ROBUST OPTIMIZATION APPROACHES TO THE VEHICLE ALLOCATION PROBLEM WITH AND WITHOUT BACKLOG

This study addresses the Vehicle Allocation Problem under demand uncertainty, considering two variants: with and without demand backlog. Two integer linear programming models based on robust optimization are proposed. The model with backlog is formulated through the dualization of constraints associated with uncertainty, while the model without backlog incorporates uncertainty via robust constraints derived from linearized recursive equations. Both models employ uncertainty sets and budgets to adjust the level of conservatism applied to the uncertain parameters. Computational experiments on 51 instances based on realistic data showed that increasing the robustness level leads to reduced profits, highlighting the trade-off between performance and risk. The model without backlog demonstrated stable solution times even under high levels of uncertainty.