A multi-objective open vehicle routing problem with overbooking: Exact and heuristic solution approaches for an employee transportation problem

Abstract

We address a bus routing problem, where individuals need to be gathered from spatially distributed pickup points and transported to a workplace. The problem is modeled as an open vehicle routing problem. Overbooking is allowed because the total seat capacity of the buses is limited. The problem is treated as a multi-objective optimization problem, where the total distance traveled by the buses and the total number of straphangers in the buses are minimized. We develop a mixed integer programming (MIP) model and employ the ε-constraint method to generate the Pareto-optimal frontier. Due to the high computational requirements of the exact model, two heuristic approaches are developed: a heuristic algorithm that is based on a cluster-first and route-second algorithm and a multi-objective evolutionary algorithm. We also develop another MIP model that provides an alternative bound to evaluate the quality of the heuristics’ solutions. Experiments on a small and a moderate-sized problem show that the heuristics are fast and approximate the optimal solutions well. The heuristic approaches are then used to solve the actual problem having 103 pickup points, 50 buses and 1986 individuals. A set of approximate solutions whose total transportation distances are at most 14% worse than the best lower bounds are obtained.