对车辆路径问题的一个子类型进行分类

Question

I've worked on VRP problems previously, but its been several years and going through literature hasn't helped much because the variations in the problem change a lot about the solution. So I was hoping, if I laid the problem description out, someone with a bit more insight could help me identify what flavor of VRP I'm working on, or if it more closely matches something else entirely.

The problem I have is a set number of locations, 10 in my current case but this is variable. Each location has a set of shipments that need to be sent out to the other locations, the number of shipments and destinations are random so location 0 could have 1 shipment for each of the other locations, it could have 10 shipments all to location 5, or anywhere in between. All locations are directly connected, although the distance between each location is not uniform, all distance is Euclidean, so there is an element of needing to travel the longer distances as few times as possible. There is only 1 vehicle, and it can only carry 6 shipments at once, but shipments are NOT held in a queue or stack so any shipment that has been picked up can be delivered to its destination at any time regardless of when other shipments are picked up. The vehicle can carry any mix of shipments, to between 1 and 6 destinations at a time. There is no time constraint such as pick up or drop off only possible during certain hours. The vehicle can start at any one of the locations and can end at any location, and there is no limit to the number of stops at each location or number visits to each location, except that total distance traveled needs to be minimized.

It is also possible to pick up shipments, move them, and unload them at a location that is not their proper destination. This won't count as a successful delivery, but after being moved the shipment could be picked up and moved again later. I'm not sure if this changes anything about the problem since I'm restricting the problem to 1 vehicle, but it is an allowed action.

Given that description I've been trying to classify this as capacitated VRP with pickup and delivery, but when I compare my problem to examples in that area it doesn't seem like a match when I listen to lectures over it or in literature. I'm not sure if having my all locations as potential pick-up and delivery targets is skewing my understanding, or if I'm just making this problem more complicated than it needs to be, maybe it matches a simpler interpretation.

If after you read this you think I'm on the right track and that I've identified everything correctly, could you please advise me as to where/how to start or learn more. At this point if I have correctly classified the problem then I'm not really sure what my next step should be since what I've gone over in other solutions doesn't seem to match what I'm working with. Thank you.

-i used a ø in problem, because Vehicle Routing Problem wasn't allowed in the title. Sorry.

Answer 1

It is also possible to pick up shipments, move them, and unload them at a location that is not their proper destination. This won't count as a successful delivery, but after being moved the shipment could be picked up and moved again later. I'm not sure if this changes anything about the problem since I'm restricting the problem to 1 vehicle, but it is an allowed action.

The key question is whether this can actually make routes more efficient or not. If it doesn't, you can ignore this (ie don't do it) and the problem is a capacitated pickup delivery vehicle routing problem. (ie a vehicle routing problem where items are picked up from one location, dropped at another, where neither location is the vehicle depot). If you've only got one vehicle you could probably call it a "capacitated TSP with pickup and deliveries" or something similar.

If this does make routes more efficient, you're doing some kind of crossdocking, and this becomes a very complex/rich vehicle routing problem requiring a custom algorithm. This paper may be of some use?