This paper investigates an optimal search policy, with stopping for a stationary target being in one of n boxes. It is assumed that the search is conducted continuously with a total search cost C per unit time and the search in box i costs c_i Per unit search effort. The conditional probability of detecting the target with unit search effort is a_i and a reward R_i is given to the searcher when he successfully detects the target in box i. We derive conditions for the optimal search and stop policy which minimizes the expected risk of the search (the expected search cost minus the expected reward). The physical meaning of the conditions and several properties of the optimal policy are elucidated. The optimal policy for two-box case is examined in detail, and necessary and sufficient conditions for the optimal policy and the closed form risk function are obtained.

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The object of this paper is to investigate the impact of uncertainty in a dynamic job search model where the states of the economy follow a Markov chain and the cost of search does not only depend on the state but on the period. Especially, we explore whether or not increasing the uncertainty about the states of the economy, the wage distribution, the number of job offered at a time and other search environments is beneficial to the searcher.

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For the problem of finding the shortest paths from a prescribed vertex to the other vertices in a given network with nonnegative arc lengths, we investigate practical efficiencies of typical existing algorithms, i.e., the label-correcting method with a FIFO and that of a two-way sequence, and the label-setting method with a heap and that with a 1- or 2-level bucket system. We propose also a new method with a variable bucket system and compare it with those existing methods. Among the existing methods, the label-correcting method of a two-way sequence and the label-setting method with a 1-level bucket system have been found efficient in most cases. The new proposed method is not only as efficient as those but it is also robust for a large variety of networks, so that it may be recommended for practical use.

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This paper proposes two kinds of techniques which improve the computational efficiency of the restart methods; including the (n+1)-, 2n-, 2^n-, (3^n-1)- and Merrill's methods, which have been developed in the field of the fixed point and complementarity theory for approximating solutions of a system of nonlinear equations: f(x)=0 . Here we assume that f is a continuously differentiable mapping from the n-dimensional Euclidean space into itself. The one of the techniques which will be proposed is concerned with a grid size control of simplicial subdivisions which are used in each cycle of the restart methods. This aims at saving function evaluations in earlier cycles of the global convergence from a given initial point to a rough approximate solution. The other technique is concerned with combination of the restart methods with the quasi-Newton method. So far the quasi-Newton method has been used to improve the local convergence of the restart methods. In this paper, we assert that it should be used as much as possible even in earlier cycles of the restart methods unless its use does not destroy the global convergence. We show the necessity of introducing these techniques into the restart methods to improve the computational efficiency by using some numerical examples, and then report some computational experiences which support that they work very effectively.

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This paper deals with the GI/G/m queueing system with group arrivals via diffusion approximation. We present approximate formulae for the distribution of the number of customers, the mean number of customers and the mean queue length. Moreover a modified approximation is considered to improve the accuracy of these formulae. The accuracy of the approximate formulae is numerically examined in some examples.

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