The terror scenario is a nightmare, but not at all impossible. A highly contagious and deadly disease like anthrax suddenly appears in a major American city — say, Los Angeles. Effective drugs exist, but time is critical and the limited supply of drugs has to go where it is most needed. How can authorities make an advance plan that will treat the most people fastest?
A team of researchers led by Professor Maged Dessouky of Viterbi School's Daniel J. Epstein Department of Industrial and Systems Engineering tackled the problem. They created a mathematical model of such a disaster in which a number of critical variables could be adjusted — most critically, the number and location of distribution points for the drugs — and then compared different ways of making these distributions.
Maged Dessouky
“The model,” wrote Dessouky and his co-authors in the study recently published in Socio-Economic Planning Sciences Economics, “decides the locations to open and the amount supplied to each location.”
The group applied their model to the geography, population distribution, resource base, transportation system and other relevant attributes of the L.A. Metro Area, assuming that (as is planned) medical supplies from the Strategic National Stockpile (SNP) arrived one day after the outbreak for distribution by local authorities.
The study, partially funded by the USC-based National Center for Risk & Economic Analysis of Terrorism Events (CREATE), built on a large corpus of earlier studies of where to put disaster response locations. However, these earlier models do not take into account spatial uncertainty in demand.
And, the authors write, “In an application like the one presented in this paper, where the number of people affected by a large-scale emergency and its location are unknown well in advance, facility location modeling under uncertainty is vital. Our model assigns the supply to be stored at each facility by considering it as a decision variable that depends on an unknown demand.”
For Los Angeles these possibilities are formidably large and complex. A first step is designating demand points,
defined for the purpose of the study as the center of census tracts. For the LA area, this meant a total of 1329 demand points, covered by about 200 medical facility sites.
Los Angeles demand points. How to best distribute the cure?
The key factors that need then to be evaluated is how many patients will be able to receive treatment and how fast, based on the distance between homes and distribution points, and based on where the outbreak takes place.
The group used a variation on the assumptions of earlier work to create a new model, a ‘locate-allocate heuristic’ to make decisions about locations and quanties, and compare the likely results with the coverage found in the old fixed model.
The difference: as much as 20 percent better coverage, which could mean thousands of lives in a fast moving anthrax emergency.
Working with Dessouky on the study were Epstein Department Associate Professor Fernando Ordóñez and Pavankumar Murali, who received his PhD from the department in 2010.
