In this paper, we analyze a facility location model in which a facility with shorter expected required time is utilized. Required time for facility consists of the round-trip travel time and the sojourn time, and each facility has a single server with exponentially distributed service time. An area in which customers live is divided in a form of meshes. Demand from each mesh forms a Poisson process. Customers first visit the nearer facility, but if one facility is congested, a part of customers who visited the facility will go to another facility. Then in a steady state each customer visits a facility with shorter expected required time, and the area is divided to two stable regions. The two-facility location model with the stable regions is formulated by using queueing theory, and a computation method for deriving a boundary line dividing these regions is proposed. From this boundary, overall expected required time and required time distributions for all customers can be derived. Properties of the stable regions are discussed by numerical examples.

View full abstract

This paper discusses optimal selection of R & D projects under uncertainty. The stochastic optimization models for R & D project selection are not almost studied except Ringuest et al. (2004). We formulate two kinds of mean-variance capital budgeting models for R & D project selection. One is the standard model with zero-one variables, in which the value is zero if the project is rejected and one if the project is accepted. The other is the practical model with inequality constraints with zero-one variables, in which the value is zero if the project is rejected and more than lower limit if the project is accepted. Multiple scores evaluated by multiple specialists are used as future scenarios of projects. We run these models with hypothetical data and examine the results.

View full abstract

In the thesis, I discuss the estimation of default dependency using historical default data. 2-factor model is used to represent category-separated variability of latent variables as proxy for obligor credit. For simplification, one numerical calculation for maximum likelihood estimation of factor loading and in turn asset correlation is employed. By Monte Carlo analysis of the estimator's robustness and by real estimation with historical default data, it is confirmed that the model requires less computing power than existing methods, and generates more robust estimator than other category-blinded models that deal with real data. This shows that it is important for the robust estimation of default dependency to use multiple-category default data and estimate inter-category correlation, even when only correlation within one category is required for estimation.

View full abstract

Complex procedures are used in the formulation of dual scaling for successive categories data proposed by Nishisato. However, in a mathematical programming approach, successiveness is easily represented as constraints. Moreover, in a mathematical programming approach it is easy to add and modify objective functions and constraints. Thus mathematical programming models with various objective functions are proposed. Also a model that treats fuzzy numbers is proposed for the purpose of representing lack of assurance or vagueness in answers. The usefulness of these methods is shown by applying them to three data sets.

View full abstract

In recent studies on network formation, it is assumed that a player directly receives a utility from the network, namely she/he receives a utility from any other players by forming links with them. Jackson and Wolinsky (1996) gave a simple model leading the empty, the complete, or the star network as the stable networks. The star network consists of one central player and other peripheral players who form links only with the central player. Under a different condition of link formation and deletion, Hummon (2000) showed that the ring network can be also stable. In the real world, however, we often observe a general structure of social networks rather than simple ones such as the empty, the complete, the star and the ring networks. In a certain social network such as an environmental conservation group network, however, it is natural that a player receives a utility not from a network but from the corresponding public goods. In such a group, forming links means that a player joins in conservation activities of public goods such as the global environment, and it improves the level of the public goods. In this paper, we treat a mathematical model which is taking into account the effect of individuals' reputation in a society with interest in public goods, and we show that a general structure of networks in which there exist multiple disjoint components connecting some star networks is also stable.

View full abstract

When fund managers or traders in the financial institutions trade a large volume of a stock, the trading volume might impact the stock price. This paper discusses optimal execution strategies with linear price impact functions for trading a large volume of a stock. At first, we verify the fact that an optimal solution derived by dynamic programming algorithm can be satisfied with the optimality condition via mathematical programming formulation if a random variable in a price impact function is independently and identically distributed. We formulate the mathematical programming model with non-negativity constraints. The type of the problem can be formulated as a quadratic programming, but it is not always convex. In this paper, we decompose the matrix derived from the linear price impact function, and we calculate a closed-form condition that the matrix is positive definite. Similarly, we propose a model using matrix decomposition to solve the problem fast. We examine the model using a linear impact function of Huberman and Stanzl(2001) with numerical examples. We analyze the sensitivity of various parameters for seven kinds of the coefficients of linear price impact.

View full abstract