This paper attempts to model capital budgeting problems by a new technique of dependent-chance integer programming as well as dependent-chance multiobjective programming and goal programming. Some examples are provided to illustrate the potential applications in the area of capital budgeting. A stochastic simulation based genetic algorithm is also designed to solve both chance constrained integer programming and dependent-chance integer programming models.

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We consider a joint chance-constrained linear programming problem with random right hand side vector. The deterministic equivalent of the joint chance-constraint is already known in the case that the right hand side vector is statistically independent. But if the right hand side vector is correlative, it is difficult to derive the deterministic equivalent of the joint chance-constraint. We discuss two methods for calculating the joint chance-constraint. For the case of uncorrelated right hand side, we try a direct method different from the usual deterministic equivalent, for the correlative right hand side case, we apply numerical integration. In this paper a chance-constrained programming problem is developed for electric power capacity expansion, where the error of forecasted electricity demand is defined by a random variable. Finally we show that this problem can be solved numerically using the trust region method and numerical integration, and we present the results of our computational experiments.

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In this paper, a class of stable and coalitionally nonmanipulable social choice correspondences is presented. Each correspondence in this class, called the hypercore, is induced from a social choice function with restricted domain of preference profile. It is proved that the correspondence is the intersection of cores over an equivalent class of profiles. On the contrary to Demange's max-max criterion, max-min criterion is adopted for defining a coalitional nonmanipulability. Although the core induced from a coalitionally nonmanipulable social choice function with a restricted domain does not necessarily satisfy the nonmanipulability in the max-min sense, it is shown the hypercore does.

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大企業などの組織体は, 一般に複数の活動主体(支店など)をもっている. この組織体の経営活動には, 二つの立場があると考えられる. 一つはそれぞれの活動主体における「管理者」の立場であり, もう一つはその活動主体を統括する組織体全体の「経営者」の立場である. そして, それぞれの活動主体は人材や材料などの資源を投入して, 製品やサービスを産出するシステムと考えることができる. ここで用いられる経営資源はほとんどの場合, 無限に利用可能というわけではないので, これらの有限な資源を有効に利用することは重要である. 組織体全体の経営者は, 活動主体群全体の業績(産出)に関心を持つであろうし, 各活動主体の管理者は, 各々の活動単位の業績や他の活動単位に比べてどのくらい優れた(もしくは劣った)活動をしているかということに主なる関心をもつ. 本論文では, このような組織体に対して多入力多出力のシステムの相対的効率性評価の手法であるDEAの考え方を利用し, 各活動主体(DMU)の現状の活動を評価した上で, DMU群全体でより大きな産出を得ることができるような資源再配分を行うモデルを提案する. このモデルは, 規模の効率性を考慮したBCCモデルの生産可能領域をもとに, より効率のよい活動を目指すような各活動単位への資源の配分を決定する. また, 同様の考えでDMU群へ投入する資源量を抑えるモデルを提案する.

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This paper investigates a search problem for a moving target on a network in which any time information of the target position is not available to a searcher. The searcher has to distribute the limited amount of search efforts on a search space to detect the target, knowing only route information of target paths but not time information about when the target passes there. On detection of the target, the searcher gains some value but expends search cost. There have been few papers which mathematically deal with such a search model without any time information of the target position so far. We formulate the search-efforts-optimizing problem under the expected reward criterion as a convex programming problem and obtain necessary and sufficient conditions for optimal solutions. Using the conditions, a new algorithm is proposed to give an optimal solution. It is shown that the algorithm has the high efficiency for computational time and the robustness for the size of problems comparing with some well-known methods for non-linear programming problems: the gradient projection method and the multiplier method, by numerical examinations. We also elucidate some properties of the optimal solution by the sensitivity analysis of system parameters.

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The dominant alternatives method by Kinoshita and Nakanishi (1997) is a new type of AHP-Analytic Hierarchy Process-designed to deal with the case in which the weights of criteria vary in accordance with the alternative chosen as the dominant viewpoint. This study clarifies differences between the general viewpoint and the dominant viewpoint, and features of the relative and the absolute measurements under both views. When conducting continuous surveys, additional data from the latest survey have to be reflected into the result of the previous survey in a certain scheme. This paper proposes "concurrent convergence" as a processing technique for additional data in an application of the dominant alternative method. When there are more than one dominant alternative, the technique requires a convergent calculation toward the coincidence among derived weights of criteria on each alternative. By adopting the convergent values in the overall evaluations, every evaluation value on every alternative will be equal. This technique, therefore, enables us to reserve the essential features of the dominant alternative method.

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Recently a regular (unconditional) decision process has been mathematically formulated from the multistage decision process in Bellman and Zadeh's paper "Decision-making in a fuzzy environment". According to the available information on total fuzziness, we propose two types of conditional decision process for regular decision process. One is an "a posteriori conditional decision process" and the other is an "a priori conditional decision process." The a posteriori process is formulated through taking at each stage backward conditional expectation of remaining process after performing take-action for the regular decision process. The a priori is through taking at each stage backward conditional expectation before take-action. We derive recursive equations for both a posteriori and a priori processes with numerical illustrations.

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The eigenvalue method(EM), that is to find the principal eigenvector of a pairwise comparison matrix, is widely used and known to be practical in Analytic Hierarchy Process(AHP). However, the validity of EM has never been fully proved. In this article, we present an equilibrium model and four optimization models to show the logical justification for using EM in AHP. By introducing two concepts, self-evaluation and non-self-evaluation, into AHP, the fundamental theorem (Frobenius' Theorem) for EM is interpreted as two optimization problems. From these two concepts, a noncooperative game with a pairwise comparison matrix is also formulated and its equilibrium solution is the principal eigenvector. We propose two discrepancy indices between self-evaluation and non-self-evaluation and formulate four discrepancy-minimization problems. An optimal solution for two minimization problems among them is equal to the principal eigenvector.

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