A railway fare for a specific path is usually determined by the distance, i.e. the longer the distance, the higher the fare. The fare rate, however, is sometimes different by area even within the same railway company. In addition, many of companies have additional rules to be used in the fare calculation, e.g. discounts for specific paths. In order to calculate the fare between a given pair of stations, we have to find the minimum cost path, but the shortest path (in the physical sense) is not always the minimum cost path for the reasons mentioned above. In the past, most of the efforts have been focused on an 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. This approach has inevitably led to a problem of a very large computational time. In this paper, we propose a much more efficient algorithm which basically uses the Dijkstra's algorithm with a modification which reflects the existence of a set of subnetworks which have their own fare rates. Our algorithm dramatically reduces the computational time, because the algorithm need not enumerate a large number of paths for every pair of stations.

View full abstract

Credit risk is the risk of loss stemming from borrower's default. We consider the credit risk minimization problem and propose an optimization method for minimizing the risk measured by Conditional Value-at-Risk (CVaR) criterion. Default of firms is modeled by the corporate valuation model and the factor analysis of time series data of TOPIX Sector Indices, scenarios of defaults are generated, and then CVaR minimization problem is solved. By varying the number of factors incorporated in the model as well as the coefficient that determines the impact of factors peculiar to industry type, we observe how economic trend, industry type and rating of the firms influence the defaults and the credit risk. A large number of scenarios are required to obtain a reliable implication; however, the CVaR minimization problem becomes harder to solve. We propose a simple but effective pre-treatment of the scenarios and also a solution technique. We solved the problem with a hundred thousand scenarios in about 7 seconds and that with half a million scenarios in about 35 seconds.

View full abstract

Exact closed-form solution of (2-2)-thinning input queue with exponential single server is given in this paper. The (2-2)-thinning input queue is a special case of general (m-n)-thinning input queue. The (m-n)-thinning input process is constructed by thinning customers from a Poisson arrival process repeating the thinning procedure such that m-consecutive arrivals are picked up and next n-consecutive arrivals are discarded. Interarrival-time sequence of the (m-n)-thinning input process is not a sequence of i.i.d.r.v's. To analyse the (2-2)-thinning queue, generating function, phase-method, Rouche's theorem, and Sturm's theorem are used.

View full abstract

The shortest path problem can be widely applied not only to route search in large-scale network but to other optimization problems where the shortest path problems are used as subproblems. Although there exist stable and efficient algorithms for the shortest path problem, we need fast implementations when solving large-scale shortest path problems. In this paper, we discuss how to make fast and general implementations of Dijkstra's algorithm, where the memory hierarchy is carefully considered to specify the bottleneck of the algorithm and to improve the performance. Our implementations with the binary heap are superior to other existing implementations when taking three factors (performance, robustness, and required computational memory) into consideration. We show that our implementations can get optimal routes very quickly and require smaller computational memory compared with other implementations through systematic numerical experiments. We also explain the Web service for large-scale shortest path problems, which employs our implementations.

View full abstract

Since baseball has been a big business that produces a large amount of money, it becomes important for baseball teams to compose an optimal batting order that maximizes expected runs, Using "markov chain model to estimate the expected runs (Covers et al. 1977)", an expected runs of a certain batting order will be computed. However, it takes an O(n^9) time to reach an optimal batting order in the case of n-batters set. Therefore, we adopt a kind of heuristic method to find a near-optimal batting order instead of finding an optimal one by modeling this problem as a matching problem. To define it as the matching problem, which assigns players to proper line-up positions, we need to quantify "required function of each line-up position", "ability of each player", and "degree of conformity of each line-up position with each player". In this paper, we focus on quantification of "required function of each line-up position". In our quantification method, the required function of each line-up position is quantitatively extracted for giving an evaluative to find a near-optimal batting order. In addition, we evaluate our method in two steps. First, we evaluate the valid of "our quantification method of required function". Second, we evaluate "our matching problem" from the following four viewpoints: 1. Accuracy of expected runs; 2. Computational Effort; 3. Scalability of the method; 4. Conviction of the method; by comparing existing methods.

View full abstract

We introduce a maximal covering model for EMS-Helicopter system in which helicopters are used to transfer patients in critical need of care to a hospital. Locations of both helipads and stations are determined so as to maximize demands accessible to helicopter transportation. We focus on two different dispatching rules on transportation time; one is the total time of transporting a patient to a hospital by helicopter and the other is the amount of time reduced by transporting a patient to a hospital by helicopter compared with transporting a patient directly to the hospital by ambulance. Two types of coverage objectives are introduced for these rules. The first type considers that a given demand is covered when the transportation time is within the given threshold while the second type considers that a given demand is covered when the amount of time reduction is short enough. Optimal locations of both helipads and stations are analyzed using an idealized city model for various values of coverage times. We also examine how the existence of a geographical barrier affects the optimal design of EMS-helicopter system.

View full abstract

In this paper, we propose a fuzzy approach for fuzzy random multiobjective linear programming problems (FRMOLP), in which the criteria of probability maximization and fractile optimization are considered simultaneously. In a probability maximization model for FRMOLP, the decision maker is required to specify permissible objective levels for the objective functions involving fuzzy random variables. However, the less values of permissible objective levels for minimization problems results in the less values of the corresponding distribution function because of the con icts between them. Similarly, in a fractile optimization model for FRMOLP, the decision maker is required to specify permissible probability levels for the distribution function of the objective functions involving fuzzy random variables. However, the larger values of permissible probability levels results in the larger values of the corresponding objective function for minimization problems because of the con icts between them. In this paper, it is assumed that the decision maker has fuzzy goals for not only permissible objective level of a probability maximization model but also permissible stochastic level of a fractile optimization model, and such fuzzy goals are quanti ed by eliciting the corresponding membership functions. According to the fuzzy decision, the satisfactory solution of the decision maker for FRMOLP is obtained on the basis of linear programming technique.

View full abstract