Ushio Sumita

Optimal threshold analysis of segmentation methods for identifying target customers

In CRM (Customer Relationship Management), the importance of a segmentation method for identifying good customers has been increasing. For evaluation of different segmentation methods, Accuracy often plays a key role. This indicator, however, cannot distinguish two types of errors. The purpose of this paper is to overcome this pitfall by introducing two different indicators: Recall and Precision. Assuming that a promotion is addressed exclusively to the selected target customers, the financial effectiveness of the underlying segmentation method is expressed as a function of Recall and Precision. An optimization problem is then formulated so as to maximize the financial measure by finding the optimal threshold level in terms of the severeness for estimating the target set. By introducing a functional form which represents correctness and mistakes about the target set, the unique optimal solution is derived explicitly. The proposed approach is validated by using real customer purchase data.

Dynamic Analysis of a Unified Multivariate Counting Process and Its Asymptotic Behavior

The class of counting processes constitutes a significant part of applied probability. The classic counting processes include Poisson processes, nonhomogeneous Poisson processes, and renewal processes. More sophisticated counting processes, including Markov renewal processes, Markov modulated Poisson processes, age-dependent counting processes, and the like, have been developed for accommodating a wider range of applications. These counting processes seem to be quite different on the surface, forcing one to understand each of them separately. The purpose of this paper is to develop a unified multivariate counting process, enabling one to express all of the above examples using its components, and to introduce new counting processes. The dynamic behavior of the unified multivariate counting process is analyzed, and its asymptotic behavior as 𝑡→∞ is established. As an application, a manufacturing system with certain maintenance policies is considered, where the optimal maintenance policy for minimizing the total cost is obtained numerically.

Analysis of value chain coordination via revenue-sharing for improving the expected profits

Recently, the value chain coordination has been drawing much attention of both researchers and practitioners. One of the most prevalent approaches would be “revenue-sharing”, where a supplier providing products to a retailer works together with the retailer, and the two parties agree upon a contract so as to increase their respective profits. More specifically, the wholesale price of the supplier to the retailer is reduced to w, and in exchange, the retailer would return the (1 – θ) portion of its revenue to the supplier. The purpose of this paper is to analyze this revenue-sharing scheme by exploring the θ - w plane and the order quantity Q for improving the expected profits of both the supplier and the retailer. In particular, the region of (θ, w) is identified explicitly, in which the improvement for both would be assured. Furthermore, several new scenarios are proposed, along which the two parties may reach agreement comfortably.

On non-existence of Nash equilibrium of M person game with pure strategy for delivery services

A competitive market model is considered with M suppliers and N customers, where each supplier provides a homogeneous service such as delivering propane gas cylinders and has to offer a uniform price upon delivery to all customers. Given a price upper bound U, the model is formulated as an M person game with pure strategy. It is shown that the M person game has the unique Nash equilibrium if and only if each customer can be serviced by at most one supplier. Furthermore, this unique Nash equilibrium is peculiar in that all suppliers adopt the same upper bound price U. In general, the M person game does not have any Nash equilibrium. For such a case, it is demonstrated that the suppliers continue to exercise their price strategies in a cyclic manner indefinitely.

Impact of skeleton imports on hollowing out production bases outside Japan

Many Japanese manufacturing companies have moved their production facilities partially or completely to China and other Asian countries, and the products produced at such oversea production bases are reversely imported into Japan. While this hollowing out production bases outside Japan enables them to reduce the labor and other operation costs, it incurs the extra logistics costs. In addition, the market lead time becomes inevitably longer, resulting in the increased inventory costs. In order to compensate these negative effects, certain Japanese companies have been implementing the SI (Skeleton Imports) strategy, where a variety of products in small quantity would be designed in such a way that a common frame (called Skeleton) can be used for all the products and various product specifications can be mounted onto the common frame to produce a variety of products in small quantity efficiently. The purpose of this paper is to analyze the positive effects of the SI strategy via simulation.