# Are you sure that goes there?

In this project, Josh Wilde and I used robust optimization and machine learning to capture emergency demand uncertainty in the joint humanitarian facility location and inventory pre-positioning problem.

**Deliverables:**

### 15.094J Robust Modeling, Optimization and Computation

*Spring 2019*

Jahre *et al.* model the humanitarian network design problem for the UNHCR as a two-stage stochastic optimization problem. The first stage is a facility location problem, and the second stage is a stock pre-positioning problem that depends on the selected facility locations.

Josh and I augmented this work using robust optimization, whose theory seeks decisions that successfully navigate the trade-off between expected optimality and mitigation of parametric uncertainty. Emergency humanitarian demand can wildly oscillate between negligible and astronomical levels from year to year, distinguishing humanitarian network design from the typical facility location problem. Because historical demand is consequentially not a reliable indication of future demand, we capture emergency demand uncertainty using machine learning demand forecasts. We build a robust optimization formulation by embedding these forecasts into uncertainty sets for the emergency demand parameters.

We find that optimal facility locations are agnostic to emergency demand uncertainty, which lends confidence to this more permanent first-stage decision. Fulfillment costs meaningfully decrease as a result of the incorporation of demand forecasts into uncertainty sets, but inventory allocations are highly paranoid and sensitive to the specific demand forecast. This conclusion together with the invariant optimal network configuration indicates that the robust demand pre-positioning problem can be divorced from the facility location problem.