Emergency logistics in disasters is fraught with planning and operational challenges, such as uncertainty about the exact nature and magnitude of the disaster, a lack of reliable information about the location and needs of victims, possible random supplies and donations, precarious transport links, scarcity of resources, and so on. This paper develops a new two-stage stochastic network flow model to help decide how to rapidly supply humanitarian aid to victims of a disaster within this context. The model takes into account practical characteristics that have been neglected by the literature so far, such as budget allocation, fleet sizing of multiple types of vehicles, procurement, and varying lead times over a dynamic multiperiod horizon. Attempting to improve demand fulfillment policy, we present some extensions of the model via state-of-art risk measures, such as semideviation and conditional value-at-risk. A simple two-phase heuristic to solve the problem within a reasonable amount of computing time is also suggested.Numerical tests based on the floods and landslides in Rio de Janeiro state, Brazil, show that the model can help plan and organise relief to provide good service levels in most scenarios, and how this depends on the type of disaster and resources. Moreover, we demonstrate that our heuristic performs well for real and random instances.

An effective two-stage stochastic multi-trip location-transportation model with social concerns in relief supply chains Revised submission to

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Extreme events such as disasters cause partial or total disruption of basic services such as water, energy, communication and transportation. In particular, roads can be damaged or blocked by debris, thereby obstructing access to certain aected areas. Thus, restoration of the damaged roads is necessary to evacuate victims and distribute emergency commodities to relief centers or aected areas. The Crew Scheduling and Routing Problem (CSRP) addresses decisions in postdisaster situations with the aim of minimizing the time that aected areas remain inaccessible. The integration of crew scheduling and routing decisions makes this problem too complicated to be eectively solved for practical instances using mixed integer programming (MIP) formulations recently proposed in the literature. Therefore, we propose a branch-and-Benders-cut (BBC) algorithm that decomposes the integrated problem into a master problem (MP) with scheduling decisions and subproblems with routing decisions. Computational tests based on instances from the literature show that the proposed exact method improves the results of MIP formulations and other exact and metaheuristic methods proposed in literature. The BBC algorithm provides feasible solutions and optimality gaps for instances that thus far have not been possible to solve by exact methods in the literature.

We address the robust vehicle routing problem with time windows (RVRPTW) under customer demand and travel time uncertainties. As presented thus far in the literature, robust counterparts of standard formulations have challenged general-purpose optimization solvers and specialized branch-and-cut methods. Hence, optimal solutions have been reported for small-scale instances only. Additionally, although the most successful methods for solving many variants of vehicle routing problems are based on the column generation technique, the RVRPTW has never been addressed by this type of method. In this paper, we introduce a novel robust counterpart model based on the well-known budgeted uncertainty set, which has advantageous features in comparison with other formulations and presents better overall performance when solved by commercial solvers. This model results from incorporating dynamic programming recursive equations into a standard deterministic formulation and does not require the classical dualization scheme typically used in robust optimization. In addition, we propose a branch-price-and-cut method based on a set partitioning formulation of the problem, which relies on a robust resource-constrained elementary shortest path problem to generate routes that are robust regarding both vehicle capacity and customer time windows. Computational experiments using Solomon’s instances show that the proposed approach is effective and able to obtain robust solutions within a reasonable running time. The results of an extensive Monte Carlo simulation indicate the relevance of obtaining robust routes for a more reliable decision-making process in real-life settings.