Yukihiro Maruyama

The Multiobjective Optimization Problem of Set Function

Abstract The multiobjective optimization problem of a set function defined on a σ-algebra If in a finite atomless measure space (X, II, m) is investigated. A constrained local minimum is formulated and its necessary conditions are derived. Also, the sufficient conditions of a constrained local lower efficient point are given. Further, a necessary condition of a constrained minimum is shown in a form of a saddle point of a Lagrangian set function and a theorem for Lagrangian duality is given.

Strong representation theorems for bitone sequential decision processes

Making use of automata theory, we will make clear the relation between a given discrete decision process (ddp) and a bitone sequential decision process (bsdp) which is a subclass of sequential decision process (sdp). Then we define subclasses of bsdps, which have simpler structures than that of bsdp. Assuming that the original discrete optimization problem is given in the form of the process (ddp), for each subclass of bsdps we will present a strong representation theorem that provides a necessary and sufficient condition for the existence of the subclass of bsdps with the same set of feasible policies and the same cost value for every feasible policy as the given process ddp.

Shortest and longest path problems

This paper considers a wide class of shortest path problems in acyclic digraphs, where path lengths are given by the multiplicatively additive value. The problems are solved through bynamic programming, [4]. The bynamic programming formulation for the class has a system of two interrelated recursive equations. By solving the system, simultaneously both shortest and longest path lengths can be found. Two types of sequences which converge to the solution are proposed. By use of a directed network, two actual examples of finding both shortest and longest paths are illustrated.

Range Adjusted Measure Network DEA Model

In this paper, we propose a range adjusted measure network data envelopment analysis (DEA) model that can deal with the overall efficiencies as well as divisional ones in a unified framework. We show some properties of this model.

STRONG REPRESENTATION OF A DISCRETE DECISION PROCESS BY POSITIVELY/NEGATIVELY BITONE SEQUENTIAL DECISION PROCESS

In this paper, we will introduce a new subclass of bitone sequential decision process (bsdp) and give a representation theorem for the subclass called positively/negatively bsdp, shortly, p/n bsdp, that is, necessary and sufficient condition for p/n bsdp to strongly represent a given discrete decision process (ddp).

On a negative-equivalency theorem in associative optimal path problems

In this we study a wide class of optimal path problem in acyclic digraphs, where path lengths are defined through associative binary operations:addition, multiplication, multiplication-addition, fraction and so on. Solving a system of two interrelated recur-sive equations, we simultaneously find both shortest and longest path lengths, Further, for every problem (primal problem), we associate the other related problem (negative-equivalent problem) where each path length is defined through the associative operation connected to it in the primal problem by DeMorgan’s law. The main objective of this paper is to derive a negative-equivalency theorem between the primal problem and the negative-equivalent one