JORSJ Vol. 50 No. 2 Abstract & Keywords 1. Study on Longer and Shorter Boundary Duration Vectors with Arbitrary Duration and Cost Values Yi-Kuei Lin abstract We use the project network in AOA form (arrows denote the activities and nodes denote the status of the project) to represent a large-scale project. The activity duration and the activity cost are both random variables which take arbitrary integer values with the arbitrary probability distribution. Under the project time (the deadline to complete the project) constraint and the budget constraint, this paper studies how to schedule all activity durations of the project. Two algorithms are proposed to generate all upper and lower boundary vectors for the project, respectively. All feasible activity durations of the project are among such upper and lower boundary vectors. keywords Project planning, activity duration, activity cost, upper and lower boundary vectors, minimal path 2. Dynamic Control of the Address Binding Update for Mobile Nodes in a Hierarchical Mobile IP Network Sang-Yong Kim and Hideaki Takagi abstract Hierarchical Mobile Internet Protocol version 6 (HMIPv6) has been proposed by the Internet Engineering Task Force (IETF) as an enhancement of the MIPv6. It is designed to reduce the amount of required signaling and to speed up the hand-off operation for mobile connection by means of hierarchical routing. In the HMIPv6, a router called the Mobile Anchor Point (MAP) serves mobile nodes (MNs) to aid their address binding and update as a local home agent. However, as the number of MNs increases in a MAP domain, the resource of the MAP becomes scarce, which increases the chance of failing in admitting new and hand-off MNs. Therefore some control scheme is needed in order to guarantee the quality of service (QoS) of the network. In this paper, we propose a dynamic control of the address binding update for the MNs in an HMIPv6 network. We consider three types of MNs entering the MAP domain, namely, a new MN, a hand-off MN in the sleep mode, and a hand-off MN in the active mode. We impose different costs on rejection of requests from these MNs, since the forced termination of an ongoing communication causes greater pain to a user than blocking a new MN. An optimal admission policy is obtained from a semi-Markov decision process with respect to the number of MNs present in a MAP domain. Based on this optimal policy, we calculate the probabilities of blocking each type of MN. We show numerically that our control reduces the probability of rejecting active mode hand-off MNs at little expense of blocking new MNs. It is also shown that our dynamic control outperforms the static control based on the guard channel scheme. keywords Telecommunication, hierarchical mobile IP network, binding update, dynamic admission control, semi-Markov decision process, value iteration algorithm 3. Estimation Methods by Stochastic Model in Binary and Ternary AHP Kazutomo Nishizawa and Iwaro Takahashi abstract New stochastic models for binary and ternary AHP are proposed, and further minimax and least square estimation methods (with parameter $\theta$) for these models are proposed. The solutions of both methods are proved to be mathematically equivalent although the principles are different. Another method based on the well-known likelihood function is applied to our model with the parameter, which can expand the application limit of the conventional likelihood method. Various examples are solved by these proposed methods and we have successful results for all. keywords AHP, binary AHP, ternary AHP, Bradley-Terry model 4. An Extension of a Minimax Approach to Multiple Classification Tomonari Kitahara, Shinji Mizuno, and Kazuhide Nakata abstract When mean vectors and covariance matrices of two classes are available in a binary classification problem, Lanckriet et al.\ \cite{mpm} propose a minimax approach for finding a linear classifier which minimizes the worst-case (maximum) misclassification probability. In this paper, we extend the minimax approach to a multiple classification problem, where the number $m$ of classes could be more than two. Assume that mean vectors and covariance matrices of all the classes are available, but no further assumptions are made with respect to class-conditional distributions. Then we define a problem for finding linear classifiers which minimize the worst-case misclassification probability $\bar \alpha$. Unfortunately, no efficient algorithms for solving the problem are known. So we introduce the maximum pairwise misclassification probability $\bar \beta$ instead of $\bar \alpha$. It is shown that $\bar \beta$ is a lower bound of $\bar \alpha$ and a good approximation of $\bar \alpha$ when $m$ or $\bar \alpha$ are small. We define a problem for finding linear classifiers which minimize the probability $\bar \beta$ and show some basic properties of the problem. Then the problem is transformed to a parametric Second Order Cone Programming problem (SOCP). We propose an algorithm for solving the problem by using nice properties of it. We conduct preliminary numerical experiments and confirm that classifiers computed by our method work very well to benchmark problems. So we preserve the effectiveness of the binary minimax approach to multiple case. keywords Optimization, multiple classification, minimax approach, second order cone programming 5. The Pricing of Options with Stochastic Boundaries in a Gaussian Economy Masaaki Kijima and Teruyoshi Suzuki abstract This article considers the pricing of options with stochastic boundaries in a Gaussian economy. More specifically, prices of corporate discount bonds and knock-out exchange options are obtained in closed form. The key tools for doing this are the change of measure and the reflection principle of a driftless Gaussian process with a deterministic diffusion coefficient. keywords Finance, reflection principle, arcsine law, change of measure, exchange option, knock-out option 6. Optimal Pricing for an Advance Sales System with Price and Waiting Time Dependent Demands Peng-Sheng You abstract This paper investigates an advance sales system wherein a firm sells an inventory over a limited planning time interval. The firm divides the planning time interval into several reservation periods and delivers the reserved orders at the end of each reservation period. The demands are considered as price and waiting time dependent. In addition, the situation in which customers may cancel their orders before receiving them is also considered. Two continuous time models are developed and analyzed. The ratio of refund to sales price is assumed to be fixed in the first model while is assumed to be time-dependent in the second model. Solution procedures are developed for both models in order to determine the number of reservation periods, the optimal sales price, and order size. keywords Inventory, price, cancellation, reservation, order