  The logistics industry in Japan is facing a severe shortage of labor.
Therefore, there is an increasing need for joint transportation allowing large
amounts of cargo to be transported using fewer trucks. In recent years, the use
of artificial intelligence and other new technologies has gained wide attention
for improving matching efficiency. However, it is difficult to develop a system
that can instantly respond to requests because browsing through enormous
combinations of two transport lanes is time consuming. In this study, we focus
on a form of joint transportation called triangular transportation and
enumerate the combinations with high cooperation effects. The proposed
algorithm makes good use of hidden inequalities, such as the distance axiom, to
narrow down the search range without sacrificing accuracy. Numerical
experiments show that the proposed algorithm is thousands of times faster than
simple brute force. With this technology as the core engine, we developed a
joint transportation matching system. The system has already been in use by
over 150 companies as of October 2022, and was featured in a collection of
logistics digital transformation cases published by Japan's Ministry of Land,
Infrastructure, Transport and Tourism.
