  This paper introduces a problem in which the state of a system needs to be
determined through costly tests of its components by a limited number of
testing units and before a given deadline. We also consider a closely related
search problem in which there are multiple searchers to find a target before a
given deadline. These natural generalizations of the classical sequential
testing problem and search problem are applicable in a wide range of
time-critical operations such as machine maintenance, diagnosing a patient, and
new product development. We show that both problems are NP-hard, develop a
pseudo-polynomial dynamic program for the special case of two time slots, and
describe a partial-order-based as well as an assignment-based mixed integer
program for the general case. Based on extensive computational experiments, we
find that the assignment-based formulation performs better than the
partial-order-based formulation for the testing variant, but that this is the
other way round for the search variant. Finally, we propose a
pairwise-interchange-based local search procedure and show that, empirically,
it performs very well in finding near-optimal solutions.
