Many real world problems, e.g. in personnel scheduling and transportation planning, can be modeled naturally as Constrained Shortest Path Problems (CSPPs), i.e., as Shortest Path Problems with additional constraints. A well studied problem in this class is the Resource Constrained Shortest Path Problem. Reduction techniques

Pickup and delivery problems discussed in the literature often allow for only particularly simple solutions in terms of the sequence of visited locations. We study the very simplest pickup and delivery paths which are concatenations of short patterns visiting one or two requests. This restricted variant, still N P -hard, is close to the traveling salesman problem with the additional choice of what patterns to visit. We compare the number of restricted and unrestricted paths, and evaluate their respective path lengths. We conclude with two polynomially solvable cases.

Abstract. We present a generic package for resource constrained network optimization problems. We illustrate the flexibility and the use of our package by solving four applications: route planning, curve approximation, minimum cost reliability constrained spanning trees and the table layout problem. 1