Geraldini, E.C.; Munari, P.; Morabito, R. The Robust Vehicle Allocation Problem under Demand Uncertainty. Submitted. Dec, 2025.

Abstract: The Vehicle Allocation Problem (VAP) models situations involving fleet allocation decisions, aiming to reduce the number of empty container trips. In this context, data uncertainty is inherent as, for example, decision-makers often need to schedule the fleet before knowing the exact demand at each distribution center, thus allocating resources based on uncertain demand. Hence, solutions obtained using deterministic approaches for the VAP are likely to be infeasible or incur extra costs when applied in real-world, especially if the uncertainty level is high. To aid decision-making in this context, we introduce a new solution approach based on the Robust Optimization (RO) paradigm, which helps in modeling and solving problems where parameter uncertainties are a concern, enhancing the likelihood of obtaining viable and efficient solutions in practice. As an advantage over other approaches of optimization under uncertainty, RO does not require the use of probability distributions to represent the random parameters. To our knowledge, there is no RO approach tailored for the VAP thus far in the literature. We propose a RO formulation based on a novel representation of the deterministic problem that enables flexible decision-making, and derive its robust counterpart based on the linearization of recursive equations for a cardinality-constrained uncertainty set. We analyze the performance of the proposed model through computational experiments using benchmark instances created from a real-world case in road freight transportation in Brazil. The results demonstrate the benefits of incorporating uncertainty into the VAP to support effective decision-making.

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