An adaptive exponential smoothing method is proposed by use of the change detection statistic for random level change in exponential smoothing, where the mean, the variance, and the limiting distribution of the statistic are derived. The comparison results with Trigg and Leach's and the exponential smoothing method by simulation show that the proposed method gives the smaller mean square error than the exponential smoothing for almost all cases, while it performs better than Trigg and Leach's for frequently occurred large level changes.

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It is well-known that the tight lower bounds determine the effectiveness of the branch and bound method for the NP-hard problems. In this paper, we present a new lower bounding procedure for the capacitated arc routing problem (CARP), one of the arc routing problems. They give the tight lower bounds and it is easy to develop an exact algorithm using their network structures.

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This paper considers ways of modelling time dependent inspection problems where there is a possibility of false alarms. For this purpose, it is assumed that safeguards procedures are notified to the inspectee by the inspector and are prima facie plausible ones. This 'inspector-leadership principle' implies that under reasonable assumptions the inspectee's strategy is legal in the sense of complying with agreed rules. The main objective of our investigation is to derive simple criteria for the determination of optimal inspection procedures from the equilibrium conditions for non-cooperative non-zero sum two-person games. It can be shown that, given the appropriate assumptions, one can arrive at 'statistical' optimization criteria. In the simplest case one gets the global probabilities of the errors of the first and second kind and in more complex cases the average run lengths for legal and illegal inspectee behavior.

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The purpose of the present paper is (i) to extend the stochastic models in the previous studies [1, 2 and 3] so as to analyze flow-reliability R(t) of an arbitrary coherent repairable network under periodically changing demand φ(t), and (ii) to prove that the flow-reliability can also be evaluated asymptotically as an exponential function under mild assumptions. In the model, flow φ(X(t)) of the network is defined as a monotonic function of state-vector X(t) = (X_1(t), X_2(t), …, X_n(t)) with X_i(t) = 1 in case of unit i being operative, and Xi(t) = 0 otherwise, at time t. Flow-reliability R(t) is introduced as the probability that flow φ(X(s)) of the network is greater than or equal to demand φ(s) for all s ∈[0, t], i.e., R(t) = P{φ(X(s)) ≥φ(s) for all s ∈[0, t]}; and the demand function φ(t) is given arbitrarily as a nonnegative periodic function with a certain period T > 0. It will finally be proved that the flow-reliability R(t) of the network is asymptotically exponential, i.e., R(t) = exp(-Λt) + Θ(t), where the parameter Λ is evaluated by expected llfe-times, repair-time distributions of the units, the structure / logic to define the flow of the network, and the demand function φ(i). It will also be proved that the error Θ(t) = R(t) - exp(-Λt) of the approximation converges to 0 as the expected lifetimes of the units increase indefinitely under certain assumptions. In the course of the proof an extended renewal equation is first derived, from which a variational equation is yielded, and its unique solution, R_0(t), is effective to characterize exp(-Λt) and Θ(t) in the present model.

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The paper deals with an optimal stopping problem with a finite planning horizon where an available search budget, the total amount of money that can be invested in search activities throughout the planning horizon, is limited and where both the probability of an offer being obtained at each point in time and the probability distribution function of an obtained offer's value may depend on the search cost invested at that time. The objective is to maximize the expected present discounted value of the sum of the accepted offer's value and the remaining search budget at that point. The optimal decision strategy for the problem consists of the two decision rules: an optimal investment rule, prescribing how much of the search budget to invest in search activities of each point in time and an optimal stopping rule, prescribing how to stop the search with accepting an offer. The present paper examines the properties of the optimal decision strategy analytically and numerically. The most interesting and important properties revealed here are the two: (1) In a recall model, the optimal stopping rule has a reservation value property, and if the given search budget tends to infinity, the reservation value becomes time-independent, implying that the optimal stopping rule has a myopic property, and (2) in both of a recall model and a no recall model, the optimal investment does not always become monotone in the amount of search budget remaining then, possibly increasing or decreasing drastically with its very slight change.

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In this article, optimal two-part tariffs of a bi-directional telecommunications service are examined. Heterogeneous users are assumed to formulate social demand for the service. Two regimes of supplier are considered: monopoly and non-monopoly. In the latter, the supplier which enjoyed monopoly is faced with the entry of a competitive supplier. Demand externalities which are conspicuous in telecommunications service are introduced into the model. The supplier is assumed to maximize the profit or to be forced to maximize the social benefit derived from the service. A nonlinear optimization method is applied to derive the optimal tariff. It is shown that the tariff diverges from conventional rules for public utility pricing.

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