We describe an approach for scheduling processes of laser drilling systems which can employ two positioning devices simultaneously. Note that these devices are contrastive: one is a high-speed, short-range device, while the other is a low-speed, long-range one. The objective is to minimize the machining time for each board. Despite this common objective, no publications have dealt with approaches for scheduling them so far for some reasons such as high flexibility for positioning. In our approach, we first introduce a scheme: the low-speed, long-range device moves straight with a constant speed. This scheme formulates an optimization problem which includes Asymmetric Hamiltonian Path Problem with Time Windows (AHPP-TW). We present a local search algorithm for the AHPP-TW. The algorithm is non-reversing 3-opt where lexicographic search strategy is applied. Computational experiments on real data drew a comparison between machining time with our approach and that with our conventional one. An excellent result was obtained: our approach cut machining time by 30% on average.

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In this paper we deal with game option introduced by Kifer which is a contract that the buyer and the seller have both the rights to exercise and to cancel it at any time, respectively. Since game option can be canceled or called by the seller, it is a callable American option. First, we review some results on the pricing of the non-callable perpetual American options to emphasize a comparison with our results. Secondly, we derive the value function of the callable perpetual option by solving differential equation and investigate the optimal boundaries of the seller and the buyer. The value function is not differentiable at the stock price which equals strike price. Finally, when the stock pays continuously dividends with a positive rate, we can obtain the pricing formula of callable American perpetual options by applying first hitting time approach of Brownian motion. Also some numerical results are presented to demonstrate analytical properties of the value function.

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In this paper, we investigate location problems of one or more facilities in a network in which several competing facilities already exist. Consider some demand points on the network. Each demand point has demand in proportion to the buying power of all customers of the point. It is assumed that customers patronize the nearest facility. If a facility is newly located within the distance from a demand point to its nearest existing facility, customers of the demand point will use the new facility. In this situation, we would like to locate given number of facilities to maximize the buying power to obtain from the existing facilities. In order to solve the problem, the network is divided into a sub-network according to the combination of the demand points and the existing facilities. And we calculate the buying power of the demand points when we locate a new facility on the sub-network. Then we formulate the problem as a maximum covering problem with p facilities. As an example, we use the road network and existing convenience stores of Seto City. This example shows that our method can be used in the city of real size.

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The meaning of load balancing is to dispatch jobs among resources of a system for maximizing the system performance. This paper deals with a discrete-time optimal load balancing problem that minimizes an expected total cost. This problem is formulated as an undiscounted Markov decision process, and is solved by the modified policy iteration method. Since the modified policy iteration method can not solve practical sized problems due to the curse of dimensionality, a near-optimal load balancing policy is computed by neuro-dynamic programming algorithms. We further compare this policy with heuristic policies such as the random policy, round-robin policy and shortest policy.

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Mortgage backed security (MBS) is a product of mortgage securitization, which is issued backed by the repayment cash flow from a loan pool consisting of many mortgage loans. Collateralized mortgage obligation (CMO) is a form of MBS, in which repayment cash flow from a loan pool is reorganized and bonds with various risks are issued. In this paper, we propose a method of designing CMO with PAC-companion structure. We divide repayment cash flow into two parts; a part in which principal repayment schedule must be satisfied (planned amortization class, PAC) and an unstable high-prepayment risk part (companion). We allow the repaid cash to be reserved in order to repay PAC bondholders in the following periods. We formulate the problem of determining an optimal PAC-companion structure as a mathematical programming problem and use a simulation-based approach to approximate the problem. We show that our model can be reformulated as an equivalent linear programming problem. Furthermore, we propose a modified model which yields a higher performance than the basic model. Finally we conduct numerical experiments and report the results.

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This research forecasts the effect of the location of a new airport to the movement in four main islands of Japan (Hokkaido, Mainland, Shikoku, and Kyushu). As for the effect, the number of user forecasts based on the shortest travel time between cities is judged as an index. We make a traffic network model to simulate the shortest travel time between cities including waiting time. A new airport is added to this model, and the number of users is estimated. Flight service of the new airport is set from the composition of the flight service of neighboring existing airports. The mechanism of the flight setting is called "flight transfer system". By the data of user numbers of existing airports and flight transfer system, we estimate the user number of a new airport. Center area near from Tokyo may be difficult to catch enough users and be inadequate points of new airport, because Shinkansen, Japanese high speed train system, runs in the area and carries many travelers. It becomes clear that appropriate points for new airport are far from Shinkansen and Tokyo.

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