topic Re: Vehicle Routing Problem Example (ending at depot node) in Mathematical Optimization, Discrete-Event Simulation, and OR

Vehicle Routing Problem Example (ending at depot node)

DanHouston — Wed, 17 Feb 2021 03:10:19 GMT

I am working through the example on the vehicle routing problem:

https://documentation.sas.com/?cdcId=pgmsascdc&cdcVersion=9.4_3.5&docsetId=casmopt&docsetTarget=casmopt_decomp_examples12.htm&locale=en

The description says the constraints will force the vehicles to start and end at the depot node. In the code it seems to setup a constraint to force the vehicle to start at the depot node, but I don't see anything enforcing it to end at the depot node.

When I look at the solution data there is no ARC back to the depot node to end the graph. Since I am pulling this back into VA do I just have to follow all the flows and artificially add the last arc back to the depot node or is there a constraint that would cause that to happen automatically?

Re: Vehicle Routing Problem Example (ending at depot node)

RobPratt — Wed, 17 Feb 2021 22:55:41 GMT

The EnterNode constraints force exactly one arc to enter any node (including the depot node 1) that is visited. The solution_data does contain one arc into the depot for each vehicle that is used (look for the value 1 in the j column), and these arcs appear in the PROC SGPLOT output. I suspect that you were looking at the Flow variables instead of the UseArc variables.

By the way, I will have some news to share about VRP very soon.

Update on 2/17/2021:

See this subsequent post for the news.

Re: Vehicle Routing Problem Example (ending at depot node)

DanHouston — Wed, 17 Feb 2021 14:19:38 GMT

Thanks Rob. I am using FLOW instead of useARC. I did look at both not sure why I settled on Flow. I will take a closer look at useARC (makes perfect sense why that would have it in there rather than FLOW).

Can't wait to hear news on VRP. I already have some additional questions on solving for larger problems (works fine for less than 50 nodes, but as soon as I go over that it is running over 24 hours).