A two-layer decision problem: strategic facility siting combined with operational vehicle routing. Minimize depot opening cost + fleet cost + total travel distance — subject to capacity and assignment constraints.
The Capacitated Location Routing Problem (CLRP) is an optimization problem that combines two layers of decision-making: strategic decisions about where to open depots and operational decisions about how to route vehicles from those depots to serve customers.
Given a set of potential depot locations (each with an opening cost, a capacity limit, and a maximum number of vehicles) and a set of customers with known demands, the goal is to simultaneously decide which depots to open, assign customers to open depots, and design vehicle routes that minimize the total cost.
These three decisions are tightly coupled. Solving them independently is feasible but far from optimal — the central challenge is exploiting their interaction.
Which depots to open from a set of potential locations. Each depot has an opening cost fi, a capacity Wi (maximum total demand), and a limit on the number of vehicles it can accommodate.
StrategicEvery customer must be assigned to exactly one open depot and visited by exactly one route from that depot. No customer can be split across depots or routes.
TacticalFor each open depot, design routes for a fleet of identical vehicles. Each route starts and ends at its depot; the total demand on a route cannot exceed the vehicle capacity Q.
OperationalA miniature CLRP instance — five depot candidates, three chosen. Every client is assigned to exactly one open depot; each open depot operates a small set of routes that respect vehicle capacity. Closed candidates are crossed out; each open depot and its routes share a color.
FIG 02 · n = 30 clients · |D| = 5 candidates · 3 opened · vehicle capacity Q = 65
A three-part objective captures the trade-off between opening fewer depots (cheaper strategically) and routing efficiency (which may require depots closer to customers).
Five constraint families define feasibility. Capacity tightness is a tuning dimension of the instance set — some instances will leave little slack.
| Constraint | Description |
|---|---|
| Customer service | Every customer is visited exactly once by exactly one route. |
| Depot assignment | Each route operates from exactly one open depot. All customers on a route are assigned to that depot. |
| Vehicle capacity | The total demand of customers on any single route does not exceed the vehicle capacity Q. |
| Depot capacity | The total demand assigned to a depot does not exceed its capacity Wi. |
| Vehicle limit | The number of routes operating from a depot does not exceed its maximum number of vehicles mi. |
The CLRP is directly relevant to Mexican industry. Companies such as OXXO, Bimbo, and FEMSA routinely face decisions about where to place distribution centers while simultaneously optimizing delivery routes. This problem captures the essence of those real-world decisions.
From an algorithmic perspective, the CLRP sits at a difficulty sweet spot: it combines strategic facility location with operational routing, so no single algorithmic paradigm dominates. The competition is open to metaheuristics, decomposition methods, branch-and-price, matheuristics, machine learning, and hybrid approaches.
Compared to the well-studied CVRP, there is significantly less benchmark saturation for the LRP. This challenge fills a genuine gap — any results carry higher novelty for the community.
Instances are generated by an open-source Python generator released in June 2026. Variation across dimensions prevents over-specialization.
The mathematical formulation, instance file format, solution file format, and the solution verifier will be published alongside the instance generator in June 2026. A set of mock instances with feasible solutions will also be provided at that time.