The Travelling Salesman Problem with pick-up and delivery

Demand points for pick-up and delivery are located in the plane. A single vehicle of a given capacity performs both pick-ups and deliveries. The objective is to find the shortest feasible tour. A real life application is described. We compare this problem with the classic Travelling Salesman Problem. Based on their similarity we develop a simple heuristic consisting of pick-up and delivery along the travelling salesman tour. Asymptotic behavior and worst case analysis are provided. We then introduce an alternative solution method which is an extension of the well known Cheapest Insertion heuristic. Performance of both heuristics is tested on various-size simulated problems.