Distribution Network Configuration Considering Inventory Cost

Inter-city distribution network structure is considered as one of which determine the quantity of economic activities in each city. In the field of operations research, several types of optimal facility location problem and algorithms for them have been proposed. Such problems typically minimize the logistic cost with given inter-city transportation cost and facility location cost. But, when we take inventory to coop with fluctuating demands into account, facility size becomes different for each location reflecting the level of uncertainty of demand there. As observed in many developed countries, customers require more variety of commercial goods, and we must prepare more number of commercial goods. Moreover, life length of each product becomes shorter. Without highly organized management, large inventory for many products yield large risk of depreciation of commercial value as well as large cost for floor space for stocking. Considering those, inventory cost should be explicitly considered in distribution network configuration problem. There is an essential trade off between inventory cost and transportation cost: when you set smaller number of distribution center having thicker demands there, relative stock size to coop with fluctuations become small and then, we need less inventory cost. But such concentrated location pattern results longer transportation to the customers and larger transportation cost. Nozick and Turnquist(2001) formulated a two-echelon distribution network formation problem considering inventory cost at plant and distribution centers. They used optimal inventory assignment considering the expected penalty of distribution center stock-out and plant stock-out. Stock-out was considered as the situation when Poisson distributed demand exceeded stock size, and the mean demand there was given by optimal facility location model. Inventory size of distribution center alters the location cost of distribution center, therefore optimal facility location problem was refreshed and solved again. The paper proposed iterative algorithm to get optimal inventory locations. Our paper expands their model in two ways; first we admit the difference of unit location cost for distribution centers by geographical locations, and secondly, we consider different uncertainties for customer orders by departing from simple Poisson distribution. The first alternation gives new explanation for the following situations: highly dense metropolitan regions have relatively larger number of centers and smaller coverage of each center. But such propensity usually contradicts with the land price; then center location should be limited considering higher land price in metropolitan areas. Then the optimal locations cannot be prospected in straight forwardly. The second model expansion allows our model to analyze how regularity of demands affects on the network structure. Our paper applies the model to the realistic Japanese transportation network, and show which cities may possess distribution center function in the nationwide distribution network. Without the back-stock in plant level, each distribution center must prepare inventory for their demand, but such inventory sometime requires unrealistic large location cost in metropolitan area such as Tokyo. On the other hand, if distribution center can rely on the back stock in plant, the centers in metropolitan regions stand without their own inventory.

Robustness of optimal inter-city railway network structure in Japan against alternative population distributions

It takes long time and huge amount of money to construct inter-city railway network. Careful demand forecasting and rational service planning are therefore required. However, long ranged demand forecasting is always facing to unintended change of regional population or change of the service level of competing transportation modes such as airline and inter-city express bus. Those changes sometimes resulted in severe decrease of demand for the constructed railway lines and discussion of abolishment of train service occurs. In order to avoid such tragedy, we want to build a robust network plan not vulnerable for the changes in forecasting conditions. This paper discusses the robustness of optimal inter-city railway network structure in Japan against alternative population distributions. Genetic Algorithm is applied to find best mixture of maximum operation speed category and number of daily train service for each link, which maximize the total consumer surplus of inter-city railway passengers. Consumer surplus is assessed by a gravity demand model considering service level along several routes for each OD pair. Travel time calculated by allocated link speed category, allocated train frequency, and estimated fare regressed by travel speed, will be summarized as route service level via ML route choice model parameters. In the GA, we consider a chromosome consists of two parts; speed category of 275 links and relative operation distance of trains in those links. Besides the real distribution of population in 197 Japanese local areas in the year of 1995, we set four other hypothetic population distributions; two of them concentrate in megalopolises like Tokyo, others disperse along geographically remote areas. We first obtain network structures optimized by the GA for each population setting. Speed category allocation will be compared for the five network plans. Secondly, we calculate total consumer surplus of each network plan under the different population settings and discuss the vulnerability of those plans. Thirdly, we optimize train operation plans for different population settings under the given speed category arrangements. The results shows that spatial arrangement of high speed railway service in 1995 keeps optimality for wide range of population settings, if we adjust number of trains according to alternative population distribution.

U_A(1) Breaking Effects on the Light Scalar Meson Spectrum

Effects of the U_A(1) breaking interaction on the low-lying nonet scalar mesons are studied using the extended Nambu-Jona-Lasinio model. The strength of the U_A(1) breaking interaction is determined by the electromagnetic decays of the eta meson. We find that the U_A(1) breaking interaction gives rise to about 150 MeV mass difference between the sigma and a_0 mesons. We also find that the strangeness content in the \sigma meson is about 15%. The calculated mass of the I=1/2 state is about 200 MeV heavier than that of the I=1 state. The order of these masses is not likely to change within this model.Comment: 10 pages, 3 figure

Robots and Privacy in Japanese, Thai and Chinese Cultures. \ud Discussions on Robots and Privacy as Topics of Intercultural Information Ethics in ‘Far East’

In this paper, I will analyze ‘cultural meanings and values’ associated with some of the important IIE(intercultural information ethics) topics in ‘Far East, ’i.e. ‘human and robot interaction(HRI)’ and ‘privacy.’ By focusing on these relatively newly emerging topics in ‘Far East,’ I will attempt to make the cultural Ba (locus/place where different\ud meanings of things, events, people’s experiences come together; or frameworks for understanding meanings of phenomena and events) visible through analysis of research data done in Japan, Thailand and China in the past several years. The research data shown in this paper suggest that we can’t understand people’s attitudes toward robots and privacy in ‘Far East’ without taking into consideration people’s broader views on ‘what is a good life?’ and ‘what is a virtuous life?

Iteration Algebras for UnQL Graphs and Completeness for Bisimulation

This paper shows an application of Bloom and Esik's iteration algebras to model graph data in a graph database query language. About twenty years ago, Buneman et al. developed a graph database query language UnQL on the top of a functional meta-language UnCAL for describing and manipulating graphs. Recently, the functional programming community has shown renewed interest in UnCAL, because it provides an efficient graph transformation language which is useful for various applications, such as bidirectional computation. However, no mathematical semantics of UnQL/UnCAL graphs has been developed. In this paper, we give an equational axiomatisation and algebraic semantics of UnCAL graphs. The main result of this paper is to prove that completeness of our equational axioms for UnCAL for the original bisimulation of UnCAL graphs via iteration algebras. Another benefit of algebraic semantics is a clean characterisation of structural recursion on graphs using free iteration algebra.Comment: In Proceedings FICS 2015, arXiv:1509.0282

Mixing property and pseudo random sequences

We will give a summary about the relations between the spectra of the Perron--Frobenius operator and pseudo random sequences for 1-dimensional cases.Comment: Published at http://dx.doi.org/10.1214/074921706000000211 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org