Due to the rapid growth of electronic commerce via the Internet, there is a need to streamline the supply chain in order to reduce product distribution costs and shorten delivery lead times. Among these, the role of distribution centers that connect physical and commercial distribution has become more important. Improvement in work efficiency in the distribution centers has also become an important theme.

Aware of such problems, we focus on order picking operations where products are collected based on the customer order since it is one of the most labor-intensive activities in the distribution center. We consider methods to shorten the average traveling distance of order-picking operators from two perspectives: 1) Improving the floor layout of the distribution center, and 2) introducing better management rules to determine the storage position of products.

In the first half of the paper, the mathematical model to evaluate the average traveling distance of the picker is proposed. The model proposed assumes that the width of the aisle and the size of the shelf are sufficiently small, and obtains the value of the traveling distance analytically. In addition, improvement measures are considered from the two perspectives stated above, and are evaluated by comparing with the case in conventional Traditional Layout with horizontal and vertical aisles.

In the second half of the paper, two improvement measures combining the two perspectives are proposed based on the results of the first half of the paper. Both measures move the accumulation point of products to the center of the lower side of the floor. In addition, the first measure adopts the addition of a diagonal aisle on the floor and classbased management to determine the storage position of products. The second measure executes class-based storage in an area where the work floor is divided using diagonal straight lines, which means being equidistant from the accumulation point of products.

As a result, this paper clarifies that the two improvement measures proposed in the second half of the paper shorten the average traveling distance by 25% or more compared to case in conventional Traditional Layout.

In this paper, we propose a two-stage approach to schedule a double round-robin tournament. In the first stage, we create a home-away table (HAT) satisfying basic round-robin constraints with minimal breaks, as well as some constraints to improve the enjoyment of matches. In the second stage, we aim to find an assignment in which each team is assigned to exactly one row of the HAT generated, considering the total travel distance for each team. Finally, we show that the approach proposed successfully generates a yearly schedule for J1.League.

Hoeffding probability inequality has been known as the best theoretical way for evaluating the upper bound of upper probability about the average of some random variables based on limited stochastic properties such as the expectation, variance and codomain in each random variable. In this study, based on Hoeffding probability inequality, we address a numerical analysis procedure for improving the performance to evaluate the upper bound of upper probability about the average of some random variables.