In this paper, the (r,S) policy is considered for production/inventory systems where a single type items are produced on an item by item basis by a single production facility. The (r,S) policy considered in this paper is a pull type threshold policy which is very useful in situations where the time and cost required to setup the production facility are relatively high. The demand for the item is assumed to arrive according to a Poisson process. The processing time required to produce an item is assumed to follow an arbitrary distribution. When an item is demanded, one of the items in the inventory is delivered to the customer and the kanban on the item is removed. The removed kanban is immediately transmitted to the production facility. At the instant r kanbans are accumulated at the production facility, the operator turns the production facility on, which takes a random amount of time. In the production period, items are produced one by one and whenever each item is produced, a kanban is attached to it. When there are no kanbans at the production facility, the machine is shut off and a non-production period begins, which lasts until the number of kanbans accumulated at the production facility is raised back to r. In this paper, assuming a linear cost structure, an efficient search procedure is developed to find the optimal threshold value r as well as the optimal number of kanbans S, which minimizes the expected cost incurred per unit time.

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This paper presents a relaxed projection method for variational inequality problems over a polyhedral set K. Unlike standard projection methods, each iteration of the proposed method solves a modified variational inequality problem over an ellipsoid approximating the original set K. By choosing an appropriate radius of the ellipsoid, the projected point can be obtained in a closed-form. Convergence property of this method is investigated. The limited computational experiments yield promising results.

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We will propose a mean-variance-skewness(MVS) portfolio optimization model, a direct extension of the classical mean-variance model to the situation where the skewness of the rate of return of assets and the third order derivative of a utility function play significant roles in choosing an optimal portfolio. The MVS model enables one to calculate an approximate mean-variance-skewness efficient surface, by which one can compute a portfolio with maximal expected utility for any decreasingly risk averse utility functions. Also, we propose three computational schemes for solving an associated nonconcave maximization problem, and some preliminary computational results will be reported.

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This paper clarifies the diffusion mechanism of new product, which is needed under social considerations, from the viewpoints of technological advances (TA), market and public subsidy policies. First, a linear model is constructed and analyzed to grasp a trend of the diffusion process, taking into account pricing for new product and effects of TA on production and market. Next, economic effects of subsidy policies are discussed on the pricing and technical development, and some important viewpoints are presented. Finally, this model is extended to the case where there is a potential demand peculiar to new product and the difference in pricing between the original and extended models is examined.

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Many kinds of reorder point - reorder quantity policies with an emergency order, in which we can decide when the expedited order point is reached and then we place an expedited replenishment order, have been presented in earlier contributions. Very few studies on cyclic. inventory control with an emergency order, however, have been reported. The purpose of this pa,per is to establish some analytical results on the continuous review cyclic inventory policy with two kinds of lead times. We derive necessary and sufficient conditions for the existence of the optimal ordering time which minimizes the long-run average or the expected total discounted costs. Also, we give explicit formulae of the expected costs by specifying demand processes. Poisson and Brownian motion processes are assumed as the demand processes. Finally, we numerically calculate the optimal ordering time and the optimal order quantity, and refer to the sensitivity of model parameters for the optimal policy.

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Two outer approximation algorithms for lower rank bilinear programming problems are developed. The first algorithm can generate an ⋴-optimal solution rather efficiently when the rank of the objective function is less than five. The second algorithm is exact, and finitely convergent, yet with slower convergent property, compared to the first.

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This paper presents an analysis of a cyclic-service tandem queue (M/G/1 type queue) with exhaustive services and multiple server vacations, in which a single server takes repeated vacations until it finds at least one message in the first queue after emptying the queueing system. It is assumed that the vacation time is generally distributed, and switch-over times are zero. This paper analyzes queue-length distributions and message sojourn time distributions. By using the results of the two-stage tandem-queue analysis and the decomposition property in vacation models, some explicit formulas are derived for the mean total sojourn time in the multi-stage tandem queue and the mean waiting time in the first stage. These results are applicable to the performance analysis for message processing in packet switching systems.

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A target is moving on a finite number of cells in discrete time. Knowing the probabilities of the target's path selection, a searcher is searching for the target in this search space with constraints that he can move from cell i to one of the adjacent cells. He gains a value V(t) on the detection of the target at time t but expends cost c_0(i,t) for the search in cell i at t. In this paper, we propose a method to find an optimal path for the searcher, which maximizes the expected reward defined as the expected value minus the expected cost. We use a branch and bound procedure with an upper bound estimation given by solving the problem relaxed in continuous search effort.

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