Hao-Ching Hsia

Optimal location policy for three competitive facilities

Competitive facility location problems have been investigated in many papers. In most, authors have applied location models with two competitors. In this paper three companies, which are mutually competitive, intend to locate their facilities in a linear market. It is well-known that Nash equilibrium solution for location problem does not include three competitive facilities. In this paper we present the optimal location strategies for three facilities. In our model we assume that the demands are continuously distributed in a linear market and the facilities are locating according to a specific order of sequence, A, B and C. We apply the Stackelberg equilibrium solutions for competitive location problems with three facilities. In our model, we consider the decision problems in three stages. In the first stage, we decide the optimal location of facility A, which is located optimally in respect to the remaining two facilities B and C. In the second stage, we determine the optimal location of facility B which is optimally located in respect to facility C, by utilizing the information on the location of facility A. Finally in the third stage problem we decide the location of facility C, optimally located by utilizing the information on the location of A and B. In the first stage, we need the optimal solutions of the second and third stages. In the second stage we need the optimal solution of the third stage problem. Therefore, first we solve the third stage problem which is the simplest. After that, we solve the second stage problem utilizing the optimal solution strategy of the third stage problem. In this paper we present the optimal location strategies for three facilities.

Competitive Facility Location Problem with Demands Depending on the Facilities

In this paper, we deal with competitive facility location problems in which the demand of each customer depends on the facilities. In our models two competitive companies intend to locate their facilities on the market in order to maximize the total demand acquired from the market. The distances between the facilities and the demand points are measured by rectangular distance. At first we consider the linear model and derive the optimal policy for locating the facilities. We then extend the model to planar case and also derive the optimal policy.

On optimal location for three competitive facilities

The competitive facility location problems are investigated on many papers. In most of their papers the competitive location model with two competitors are investigated. In this paper three companies which are mutually competitive intend to locate their facilities on linear market. It is well-known that Nash equilibrium solution for location problem does not exist for three competitive facilities. In our model we assume that the demands are continuously distributed on the linear market and their facilities are locating according to specific order of sequence, A, B and C. In this paper we consider Stackelberg equilibrium solution for competitive location problems with three facilities. In our model we consider the decision problems of three stages. In the first stage problem we decide the location of the facility A which is optimally located for the remaining two facilities B and C. And in the second stage problem we decide the location of the facility B which is optimally located for C by utilizing the information on the location of facility A. Finally in the third stage problem we decide the location of the facility C which is optimally located by utilizing the information on the location of the facilities A and B.

Estimation of geographical advantage for network both within and beyond the region

In this paper we think the land price reflects to the geographical advantage. In order to analysis of accessibility, the spatial interaction model is known as a general model because it has been developed by entropy maximization principle for a long history. From observed data about traffic flow, our model can estimate traffic volume among inside and outside of target area by using observed traffic flow data. It can be regarded as a merged concept between the geographical advantage and accessibility of the spatial interaction model in unified way. The parameter estimation procedure for the proposed model is developed.

On shortest paths in free spaces including obstacles with fuzzy boundaries

In this paper we introduce definitions of norms and gauges in linear spaces in order to find shortest paths in free spaces with obstacles. Secondly, Euler-Lagrange equations in the calculus of variation give the optimal solutions for the problems of shortest paths. Thirdly we consider a linear structure in a sets of fuzzy numbers and also introduce norms in fuzzy linear spaces. Finally we discuss shortest paths in free spaces including obstacles, with fuzzy boundaries. It is useful in finding shortest paths in realistic environment with natural damage, for example, earthquakes etc.

Data Mining of Geographical Accessibility for Tourism in Regional Area

Based on an entropy maximization principle both the spatial interaction model and the discrete choice model are discussed first to clarify the meaning of the accessibility and the utility function. We next introduce a mixture of expert that is one kind of probabilistic neural network and define the preference function in the MoE. The presented model can be consider a merged one of the spatial interaction model and the discrete choice model, so the relations among the utility, preference and accessibility can be shown in a unified way. Goal is to show availability of application of those properties to data mining of geographical accessibility for tourism in regional area.

Derivation of Relations among Utility, Preference and Accessibility and Its Estimation for Urban Planning

In this study we will propose framework of derivation mechanism of utility, preference and accessibility of user based on statistical modeling. Especially, we focus on survey questionnaires such as facility location relating road administration, administration of city sight and welfare policy. In the urban planning, questionnaire survey is often used for extracting useful information. It has, however, been difficult to obtain meaningful rules for facility location problem, because such sampling data involve much ambiguity. We can list utility function, preference function and accessibility for selecting facility, as main problems which should be treated carefully. From theoretical view point, these problems should be solved in unified way for establishment of estimation. So we propose mechanism like space interaction model and discrete selection model by utilizing maximum entropy method.