Prepositioning Emergency Inventories Under Uncertainties of Time, Location, and Quantity

An emergency incident will occur in the coming years, somewhere. It will be an earthquake, a landslide, a volcanic eruption, an epidemic of infectious disease, or some other disaster. Positioning an emergency or humanitarian inventory in advance is a response that can greatly mitigate the effects of the expected incident. However, the problem is to put the emergency inventory in the right location to use the right quantity and to do so at the right time—taking into account that the location, timing, and magnitude of the incident may be random variables. This paper presents a model for the triple uncertainty of the inventory problem (location, timing, and quantity) and shows how the solution can be optimized analytically and numerically, even in cases where there is a statistical dependence between the random variables. An important contribution of the paper is the addition of the dimension of timing to the inventory problem. One result of the model can be an immediate establishment of an emergency inventory with the optimal quantity and location of materials, another can be a “wait and see” strategy with periodic updating of the model as newer information becomes available. The paper provides benchmark solutions that can help decision-makers make wiser choices about the timing, location, and quantity of inventories positioned in anticipation of an emergency incident. The model is useful especially for disasters with a long mean time between occurrences (years), which motivate decision-makers to adopt the wait and see strategy.