Optimal sequential resource allocation under error-prone success assessment
K. Kalyanam, M. Pachter and D. Casbeer
https://doi.org/10.19124/ima.2018.001.12
Abstract
We formulate a stochastic optimization problem, wherein finite resources are sequentially allocated to incoming tasks so as to maximize a cumulative reward. At each decision stage, the incoming task has known value. However, upon allocating a resource, a task is completed with probability less than one. Furthermore, the decision maker is informed about the task completion status via an error-prone feedback mechanism that is subject to both type I and type II classification errors. The decision maker may choose to reallocate a resource to the current task or move on to the next task in the sequence. We show that a resource is allocated if and only if the expected reward from a task exceeds a threshold. Furthermore, we establish a lower bound on the task completion probability under which the threshold is monotonic decreasing in the number of remaining resources.