Across Japan, a quiet revolution in the way cargos share space is unfolding. A team from Kyushu University’s Institute of Mathematics for Industry, in partnership with the Japan Pallet Rental Corporation, has built a mathematical compass for logistics that points toward fewer miles and cleaner trucks. The centerpiece is a form of joint transport they call mixed transportation, where several shipments ride together in a single truck and unload in a reverse sequence. The payoff is simple to measure: the total distance driven is shortened when shipments cooperate.
Lead author Akifumi Kira and colleagues have turned this idea into a computational tool that can enumerate all practical mixed transports that meet a target efficiency, far faster than brute-force checking. In a field where every extra path to a solution can waste time and fuel, speed is more than a convenience—it’s a lever for real-world adoption. The work sits at the intersection of math, computer science, and logistics policy, and it ties directly into programs like TranOpt, a matching service developed with JPR that already serves hundreds of companies as of 2024.
What is mixed transport and why it matters
The basic idea is deceptively simple: instead of sending one shipment at a time, a single truck carries several lanes at once, loading them in a given order and unloading in reverse. When the trucks travel together, their routes form a kind of three-point triangle, and the distance saved comes from avoiding backtracking and extra trips. The study formalizes this idea with a handful of distance variables that describe how far each leg of the journey is when shipments are combined versus when they go solo.
What makes it powerful is the reduction rate: a single number that captures how much the total loading distance shrinks when cooperation happens. The reduction rate has a theoretical floor at 1/3 in the simplest three-lane case, but the real magic is in the algorithmic ability to sift through thousands of potential triplets and show you which ones actually pay off. In practice, this means logistics planners can see viable partners and mixed routes almost instantaneously, rather than waiting hours for optimization to run its course.
In context, the idea isn’t just math for math’s sake. Logistics companies in Japan and beyond face driver shortages and pressure to reduce emissions. Government policy increasingly enshrines collaboration as a route to higher productivity, a shift from isolated optimization to broader, cooperative optimization. TranOpt is already used by more than 260 companies as of November 2024, a testament to how quickly such ideas can move from theory to practice.
How the pruning algorithm turbocharges discovery
The simple brute-force approach to finding mixed transports would try every possible pair of partners for a given first lane, then check whether the resulting journey meets the target reduction rate. That naive method explodes in number of combinations as the network grows—a few thousand lanes balloon into tens of millions of checks. The paper proposes a smarter plan: a pruning strategy that rules out impossible branches early by exploiting distance bounds and the structure of mixed transport logs.
Central to the method are a sequence of necessary conditions, captured in what the authors call Lemmas 3.1 through 3.4. In plain terms, they encode simple geometric truths: if certain distances are already too large, or if combining a candidate third lane would push the reduction rate above the target, then we can stop worrying about that branch. That lets the algorithm skip vast swaths of the search space without sacrificing correctness, delivering speed-ups that feel almost magical in the numbers the paper reports.
The authors also show how to extend the basic approach to return the top k mixed transports—those with the smallest reduction rate—so decision-makers can pick the very best options. They implement a practical version using a binary heap to keep only the best candidates, and they demonstrate dramatic performance improvements in large real-world datasets: on a set of about 17,000 lanes across Japan, the fast-pruning version ran thousands of times faster than brute force. In one scenario, it was about 7,000 times faster; in another, around 400,000 times faster.
What this could mean for logistics and the planet
At first glance, this is a piece of specialized mathematics. But its ripple effects could touch the way goods move around the world. A higher-speed way to enumerate effective joint transports means logistics networks can be coordinated more nimbly, reducing empty miles and idle driving, cutting fuel use, and lowering emissions. The paper notes that truck loading efficiency is already surprisingly low—under 40 percent in typical operations—and supplies a blueprint for lifting that performance through collaboration rather than individual optimization alone.
Beyond the numbers, the study speaks to a broader shift in how businesses think about competition and cooperation. If a tool can reveal the best partnering combinations in a glance, small and medium shippers gain access to efficiency that used to be the preserve of large fleets. The work is tied to real-world projects, including a NEDO-funded push for white logistics, where cross-industry cooperation becomes a shared infrastructure for a more reliable supply chain. Kyushu University and JPR are named partners, with the Institute of Mathematics for Industry leading the mathematical development.
There are caveats, of course. The research focuses on triads of lanes (three-way mixed transport) and uses historical lane data rather than live, dynamic routing. Extending the approach to larger groups or to real-time changes will require new ideas and careful validation. Still, the core insight stands: with the right data and the right pruning logic, the math can turn a sprawling search into a precise, actionable list of options in seconds rather than hours. If these ideas scale, the logistics industry might move closer to a world where cooperation is the default, not the exception.
