A Hybrid Method to Solve a Pick-up and Delivery Problem with a Helicopter

The pick-up and delivery problem (PDP) consists in finding a set of optimal routes for a fleet of vehicles respecting the precedence and pairing constraints and visiting all transportation requests. The transport of personnel on oil platforms is a real application of PDP which we are interested in. The problem is modeled as a set covering problem that is solved via a column generation technique. A hybrid method, Dynamic Programming/Taboo Search, is presented to solve the subproblem and obtain valid routes. Based on all the routes found, the relaxed master program is solved and a lower bound is found. Starting from this partial solution a branch and bound method is used to find an integer solution. The algorithms are tested on random and real instances. The results show that the hybrid method reduces the CPU time and increases the number of problems solved. Introduction. The Pick-up and Delivery Problem (PDP) consists in finding a set of optimal routes for a fleet of vehicles in order to serve all of the transportation requests. Each one of these transportation requests is defined by a pickup and a delivery location, and a load. Several types of Pick-up and Delivery problems exist: these problems can comprise time windows (PDPTW) or not (PDP) and can have one vehicle (1-PDP) or several (m-PDP) vehicles. The objective function can also vary. In the majority of these problems, the vehicles are cars (passenger transportation) or trucks (freight transportation). A summary of methods to solve 2000 Mathematics Subject Classification. Primary: 90B06, 90C08; Secondary: 90C39, 90C90.