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This paper considers the vehicle routing problem with stochastic demands under optimal restocking. We develop an exact algorithm that is effective for solving instances with many vehicles and few customers per route. In our experiments, we show that in these instances, solving the stochastic problem is most relevant (i.e., the potential gains over the deterministic equivalent solution are highest). The proposed branch-price-and-cut algorithm relies on an efficient labeling procedure, exact and heuristic dominance rules, and completion bounds to price profitable columns. Instances with up to 76 nodes could be solved in less than five hours, and instances with up to 148 nodes could be solved in long runs of the algorithm. The experiments also allowed new findings on the problem. The solution to the stochastic problem is up to 10% less costly than the deterministic equivalent solution. Opening new routes reduces restocking costs and in many cases results in solutions with less transportation costs. When the number of routes is not fixed, the optimal solutions under detour-to-depot and optimal restocking are nearly equivalent. However, when the number of routes is limited and the expected demand along a route is allowed to exceed the vehicle capacity, optimal restocking may be significantly more cost-effective than the detour-to-depot policy.

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Freight distribution with electric vehicles (EVs) is a promising alternative to reduce the carbon footprint associated with city logistics. Algorithms for planning routes for EVs should take into account their relatively short driving range and the effects of traffic congestion on the battery consumption. This paper proposes new methodology and illustrates how it can be applied to solve an electric vehicle routing problem with stochastic and time-dependent travel times where battery recharging along routes is not allowed. First, a new method for generating network-consistent (correlated in time and space) and time-dependent speed scenarios is introduced. Second, a new technique for applying branch and price on instances defined on real street networks is developed. Computational experiments demonstrate the effectiveness of the approach for finding optimal or near-optimal solutions in instances with up to 133 customers and almost 1,500 road links. With a high probability, the routes in the obtained solutions can be performed by EVs without requiring intermediate recharging stops. An execution time control policy to further reduce the chances of stranded EVs is also presented. In addition, we measure the cost of independence, which is the impact on solution feasibility when travel times are assumed statistically independent. Last, we give directions on how to extend the proposed framework to handle recourse actions.