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<p>The Sequential Testing Problem (STP) seeks to minimize the total expected cost of administering a series of tests which determine the state of a <i>k</i>-out-of-<i>n</i> system. In the baseline case of the STP where the probabilities of passing or failing a test are independent, the problem can be solved to to optimality in polynomial time. However, there is little research exploring the effect of dependency between tests, which greatly complicates the problem. Motivated by the process of evaluating living kidney donors, we explore a variant of the STP where the probability of passing a given test in an <i>n</i>-out-of-<i>n</i> sequence is approximated as the probability of passing the test given that the donor has passed the preceding test. We refer to this variant as the Single-Dependence Sequential Testing Problem (SDSTP). We present an optimization model to solve the SDSTP to optimality and simple—but effective—methods to approximate the solution. Our experiments show that the model can be solved to optimality for many practical applications where the set of tests is small (say, less than 20), and our proposed algorithms also find near-optimal solutions in rapid time even for large numbers of tests.</p>

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The single-dependence sequential testing problem for the living kidney donor workup process

  • 期刊论文

  • 发表日期：

    2026年5月21日

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  • Joshua Nielsen,
  • Hadi El-Amine,
  • Monica Gentili,
  • Naoru Koizumi

摘要

The Sequential Testing Problem (STP) seeks to minimize the total expected cost of administering a series of tests which determine the state of a k-out-of-n system. In the baseline case of the STP where the probabilities of passing or failing a test are independent, the problem can be solved to to optimality in polynomial time. However, there is little research exploring the effect of dependency between tests, which greatly complicates the problem. Motivated by the process of evaluating living kidney donors, we explore a variant of the STP where the probability of passing a given test in an n-out-of-n sequence is approximated as the probability of passing the test given that the donor has passed the preceding test. We refer to this variant as the Single-Dependence Sequential Testing Problem (SDSTP). We present an optimization model to solve the SDSTP to optimality and simple—but effective—methods to approximate the solution. Our experiments show that the model can be solved to optimality for many practical applications where the set of tests is small (say, less than 20), and our proposed algorithms also find near-optimal solutions in rapid time even for large numbers of tests.