Shogo Shiode

A competitive facility location problem on a tree network with stochastic weights

Abstract We consider n demand points on a tree network. Two competitive companies plan to construct their own facilities on this network in a certain order. We assume that the weights of demand points at the entry time of the follower, used by the leader in his decision, are stochastic. We also assume that each customer utilizes the nearest facility to him. The objective of each company is to locate its facility so as to maximize the captured buying power after the follower’s entry. We analyze the problems and present an efficient solution procedure to find a Stackelberg equilibrium solution.

A Threshold-Satisfying Competitive Location Model

In this paper we consider a location model based on the threshold concept. We find the best location such that the probability of revenue falling short of the threshold is minimized. This objective is appropriate when a firm will not survive if its revenue falls below a known threshold. A new store is to be located. Demand is not deterministic but rather has a statistical distribution. We seek the location at which the probability that the revenue (expressed as market share attracted by the new store) is below a given threshold is minimized. The model is formulated and solved, and computational results are given.

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.

Analysis of unplanned purchase rule based on rough set

The consumer with some intention to buys visits the store, and he purchases some commodities including the commodity that fills the intention. Such consumers purchase decision making in the shop is divided into planned purchases and unplanned purchases. Planned purchases are that the consumer purchases it based on the intention to buy formed before the consumer visits the shop. The unplanned purchase is that the intention of the purchase that the consumer has not expected before it enters the shop is generated in the store, and the consumer purchases it. It is clarified that unplanned purchase rate in the retail store is higher than the United States in Japan. Therefore, it is important for sales increase to analyze unplanned purchases of the consumer in the inside of a store. Some conventional researches have reported the situation where unplanned purchase happens and the occurrence factor of impulse buying from the consumers viewpoint. Although conventional research has connected the regulation factor to the unplanned purchase directly, a consumer may constitute potential purchase desire. So, in this research, we analyze unplanned purchase based on rough set. Using the results, we clarify the process which results in unplanned purchase.

A distribution map for the one-median location problem on a network

In this paper we consider the Weber (one-median) location problem on a network. The weights at the nodes are drawn from a multivariate normal distribution. We find the probability that the optimal location is at each of the nodes. This set of probabilities is the distribution map. The methodology is illustrated on two networks of 20 nodes each.

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.

Improvement of Achievement Level Using Student’s Relational Network

The teacher is requested to do a high-quality lecture to the solution of the issue of decline in academic ability. It is difficult to understand for the teacher the student’s achievement level. Therefore, there is a difference of understanding between the teacher and the student. Then, to understand student’s achievement level, we execute the questionnaire. And, we discuss the method of making the best use of the result from the analysis for the lecture improvement. As a result, the teacher can control the degree of progress of the class. Thereby, it is thought that the student can deepen understanding of the learning more. Furthermore, it is thought that we can expect the improvement of the achievement level by sending a student having a high achievement level of the group if I can constitute the social network of the friendly relations of the student.

The Self-Organizing Map Applying the "Survival of the Fittest Type" Learning Algorithm

The self-organizing map that Kohonen has proposed maps high-dimensional vector data to low-dimensional space by phase conservation. And, it generates the feature map that visually catches the similarity among data. In addition, the reference vector where the unit in a competitive layer of SOM is achieved can interpolate an intermediate vector of the input vector data. In the pattern recognition of the class label, SOM that adds the class label to the element of the pattern and learns is especially called to be the supervised SOM. We propose SOM based on the survival of the fittest type learning algorithm to solve the problem of the delay and the over-training. As a result, the learning of the survival of the fittest type becomes possible, a needless node is excluded, and the probability density function can be presumed by the optimal number of nodes.

Location Game with Facility Dependent Fuzzy Demand

We consider a non-cooperative facility location game by two competitive companies on a linear and a planar market with discrete demand points. The leader and the follower locate their branch shops in the market one by one in order to maximize their own profit, which is assumed to be proportional to the amount of demand taken in their territories. The feature of this paper is that the demand is assumed to be vague and different according to each facility. We consider two types of problems, i.e., to find the optimal location for the follower and to find that for the leader. We formulate these problems with fuzzy number and solve them by using some properties derived in this paper.