Optimization of occupancy rate in dial-a-ride problems via linear fractional column generation

In this paper, we consider a dial-a-ride problem where the objective is to maximize the passenger occupancy rate. The problem arises from an on-demand transportation system developed in a rural zone in France, where the objective of encouraging people meeting is pursued. We address the solution of the problem with a column generation approach, applied to a set partitioning formulation where the objective function is fractional. Based on the literature on linear fractional programming, two methods are developed to deal with this fractional objective. Experiments permit to compare these two approaches and to evaluate the impact of the new objective compared to a standard min-cost or min-time optimization.