The split-demand one-commodity pickup-and-delivery travelling salesman problem

•Our problem generalizes the capacitated vehicle routing problem with split demands.•It allows that commodity can temporally be saved in a customer if convenient.•We present a flow-commodity formulation and also a Benders’ Decomposition approach.•It also solves the routing problem with split demands and minimum delivery amounts.

This paper introduces a new vehicle routing problem transferring one commodity between customers with a capacitated vehicle that can visit a customer more than once, although a maximum number of visits must be respected. It generalizes the capacitated vehicle routing problem with split demands and some other variants recently addressed in the literature. We model the problem with a single commodity flow formulation and design a branch-and-cut approach to solve it. We make use of Benders Decomposition to project out the flow variables from the formulation. Inequalities to strengthen the linear programming relaxation are also presented and separated within the approach. Extensive computational results illustrate the performance of the approach on benchmark instances from the literature.