Or-tools: Global SpanCost coefficient

[TeodoraB21]

Can someone explain me, on an example, how is the cost calculated if I set global span cost coefficient over the distance dimension?

[Mizux]

You can then set a cost equal to the maximum of the total distances along each route.

https://developers.google.com/optimization/routing/vrp#distance_dimension

which is computed as:

cost_coefficient * (
  max({CumulVar(end_1),...,CumulVar(end_k)}) - 
  min({CumulVar(start_1),...,CumulVar(start_k)})
)

https://developers.google.com/optimization/routing/vrp#dimension_details

note: usually your vehicles start at 0 (if you set start_cumul_to_zero to True)

e.g. in the VRP examples https://developers.google.com/optimization/routing/vrp#solution you have:

Route for vehicle 0:
 0 -> 8 -> 6 -> 2 -> 5 -> 0
Distance of route: 1552m

Route for vehicle 1:
 0 -> 7 -> 1 -> 4 -> 3 -> 0
Distance of route: 1552m

Route for vehicle 2:
 0 -> 9 -> 10 -> 16 -> 14 -> 0
Distance of route: 1552m

Route for vehicle 3:
 0 -> 12 -> 11 -> 15 -> 13 -> 0
Distance of route: 1552m

So the global span cost will be: 100 * 1552 = 155200 added to the objective.
here: 100 because the example set it...

 # Try to minimize the max distance among vehicles.
  distance_dimension.SetGlobalSpanCostCoefficient(100)

[TeodoraB21]

And if I have a time matrix and I add it as a new dimension and I set a span cost coefficient, how will influence the final cost?

[Mizux]

the final cost will be the sum of all arc cost used + coef * (max(VehicleEndTimes) - min(VehicleStartTimes))

VehiclesEndTime being time_dimension.CumulVar(routing.End(vehicle_index)) for all vehicles...

Each dimension is just a "int" increasing/decreasing along the route of each vehicle with few constraints on it, so it can be distance, time(duration), capacity, whatever....