vehicle routing.
Plan routes for a fleet that serves many locations, under time windows, vehicle capacities and driving-time rules.
Which vehicle serves which stop, in which order, so every delivery lands in its window with the fewest kilometres?
The vehicle routing problem (VRP) is NP-hard, and so are its variants. These include capacitated routing with time windows (CVRPTW), pickup and delivery (PDPTW) and multi-depot routing (MDVRP). kint formulates them as mixed-integer programs and solves them with branch and bound and cutting planes. A warm start from a good route plan shortens the search. The solver then reports how far the plan can be from the optimum.
where vehicle routing gets hard.
The number of possible route plans grows factorially with the number of stops. Even a mid-size fleet has far too many plans to check one by one.
Time windows, capacities and driving-time rules pull against each other. Fixing one often breaks another, so the set of valid plans is small and scattered.
Cancellations, new orders and traffic change the problem during the day. This morning's best plan may not be the best one at noon.
from the rules to the bound.
kint's decision agent writes the model from the planners' description. In the pilot, kint's forward deployed engineers review it with the experts. Then the solver does this.
formulate the model
Each choice of vehicle and next stop becomes a yes or no variable. Capacities, windows and driving rules become constraints. The objective is total distance or cost.
tighten with cutting planes
Additional valid inequalities shrink the search space and remove large sets of poor plans without evaluating them.
search with a warm start
A good starting plan gives the solver a reference. Branch and bound then improves it and closes in on the optimum.
report the gap
The optimality gap states how far the plan can be from the best possible one. A gap of zero means no better plan exists for the model as stated.
a vehicle routing plan, with its reasons.
Below are the parts of a vehicle routing result. Planners check them before the plan is released.
the anatomy of an answer- planA route for each vehicle with stop order and planned arrival times.
- binding limitFor example: two narrow customer windows, not the fleet size, set the total distance.
- sensitivityWhat one more vehicle, or a wider window at one customer, would save.
- bound and gapBound and gap, stored with the run.
- recordData version, model version, who reviewed the model and who released the plan.
bring us this decision.
Bring one recurring vehicle routing decision with its rules and data. Your planners get a first model they can read.
- Results
- Plan, binding limit, sensitivity, bound and gap, record
- Data centres
- Operated in Germany, or in yours
- all problem types
- routes, schedules, stock and price
- Contact
- hello@kint.pro