Optimal supply location selection and routing for emergency material delivery with uncertain demands

The supply location selection and routing (SLSR) problem integrates warehouse selection, and fleet routing and scheduling to optimize the supply chain and guarantee timely material delivery for disaster areas. Demand uncertainties are the inherent nature of the emergency material supply. In this paper, the SLSR problem is studied in considering uncertain demand and formulated as a probabilistic constrained integer programming (PCIP) model. The uncertainty is measured by the joint demand satisfactory level of disaster areas. The PCIP problem is intractable in general for its nonlinear and nonconvex property introduced by the probabilistic constraints and integer variables. With the introduction of p-efficient points an equivalent deterministic integer programming model is derived. A two-level solution scheme is developed to address the challenge of unknown and possibly a large number of p-efficient points simultaneously with high computational complexity. Numerical testing results show that the new method is efficient, and can be applied to solve large scale stochastic SLSR problem.