When calculating the fare between a given pair of stations, the minimum cost path from among the many feasible paths between the stations must be determined. The railway fare for a specific path is usually calculated by distance, i.e. the longer the distance, the higher the fare. The fare rate, however, differs between railway companies and there are additional rules to be used in the fare calculation, e.g. discounts for specific paths. Therefore, the shortest-distance path is not always the minimum cost path. Most previous research efforts have focused on the enumeration of feasible paths between a pair of stations and a comparison of their resulting fares in order to choose the minimum fare for the pair. Using this approach, computational time is inevitably long. In this paper, we propose some network representations for the fare calculation of a railway network and use an efficient algorithm based on Dijkstra's algorithm to calculate fares between all pairs of 1638 stations in the area where IC-ticket (Suica/Pasmo) is usable. Our algorithm reduces the computational time because the algorithm need not enumerate a large number of paths for every pair of stations.

View full abstract

Recently, some mathematical programming approaches have been proposed for numerical analysis of stochastic processes. In this paper, we deal with the survival probability of diffusion processes, which is defined as the probability that a sample path of the diffusion process does not exceed a given value during a given time period. First, we formulate a semidefinite programming problem for the survival probability of a given diffusion process. Maximizing or minimizing the objective function representing the survival probability, we can compute upper and lower bounds for it, respectively. The constraints of the problem consist of equations derived from fundamental properties of the diffusion process and positive semidefinite conditions on moments with respect to some measures associated with the first hitting problem of stochastic processes. We confirm effectiveness of the proposed method through numerical experiments on some examples of diffusion processes.

View full abstract

In this paper, we propose to improve the applicability of the brand value evaluation model given in the "Brand value society report" published by the Ministry of Economy, Trade and Industry of Japan (the METI model). In the brand value evaluation technique, the METI model is based on publicly available financial data, so the transparency and availability of this technique are high.There is a need to select a standard enterprise in a type of business which the unit price index (Sales/Cost of sales) used for the brand value evaluation is the lowest.The unit price index of the enterprise used in the brand value evaluation is compared with that of the standard enterprise, and the brand value is calculated. However, businesses within our industry, such as telecommunications, may not have the same business operations nor cost structure. Therefore, even if the unit price index is compared, a proper calculation of brand value is difficult. We propose standard enterprise selection conditions to adjust the business domain, and cost structure. The weighted average model, which adjusts for the business domain more accurately, is proposed. The weighted average model gives a weighted average efficiency of the enterprise using the lowest unit price index, which corresponds to each business operation within the enterprise for the brand value evaluation. We examined the applicability of this proposal using an enterprise with several business operations.

View full abstract

We formulate media planning problems of newspaper advertisement as a nonlinear knapsack problem and obtain an exact solution. For ad planners, in general, decision support systems are essentials tools. An optimal media planning system, called "optimizer" in industry, plays the central role among them. However there is no guarantee that optimizers always generate truly optimal solution because computational logics equipped in those systems are usually heuristics such as greedy algorithm. In other words, planners have to blindly accept system outputs as optimal ones. We focus on the fact that many media planning optimization problems can be reformulated as problems with separable objective functions subject to a budget constraint, which can be solved by an optimization tool, called "HOPE," developed by Nakagawa et al.

View full abstract

In many universities, students are assigned to laboratories (i.e., professors) to conduct their graduation study. Since both sides of students and laboratories have their preferences, the situation resembles the stable marriage problem. But it is different in that more than one student is usually assigned to a laboratory, and only partial information about preferences is made explicit (from the consideration that the number of students is large). In this paper, we propose a scheme that contains a rational method to determine capacities of laboratories, and a modified Gale-Shapley algorithm to compute an assignment of students with a desirable stability property. Computational experiment indicates that this can be a realistic method for use in universities and other organizations.

View full abstract

In this paper, using the multi-agent cellular automaton method, we construct a simulator for evacuation dynamics of pedestrians in case of emergency, and show some natural and acceptable qualitative results. Each pedestrian decides autonomously his next target cell in his Moore neighborhood, considering environmental information in his cognitive region. Such information contains the directions of various flows in the region, the position of obstacles, indicators to the exits, the shortest paths to the exits and diffusing smoke, which are used to evaluate each cell in his Moore neighborhood. Each of these information elements has a direction and is expressed to be a vector, so called an information vector. In our simulation model two types of agents are considered, one is a leader agent who knows the shortest paths to the exits and leads non-leader agents to the exits, and other is a non-leader agent who moves depending on the flow of other agents in the cognitive region and his/her own driving force making him/her to keep the present direction. The driving force is also formulated to be an information vector. When evaluating a possibly move-to cell, we use the differences between the information vectors and the vector from the pedestrian's present position to the move-to cell, because we think that we do not necessarily move to the object showing the direction but we move along the direction. Taking account of the simple and unified approach using the difference of two vectors, we can emerge typical, easily acceptable and realistic patterns of evacuation flows and our simulator is considered to be a starting point to develop more sophisticated simulator in the future, which may be an important tool for understanding and decision making approach to complex phenomena emerged from many autonomously and interactively moving agents, for which mathematical methods may be hardly applied.

View full abstract

Metaheuristics are powerful methods used to find approximate solutions for hard combinatorial optimization problems. Successful designs of the neighborhood are required in order to construct better metaheuristics algorithms. Analysis of the neighborhood is useful for enhancing the ability of metaheuristics and will allow us to compute the probabilistic average-case analysis for the algorithm of metaheuristics. In the present paper, we attempt to construct a model that enables theoretical probabilistic analysis of the neighborhood. Therefore, we confirm the hypothesis whereby the AR(1) process captures the statistics of walks on the solution spaces of the combinatorial optimization problem and estimate the characteristic quantity on the solution spaces. In addition, we formulate a probabilistic model that captures the feature of the neighborhood using the statistics from the AR(1) process under the hypothesis that the solution variables are jointly Gaussian. However, in the common approach, the probabilistic analysis model is constructed for the restricted version of the neighborhood. Therefore, we introduce an AR(1) model that enables a probabilistic model to be formulated for various types of neighborhood. The theoretical results obtained using the concept of the AR(1) model fit the empirically observed behavior well.

View full abstract