Co-operative logistics is important to solve several logistics problems, such as a shortage of tracks and drivers, inefficient loading, NO_x Pollution and so on. While, current evolvement of computer networks makes it possible to provide various information for common use through networks. And further development of information infrastructure is under way. Under these circumstances, co-operative logistics is socially desired in order to solve logistics problems. However, cost allocation method for co-operative logistics has not been clearly stated so far, and that becomes obstacle for implementating co-operative logistics. This is the paper which gives a solution about how to allocate the transportation costs out of logistics costs. We do not adopt the traditional solutions of co-operative game theory (i.e. Shapley values, core, nucleus, etc.). Instead, we use the expantion solution of Fishburn and Pollark on the Traveling Sales-man Game. That is because the number of NP hard problems i.e. Vehicle Routing Problems for getting traditional solutions increases exponentially as the number of customers increases. Furthermore, this paper shows that participants of co-operative logistics should be able to choose their own costs allocaiton method based on their policies for rental costs and road costs, and also on allocation of saving costs by cooperation. We propose two axioms for cost allocation functions, and some saving functions as well. The furture themes of this problem are how to allocate logistics costs on various conditions (ex. time windows).

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In Data Envelopment Analysis (DEA), when there are more inputs and outputs, there are more efficient Decision Making Units (DMUs). For example, if the specific inputs or outputs advantageous for a particular DMU are used, the DMU will become efficient. Usually the variables used as inputs or outputs are correlated. Therefore, the inputs. and outputs should be selected appropriately by experts who know their characteristics very well. People who are less familiar with those characteristics require tools to assist in the selection. We propose using principal component analysis as a means of weighting inputs and/or outputs and summarizing parsimoniously them rather than selecting them. A basic model and its modification are proposed. In principal component analysis, many weights for the variables that define principal components (PCs) have negative values. This may cause a negative integrated input that is a denominator of the objective function in fractional programming. The denominator should be positive. In the basic model, a condition that the denominator must b~ positive is added. When the number of PCs is less than the number of original variables, a part of original information is neglected. In the modified model, a part of the neglected information is also used.

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After World War II, B. O. Koopman published the series of three papers on the theory of search where the search is carried out with aircraft (or ships) only. However, in the case of emergency, it seems to be reasonable that the search is carried out not only with aircraft but also with ships. Therefore, in this paper, we extend Koopman's model and consider the problem of search with ships and aircraft. By solving the problem in polynomial time, we expect that our results will contribute to the theory of search.

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A polling model with n stations and switchover times is considered. The customers are of n different types, arrive to the system according to the Poisson distribution in batches of random size, and if they find the server unavailable, they start to make retrials until succeed to find a position for service. Each batch may contain customers of different types while the numbers of customers belonging to each type in a batch are distributed according to a multivariate general distribution. The server, upon polling a station, stays there for an exponential period of time and if a customer asks for service before this time expires, the customer is served and a new "stay period" begins. Finally the service times and the switchover times are both arbitrarily distributed with different distributions for the different stations. For such a model we obtain formulas for the expected number of retrial customers in each station in a steady state. Our results can be easily adapted to hold for zero switchover times and also in the case of the ordinary exhaustive service polling model with (without) switchover times and correlated batch arrivals. In all cases mentioned above (retrial model, exhaustive model, switchover times, zero switchover times) to find the expected queue lengths we need finally to solve a set of only n linear equations (O(n^3) arithmetic operations to compute the coefficients). Tables of numerical values are finally obtained and used to observe the system performance when we vary the values of the parameters.

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We have developed an adaptive performance estimation method called Bayesian performance estimation. This method combines conventional performance evaluation with Bayesian analysis. It, is to be used for estimating the performance of networks under operation. It uses a priori information such as the performance derived by conventional methods. It does not need detailed traffic measurement, which is not, usually performed in networks, but uses the data, from a performance monitor, which is generally used. After learning the a priori estimate, the estimator updates the performance estimate through Bayesian estimation using the monitored performance. The proposed Bayesian performance estimation method is applied to VP bandwidth control in ATM networks. We show to apply this method, that is, how to determine the functions and variances in the method. Numerical examples of VP bandwidth control demonstrate the effectiveness of the method.

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In this paper, we consider the comparative statics of shifts in risk. First, we take up the stochastic order which appears in Landsberger and Meilijson [9] and also in Eeckhoudt and Gollier [2]. This order which we call, in this paper, the "monotone generalized probability ratio" (MGPR) order lies between the "monotone probability ratio"(MPR) order and the "second-degree stochastic dominance" (SSD) order. We examine the comparative statics of the MGPR shift in risk in the economic model used by Eeckhoudt, and Gollier [2] Second we consider the "third degree stochastic dominance" (TSD) shift and t,he TSD transformation and discuss their comparative statics in some economic models.

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In recent years, very high buildings have been extensively constructed to utilize the narrow urban grand space. Most of those buildings are used for offices, and some for hotels or hospitals. But, there are some plans to build a super high building to form a "compact city" which brings residence, office, and some urban facilities close together. It is expected that the people in the building can satisfy their daily needs at hand so that the amount of traffic should be reduced. In this "city type" building, the trips occur for a variety of reasons, for example, employment, school, shopping etc., which are of different types compared to those in traditional buildings. In this paper, we will discuss those traffic problems in the city type buildings. When we consider the traffic problem in a high building, the major difficulty appears in the vertical movement. Insufficient elevator area causes the complaint of the passengers for long waiting time, on the other hand, wide elevator area causes the dissatisfaction of the owner of the building having small area left for rent. For simplicity, we assume that the rest of the floor area not used for elevator are all used for residence, where people distribute uniformly. And, as for the traffic distribution, we adopt the "gravity model" in the theory of urban transportation distribution theory, in other words, a trip occurs by the interaction of a pair of people in the building, and the trip occurrence probability for the pair is equal to a constant multiplied by the deterrence factor. The deterrence factor is based on the distance between the origin and destination. We derive the equation to determine the elevator area distribution in the following way. The transportation capacity c per unit area of elevator passage is assumed to be constant irrespective of the building height. The number of trips passing through a floor is the sum of the trip occurrence probabilities for such pairs that one located above the floor and the other located below. The product of the capacity c and t,he elevator area on the floor should be equal to this amount. The equation is derived from the condition that this relation should be satisfied at each floor in the building. When the size of the building and the deterrences factor are given, the equation can be solved numerically to obtain the elevator area distribution. We solve the equations for several cases and consider the relation between the population P in the building and the number of trips T travelling through the elevator area. When the deterrence factor is small and the number of trips per person is at a high level, then population P or amount of trips per person T/P can be raised only at a very slow rate by enlarging the height, of the building. If one expects to get substantial gain in T/P or P by constructing a higher building, the deterrence factor should be made large by carefully designing the facility layout in the building. We also draw the graphs which show the suitable population size and amount of trips for the building of each height.

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There are many skyscrapers in large cities such as Tokyo, Beijing, Shanghai etc., mainly with rectangular parallelepiped shapes and some with frustum shapes, which is caused by the soaring of the land price. In a very big building with many people, it is well known that the inner traffic can not be ignored and it is important to forecast the inner traffic so that a sufficiently large inner traffic space is designed to guarantee the people to move in the building smoothly. Here, the inner traffic generally means the vertical inner traffic. Basically, there are two kinds of the inner traffic inside a skyscraper. One is the so-called Outside-Inside inner traffic, which is the traffic by the people coming from outside to inside or by the people going from inside. to outside. Another one is the so-called Inside-Inside inner traffic, which is the traffic by the people acting Within a skyscraper. As an example of Outside-Inside inner traffic, Okudaira gave a formulation in 1976. By considering the rush hours when the elevators are mostly occupied by the working people, he derived the theoretical distribution of the inner traffic area and the dwelling area in a rectangular skyscraper. Also as an example of Inside-Inside inner traffic, Taguchi gave another formulation in 1994. By considering the communication among the people inside a skyscraper, he calculated the distribution of the inner traffic area and the dwelling area in a rectangular skyscraper by combining a theoretical method and Newton numerical method. The above two models are formulated based on one kind of the inner traffic and they are reasonable for some special cases. For instance, Okudaira model may be valid for an office building during the rush hours, and Taguchi model may be valid for a residential building in the holidays. However, we daily experience that several kinds of the inner traffic generally exist in a skyscraper, for example, with respect to Inside-Inside inner traffic, there exist not only the traffic due to the communication among the people inside a skyscraper, but also the traffic caused by the allocation of a public facility etc., showing the incorporation of these traffics is meaningful. On the other hand, the above two models are limited to a rectangular skyscraper. However, there appear more and more frustum skyscrapers recently, meaning the generalization of the shape of a skyscraper is also important. Here in this paper, we give the formulation combining one Outside-Inside inner traffic and one Inside-Inside inner traffic in a frustum skyscraper. Concretely, we consider Okudaira model for Outside-Inside inner traffic, and we consider Taguchi model, the allocation problem proposed in this paper for Inside-Inside inner traffic respectively. Moreover, since most skyscrapers have the shape of rectangular type, not frustum one, also in this paper, we theoretically analyze the distribution of the inner traffic area and the dwelling area with respect to rectangular case. Finally, we apply all of them to some examples for various parameter values. The numerical analysis shows that the result obtained by Okudaira and Taguchi, which says that the remainder of building volume after taking the elevator passage is scarcely dependent on the height of the building and thus the most of the investment on a high skyscraper may be wasted, is also meaningful in such an extension. Further, it shows that the dwelling area is much more affected by the bottom area and the location of a public facility as the occuring rate of Outside-Inside inner traffic decreases in a skyscraper.

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Two characterizations are given for a valuated delta-matroid. Let (V,F) be an even delta-matroid on a, finite set V with the family F of feasible sets. It is shown that a function δ : F → R is a valuation of (V,F) if and only if, for each linear weighting p : V → R, the maximizers of δ + p form the family of feasible sets of a delta-matroid. It is also shown that δ is a valuation if and only if its conjugate function is "locally bisubmodular" at each point.

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We will discuss the role of investor's "greediness" , i.e., the investor's expected rate of return out Abstract of the investment, on the determination of the asset price in the multi-period portfolios owned by investors in the mean-variance capital market. We will derive the closed form of the equilibrium price vector and show that the average greediness of investors must be less than the expected rate of return of the market portfolio to guarantee the existence of a non-negative equilibrium price system. These results will be applied to the analysis of the "bubble" of the capital market and to the pricing of a new stock to be listed in the capital market.

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It is very important for supermarkets and convenience stores to detect fast and slow moving brands from a huge variety of merchandise as soon as possible. The present study proposes a new brand monitoring strategy for retailing where the sale of a new brand is monitored for a specific term T (> 0) and then a judgment is made in reference to whether the brand is a fast moving brand or not. More precisely, if the number of products sold on (0, T) is greater than or equal to an integer k, the brand is regarded as a fast moving brand to continue its usual sale after the monitoring period. Otherwise it, is regarded as a slow moving brand and its bargain sale is started to make space for another new brand or other standard brands. This study formulates the total loss incurred by the misjudgments under the above strategy, that is, a misjudgment of regarding a fast moving brand as a slow one and a misjudgment of regarding a slow moving brand as a fast one. The existence of an optimal strategy minimizing the total loss is then shown. Numerical examples are also presented to illustrate the proposed strategy.

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