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.