A given finite set of tasks, having known nonnegligible failure probabilities and known costs (or rewards) for their performance, can be performed sequentially until either one of the tasks fails or all tasks have been executed. The allowable task performance sequences are constrained only by certain precedence requirements, which specify that certain tasks must be performed before certain other tasks. Given the individual task failure probabilities and task costs, along with the intertask precedence requirements, the problem is to determine an optimal task performance sequence having minimal expected cost (or maximal expected reward). A number of potential applications of such "task ordering" problems are described, including R&D project organization, design of screening procedures, and determining testing points for sequential manufacturing processes. The main results of this paper are a number of reduction theorems which lead to a very efficient optimization algorithm for a large class of task ordering problems. Though these theorems are not quite sufficient for us to give a fast optimization algorithm, we do show how their use can improve upon exhaustive search techniques. © 1973.
Garey, M. R. (1973). Optimal task sequencing with precedence constraints. Discrete Mathematics, 4(1), 37–56. https://doi.org/10.1016/0012-365X(73)90113-1