I’m developing a linear program of VRP with additional features for a solver. I’m looking for a corresponding mathematical formulation of my model. The problem is a CVRP with additional features. There are 1 depot and numerous customer nodes. Each customer node has pickup and delivery demand. At first, all the pickups are collected and delivered to the depot. Then, all vehicles wait in the depo while sorting is done (sorting operation is outside the model). Afterwards, cargo is delivered from depo to delivery nodes. I found a formulation of 2echelon problem, but it doesn’t fit because I have single fleet of vehicles. Ordinary Pickup and delivery model also doesn’t fit. asked 16 Aug '16, 05:52 Ivan Zykov 
Your problem is not a VRP with pickup and delivery as pickups and deliveries are done separately. In the literature, this problem is known as the vehicle routing problem with crossdocking (the intermediate facility is known as the crossdock in the SCM and logistics). There are numerous mathematical models in the literature depicting different variations of this type of operation. I'm not sure which article considers your case as many studies considers time windows and different fleets for pickups and deliveries. However, I think the adaptation of a basic model to your case is not very hard (i.e., you have to ensure that a vehicle is not used for pickups and deliveries at the same time). The easy way is to enforce that the start of all deliveries happens after finishing all the pickups and sortings. answered 16 Aug '16, 07:33 Ehsan ♦ Thank you for the suggestion. I considered crossdocking before. As I understand, the model plans routing and sorting operations in the depo, i.e. how cargo should be interchanged between vehicles. In my case we don’t care about sorting operation, I need a simpler model. So far, I developed a modification of CVRP that seems to work, but there might be a more efficient formulation.
(16 Aug '16, 08:53)
Ivan Zykov
You're welcome. Unfortunately, I'm not aware of such formulation. In case you don't care about the sorting operations, you could omit its corresponding constraints from the model and link the pickup and delivery decisions directly. Also, if you don't have any time window constraint, then a CVRP formulation shoud be applicable to your case with some input data manipulation.
(16 Aug '16, 09:28)
Ehsan ♦
