Probability inequalities are known as an effective means to evaluate the upper bound of upper probability for an average of some random variables based on only limited stochastic properties, e.g., expectation, variance, and codomain for each random variable. Among them, Hoeffding probability inequality has been known as one of the best theoretical ways for evaluating the upper bound of upper probability about an average of several random variables based on limited stochastic properties such as expectation, variance and codomain in each random variable. In this study, the authors address a study for essentially improving the performance of Hoeffding probability inequality. In consequence, a new probability inequality with more superior performance than Hoeffding probability inequality is derived.

In warehouse operations, stock allocation that reduces shipment-work man-hours is necessary. The existing stock allocation recommended method (i.e., Sequential Storage Location Recommendation (SSLR) method) evaluates the storage period considering lot order and the delivery frequency of each product on the storing target pallet (PL), and stores the PL with a high delivery frequency and short storage period in a high-priority area. On the other hand, in SSLR, even if the PL is stored in a low-priority area, there is a problem that picking occurs from the low-priority area when days elapse and delivery from the PL is started. Therefore, we have developed a stock movement method in which the stored PL in the warehouse is evaluated with the evaluation value that considers the delivery frequency and storage period similar to SSLR, and which moves PLs with a short remaining storage period and high delivery frequency to a high-priority area. By combining SSLR and the proposed method, it is possible to reduce the number of deliveries from low-priority areas and prevent unnecessary occupancy of PLs having a long storage period in high-priority areas. Using simulations, it was confirmed that, by combining the method with SSLR, the man-hours for shipping can be reduced when compared to the case of SSLR alone.