Routing and inventory model for emergency response to minimize unmet demand

Rapid and efficient wide-scale distribution of medical supplies plays a critical role in assuring the effectiveness in managing the risks of large-scale emergencies such as a bio-terrorism attack. Important issues in the design of such an efficient distribution network involve deciding how to route distribution vehicles and how to manage these inventories. The high uncertainty, limited supply and overwhelming demand associated with a large-scale emergency may result in significant unmet demand, which is a direct representation of the most undesirable consequence - loss of life. Solving appropriate vehicle routing and inventory management problems in a coordinated manner can ensure the design of a logistic network capable of efficiently distributing medical supplies to decrease the potential fatalities in responding to a large-scale emergency. In this work, we develop models and solution approaches to solve a perishable inventory management problem and a vehicle routing problem in the context of emergency response to minimize unmet demand.;To effectively manage the huge volume of perishable medical supplies to guarantee their freshness, we present a modified Economic Manufacturing Quantity (EMQ) model for perishable items with a minimum inventory volume constraint. Minimizing the cost of maintaining such a system can be formulated as a non-convex non-differentiable unconstrained optimization problem. An exact algorithm with polynomial complexity is developed to solve this problem. To efficiently distribute the medical supplies for large-scale emergencies, a two-stage solution approach is proposed by solving a stochastic routing problem in the first planning stage and a deterministic scheduling problem in the second operational stage. We formulate a mixed integer model which incorporates the routing with profits and the traditional complete routing for the first time to address the planning stage problem. A chance-constrained approach is applied to handle the uncertainty in both demand and travel time in the stochastic planning stage model. Three recourse strategies are implemented and compared for the operational stage. We develop a tabu heuristic and approximated knapsack heuristic to solve models in both stages. Numerical experiments are conducted to evaluate our models and solution approaches based on simulated large-scale emergencies.