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In this paper, a latency location-routing problem with stochastic travel times is investigated. The problem is cast as a two-stage stochastic program. The ex-ante decision comprises the location of the depots. The ex-post decision regards the routing, which adapts to the observed travel times. A risk-averse decision-maker is assumed, which is conveyed by adopting the latency CVaR α as the objective function. The problem is formulated mathematically. An efficient multi-start variable neighborhood search algorithm is proposed for tackling the problem when uncertainty is captured by a finite set of scenarios. This procedure is then embedded into a sampling mechanism so that realistic instances of the problem can be tackled, namely when the travel times are represented by random vectors with an infinite support. An extensive computational analysis is conducted to assess the methodological developments proposed and the relevance of capturing uncertainty in the problem. Additional insights include the impact of the risk level in the solutions. • A latency location routing problem under stochastic travel times is studied. • A two-stage risk-averse stochastic program is proposed. • An effective heuristic algorithm is developed. • A sampling algorithm is developed for continuously distributed travel times. • The heuristic is competitive for solving the deterministic LLRP.
Osorio‐Mora et al. (Tue,) studied this question.