Branch-and-Price for the Stochastic TSP with Generalized Latency

Motivated by the tactical planning level of demand adaptive public transportation systems, we present the stochastic symmetric traveling salesman problem with generalized latency (STSP-GL), a stochastic extension to the symmetric traveling salesman problem with generalized latency (TSP-GL). The STSP-GL aims to choose a subset of nodes of an undirected graph and determines a Hamiltonian tour amongst those nodes, minimizing an objective function that is a weighted combination of route design and passenger routing costs. These nodes are selected to ensure that a predefined percentage of uncertain passenger demand is served with a given probability. We formulate the STSP-GL as a stochastic program and propose a branch-and-price algorithm for solving its deterministic equivalent. We also develop a local search approach with which we improve the performance of the B&P approach. We assess the efficiency of the proposed methods on a set of instances from the literature. We demonstrate that the proposed methods outperform a known benchmark, improving upper bounds by up to 85% and lower bounds by up to 55%. Finally, we show that solutions of the stochastic model are both more cost-effective and robust than those of the deterministic model.