Press Release
October 21, 2021
Japan Pallet Rental Corporation
National University Corporation, Gunma University

Rapid Listing of Combinations of Transport Routes with High Cooperative Effects
Development of Joint Transport Matching Technology
Japan Pallet Rental Corporation (President and CEO: Naomi Kano, Head Office: Chiyoda-ku, Tokyo, hereafterreferred to as "JPR") and National University Corporation, Gunma University (President: Yasuki Ishizaki,hereafter referred to as "Gunma University") have developed a joint transportation matching technology that
instantly lists and proposes combinations of highly efficient combined transportation using a database with many
registered transportation routes.
Labor shortages are emerging in the logistics industry, and there is an increasing need for joint transportationthat allows more cargo to be transported with fewer trucks. The use of AI and other new technologies to improvematching efficiency is also drawing attention as advanced initiatives. However, building a system that can
instantly respond to requests is difficult because even with computers, searching through the enormous number ofcombinations takes time.
Our newly developed technology makes good use of the hidden inequalities, such as the "distance axiom"
known in the mathematical field, to narrow down the search range without sacrificing accuracy. The system can
now instantly present highly efficient combinations of transportation routes that benefit from cooperation,
supporting triangular transportation—in which a single truck sequentially handles three transports, and mixed
transportation—in which freights from three transports are combined and transported simultaneously.
This technology has been installed as a core engine in the joint transportation matching system "TranOpt"
provided by JPR. Service for general users was launched on October 21, 2021. In addition, the system also usesmathematical principles by adding a function that displays the predicted freight rates for joint transportation andfair cost-sharing among the partner companies.
■ Background
With the recent logistic crises and the shortage of truck drivers becoming apparent, improving labor productivity
in the logistics industry has become an urgent issue. However, truck loading efficiency remains low, at less than
40% (*1) (trucks are loaded to only 40% of their capacity). One of the reasons for this is the vacant return trips inlong-haul transportation. JPR has thus far supported efforts toward joint transport by companies in otherindustries and other measures to carry more cargo with fewer trucks. In October 2019, JPR began developing acommon transportation matching system using AI technology in collaboration with Gunma University (*2)
recognizing the importance of creating a system for deploying such initiatives throughout the logistics industry.

From October 2019 to March 2021, this development was funded by the New Energy and Industrial Technology
Development Organization ("NEDO"). (The Project to Promote Data-Sharing in Collaborative Areas andDeveloping of AI Systems to Promote Connected Industries).
■ Technical issues
A series of transportation in which a single truck sequentially handles three transports is called "triangulartransport." The higher the occupied vehicle ratio value, the better the efficiency (Figure 1). In contrast,
transportation in which cargo is mixed together and transported simultaneously is known as "mixed transport."
The smaller the reduction ratio, the better the efficiency (Fig. 2). If Company A requests matching, the systemsearches for partners (Company B and Company C) from its database and present a list of efficient triangulartransportation and mixed transportation. If 10,000 transportation routes are registered, there are approximately
100 million combinations of two transportation routes. As it is also necessary to calculate the distance traveled,which differs according to the combination, a simple brute force calculation would take a long time using acalculator. In reality, one logistics company has multiple transportation routes. Thus, it is difficult forconventional methods to instantly respond to multiple matching requests from a single user or a series of requests
from multiple users.
Transportation routes

Joint Transportation Routes

Returning Empty Vehicle

Routes without Joint Transport

Occupied vehicle ratio =୐ୣ୬୥୲୦ ୭୤ ୗ୭୪୧ୢ ୐୧୬ୣ୐ୣ୬୥୲୦ ୭୤ ୗ୭୪୧ୢ ୐୧୬ୣାୈ୭୲୲ୣୢ ୐୧୬ୣFigure 1: Triangular Transportation

Reduction Ratio =୐ୣ୬୥୲୦ ୭୤ ୗ୭୪୧ୢ ୐୧୬ୣ୐ୣ୬୥୲୦ ୭୤ ୈ୭୲୲ୣୢ ୐୧୬ୣFigure 2: Mixed Transportation■ Developed Technology
Here's an easier explanation. In a marathon, after passing the 30 km point, the commentator says, "The possibilityof breaking the event record has narrowed down to the top three runners." Let us examine the reasoning behind this.
The result of the race is yet to be decided. However, we have the inequality that "each runner's pace per 10 km will
not exceed the 10,000 meters world record." This inequality allows us to calculate backward to find the time for arunner to pass the 30 km point to break the record. Similar arguments can be made at other points. Therefore, even if
there is undetermined information, we can effectively narrow it down by using the inequality behind it.

Suppose Company A requests a triangular transportation matching. In that case, the first route is Company A's, so
we already know the first route's starting point, endpoint, and transportation distance. The second and thirdsegments have not yet been finalized, as we are searching for partners. So we take advantage of the underlyinginequalities. We can use the "distance axiom" known in mathematics (the distance to the destination via anotherpoint is greater than the distance directly to the destination, etc.). Using distance axioms skillfully, we could
calculate backward the conditions required to achieve the specified occupied vehicle ratio. For instance, "the vacantdistance between the first and seconds route must be less than or equal to this value," and "the distance of the secondroute must be greater than or equal to this value." Therefore, we can significantly narrow the search scope. Byfurther devising the data structure and traversal order, faster enumeration becomes possible (*3).
■ Effects
Using approximately 17,000 anonymized transport data, we conducted experiments to enumerate efficienttriangular and mixed transports. Although the response times varied depending on the conditions specified, we wereable to accurately list combinations satisfying the given conditions 4,000 times faster (*4) for triangulartransportation search and 1,500 times faster (*5) for mixed transportation search compared with simple brute force
search. We can instantly respond to multiple matching requests from one user and a series of matching requests frommultiple users by utilizing this technology.
■ Contribution of Mathematics
In recent years, the importance of the explainability of AI output results has been emphasized. Although this system
uses advanced search logic, output results can be easily explained in the form of "all triangular transports with an
occupied vehicle ratio of 95% or above" or "all mixed shipments with a reduction rate of 40% or less." The validityof that narrowing (without removing any combinations that satisfy the conditions) has been mathematically proven.
Further, we have added a mechanism to calculate and display predicted transportation fares for triangular and mixed
transportation to users and the fair cost-sharing among the three companies. Fair cost-sharing is calculated based oncooperative game theory (*6). Thus, we are also using the results of our predecessors in the field of mathematics andmathematical science in addition to the developed technologies.
■ Future Development
This technology is installed as a core engine in the joint transportation matching system "TranOpt" by JPR, andthe service for general users was launched on October 21, 2021. We expect dramatic improvements in logistics as
this technology will be used widely in the future.
*1) General Principles of Logistics Policies (FY2021-FY2025)*2) The Social Mathematics Laboratory (Associate Professor Akifumi Kira) of the Faculty of Informatics (then Facultyof Social and Information Studies) is in charge of development.

*3) Patent rights jointly filed by Gunma University and JPR on October 20 (Japanese Patent Application No.

2021-171440)*4) Calculated based on the average response time of 1,000 different matching requests to accurately list the 100combinations with the highest occupied vehicle rate among those with an occupied vehicle rate of 85% or higher.
*5) Calculated based on the average response time of 1,000 different matching requests for the process of accuratelylisting 100 combinations with a reduction rate of 45% or less, starting with those with the lowest reduction rate.
*6) A mathematical theory that discusses the conditions under which cooperation among multiple actors can beachieved and the fair cost burden during cooperation〇For further information, contact
Public Relations Group, Business Development Department, Japan Pallet Rental Corporation
Tel:+81-3-6895-5215 / Fax: +813-6895-5201
Mail: pr@jpr.co.jp / Website: https://www.jpr.co.jp/english/
General Affairs Section, Faculty of Informatics, Gunma University
Tel: +81-27-220-7403 Mail: kk-shajyo1@jimu.gunma-u.ac.jp