Vehicle routing problems with regular objective functions on a path



We investigate the problem of scheduling a fleet of vehicles to visit the customers located on a path to minimize some regular function of the visiting times of the customers. For the single-vehicle problem, we prove that it is pseudopolynomially solvable for any minsum objective and polynomially solvable for any minmax objective. Also, we establish the NP-hardness of minimizing the weighted number of tardy customers and the total weighted tardiness, and present polynomial algorithms for their special cases with a common due date. For the multivehicle problem involving n customers, we show that an optimal solution can be found by solving math formula or O(n) single-vehicle problems. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 61: 34–43, 2014