Problem definition: Considering a mix of prepositioning and local purchasing, common to cover humanitarian demands in the aftermath of a rapid-onset disaster, we propose policies to determine preposition stock. These formulations are developed in the presence of demand, budget, and local supply uncertainties and for single-items delivery. Academic/practical relevance: The immediate period aftermath of a disaster is the most crucial period during which humanitarian organizations must supply relief items to beneficiaries. Yet, because of many unknowns such as time, place, and magnitude of a disaster, supply management is a significant challenge, and these decisions are made intuitively. The features and complexities we examine have not been studied in the literature. Methodology: We derive properties of the optimal solution, identify exact solution methods, and determine approximate methods that are easy to implement. Results: We (i) characterize the interplay of supply, demand, and budget uncertainties, as well as the impact of product characteristics on optimal prepo stock levels; (ii) show in what conditions the prepo stock is a simple newsvendor solution; and (iii) discuss the value of emergency funds. Managerial implications: We show that budget level is a key determinant of the optimal policy. When it is above a threshold, inventory increases in disaster frequency and severity, but the reverse is true otherwise. When budget is limited, the rate of savings from improved forecasts is amplified (attenuated) for critical (noncritical) items, reflecting opposing directional effects of mismatch cost and cost of insufficient funding. Our model can also be used to estimate the value of initiatives to mitigate constraints on local spend (e.g., a line of credit underwritten by large donors that is available during the immediate relief period).
On dimensioning optical grids and the impact of scheduling
