We consider the situation in which the decision-maker is allowed to have two choices and he must choose either the best or the second best from the group of N applicants. The optimal stopping rule and the maximum probability of choosing either of them are derived.

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In the reliability theory the joint life distribution of units is usually derived under the assumption of stochastic independence for the behavior of units. But it is seen in the practical situation that the stochastic dependence arises by the cause of putting the units in a same environment and so on. A shock model is used to formulate the joint life distribution in the existence of correlation. For example bivariate exponential distribution function and bivariate Erlang distribution function are ones formulated using the shock model. In the present paper the wider class of bivariate distribution function which is called bivariate shock model is defined, and some properties are discussed. Using these properties the practically observable characteristic trend is explained and some bounds for the distribution function are given.

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This work presents a different computational way in finding optimal solutions of Integer-Programming problems under irregular data spaces. In addition, a real application on advertisement problems is given, where the maximum advertisement result is achieved with the minimum value of the risk probability of our campaign under limited resources. Graph theory, Metric Spaces, Taxonomy theory, Boolean algebra and principles of the General Catastrophe theory are used.

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In this paper we consider the following variant of the resource allocation problem: Maximize Σ^n_<i=1> xi subject to Σ^n_<i=1> f_i (x_i)〓 R, and xi: nonnegative integers, where f_i's are nondecreasing convex functions defined over [0, ∞) and satisfy Σ^n_<i=1> f_i (0) 〓 R and lim___<x_i→∞> f_i (x_i) = ∞. R is a real number. We present three algorithms for this problem. The first one requires O (N*log n + n) time, where N* denotes the optimal objective value. The second one requires O (n^2 (log N^^~)^2) time, where N^^~ denotes a given upper bound of the optimal value. The third one requires O (b (n, R) + n log n) time, where b (n, R) denotes the computational time required to solve the continuous problem obtained from the original one by dropping the integrality condition on x_i's.

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This paper is concerned with stationary behaviour of the GI/G/ 1(N) queueing system. Approximate formulae for the stationary loss probability and the stationary distribution of the number of customers are explicitly derived from using diffusion approximation and renewal theory. Moreover, approximate formulae for the mean number of customers are also obtained. These results are then modified so as to be more accurate for small N. It is shown from numerical results that these approximate formulae are sufficiently accurate for a practical use.

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In this paper, we consider the procedure to estimate the various effects of the design factors in the two-stage series lines in which the first stage has an arbitrary service time. First, the system states are represented by the imbedded Markov chain and the steady state probabilities are solved by the Laplace transform with respect to the arbitrary service time distribution. Next, the efficiency, the idling time distribution, the blocking time distribution and the number of in-process works distribution are considered from the system states. Moreover the relations between the dual models are discussed.

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In many situations, it may be more economical to use a used unit than to do a new one. This paper considers an age replacement policy and a periodic replacement policy with minimal repair at failure for a used unit of age x. We discuss optimum replacement policies which minimize the expected cost rates for a specified age x. Further, we obtain an upper bound of an optimum time for an age replacement model and an optimum age of a used unit for a periodic replacement model when the replacement time is previously specified.

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