The Share-a-Ride problem with stochastic travel times and stochastic delivery locations

We consider two stochastic variants of the Share-a-Ride problem: one with stochastic travel times and one with stochastic delivery locations. Both variants are formulated as a two-stage stochastic programming model with recourse. The objective is to maximize the expected profit of serving a set of passengers and parcels using a set of homogeneous vehicles. Our solution methodology integrates an adaptive large neighborhood search heuristic and three sampling strategies for the scenario generation (fixed sample size sampling, sample average approximation, and sequential sampling procedure). A computational study is carried out to compare the proposed approaches. The results show that the convergence rate depends on the source of stochasticity in the problem: stochastic delivery locations converge faster than stochastic travel times according to the numerical test. The sample average approximation and the sequential sampling procedure show a similar performance. The performance of the fixed sample size sampling is better compared to the other two approaches. The results suggest that the stochastic information is valuable in real-life and can dramatically improve the performance of a taxi sharing system, compared to deterministic solutions.