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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In this paper, we propose a method for the resource allocation problems based on data envelopment analysis(DEA). When we consider this problem for the organization such as the large corporation, we should recognize that there are two management levels in the organization, the operator of each section (for example, the branch office or DMU), and the manager of the organization. Each operator is concerned with the performance and the efficiency of his own section. On the other hand, the manager is concerned with those in all of the organization. Generally, the management resource allocation problem with the plural sections can be treated as a selection problem from the mixed proposals in profitability analysis (the reader can be refered to, e.g., Senju et al. (1989) for its details). The management resource means, for example, manpower or material. The selection problem from the mixed proposals is to choose a plan independently from among several mutually exclusive proposals for each section so as to maximize the return of the organization. However, there are some problems in this method such as how to estimate the return of each proposal and how to consider the present activity level of the section if the manager wants to re-allocate his holding resources. To solve these problems, we use the concept of production possibility set of DEA-BCC model. First, we measure the efficiency of the present activity of each section (DMU). Next, we reallocate our holding management resources to obtain the maximum outputs, by considering the present activity of the DMU, where we assume that the efficient frontier of DEA is the mutually exclusive proposals of each DMU. Moreover, we propose another model by which we can save the ammount of input resources for the DMUs.

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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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