. We provided two directions in the research of such hyper-flexible business organization. In one direction we focus on clarifying mechanism of aligned flow of material and information. And in the other direction, we aimed at ever changing demand process and tried to take it into the business process. We got the following result. We developed gaming methodology for the analysis of corporate strategy that allows us dynamic if-then conditions, especially in servitization of manufacturers. As to marketing strategy, we designed and implemented a mechanism that allows us to use SNS in usual commerce. A wide variety of questionnaire-based research on supply chain management are conducted, and we showed some important relationship among flexibility, quality management, and others.

We proposed new memoryless quasi-Newton methods for large scale unconstrained optimization problems. These methods are based on the Broyden family with the spectral-scaling secant condition. we showed the global convergence properties of our proposed methods and investigated their numerical performance. In addition, we applied the memoryless quasi-Newton methods to composite function minimization problems and proposed inexact proximal memoryless quasi-Newton methods. We also combined the active set strategy with the memoryless quasi-Newton method for solving bound constrained minimization problems. Furthermore, we proposed a primal-dual interior point method for solving nonlinear semidefinite programming problems. In this method, the trust-region strategy was used in order to obtain the global convergence property. We considered robust supply chain network equilibrium models and showed that these could be reformulated as variational inequality problems or complementarity problems.