We consider the problem of combining a given set of diagnostic tests into an inspection system to classify items of interest (cases) with maximum accuracy such that the cost of performing the tests does not exceed a given budget constraint. One motivating application is sequencing diagnostic tests for container inspection, where the diagnostic tests may correspond to radiation sensors, document checks, or imaging systems. We consider mixtures of decision trees as inspection systems following the work of Boros et al. (Nav. Res. Logist. 56:404-420, 2009). We establish some properties of efficient inspection systems and characterize the optimal classification of cases, based on some of their test scores. The measure of performance is the fraction of all cases in a specific class of interest, which are classified correctly. We propose a dynamic programming algorithm that constructs more complex policies by iteratively prefixing devices to a subset of policies and thereby enumerating all of the efficient (i.e., undominated) inspection policies in the two dimensional cost-detection space. Our inspection policies may sequence an arbitrary number of tests and are not restricted in the branching factor. Our approach directly solves the bi-criterion optimization problem of maximizing detection and minimizing cost, and thus supports sensitivity analysis over a wide range of budget and detection requirements.
Bibliographical noteFunding Information:
Funding by the Domestic Nuclear Detection Office (DNDO), of the Department of Homeland Security, through NSF Grants # CBET-0735910 and by Department of Homeland Security Grant/Contract #2008-DN-077-ARI003-0, the Science and Technology Directorate, Office of University Programs, by the National Science Foundation #SES 0518543 3/3 and by Office of Naval Research #DOD-DON-ONR-N00014-071-0150, # DOD-DON-ONR-N00014-07-1-0299 are all most gratefully acknowledged. The authors would like to thank DIMACS, and members of the DyDAn DHS Center of Excellence for stimulating discussions. We also thank Nir Halman and an anonymous referee for suggestions to improve the presentation.
- Bi-objective optimization
- Dynamic programming
- Port security
- Sequential inspection