2020/09/23 by Hemant Gehlot, Gehlot, Hemant, Shreyas Sundaram +3
Engineering · #FOS: Electrical engineering #Reliability and Maintenance Optimization #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2009.11453
openalex publication_date 2020/09/23 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We examine a control problem where the states of the components of a system\ndeteriorate after a disruption, if they are not being repaired by an entity.\nThere exist a set of dependencies in the form of precedence constraints between\nthe components, captured by a directed acyclic graph (DAG). The objective of\nthe entity is to maximize the number of components whose states are brought\nback to the fully repaired state within a given time. We prove that the general\nproblem is NP-hard, and therefore we characterize near-optimal control policies\nfor special instances of the problem. We show that when the deterioration rates\nare larger than or equal to the repair rates and the precedence constraints are\ngiven by a DAG, it is optimal to continue repairing a component until its state\nreaches the fully recovered state before switching to repair any other\ncomponent. Under the aforementioned assumptions and when the deterioration and\nthe repair rates are homogeneous across all the components, we prove that the\ncontrol policy that targets the healthiest component at each time-step while\nrespecting the precedence and time constraints fully repairs at least half the\nnumber of components that would be fully repaired by an optimal policy.\nFinally, we prove that when the repair rates are sufficiently larger than the\ndeterioration rates, the precedence constraints are given by a set of disjoint\ntrees that each contain at most k nodes, and there is no time constraint, the\npolicy that targets the component with the least value of health minus the\ndeterioration rate at each time-step while respecting the precedence\nconstraints fully repairs at least 1/k times the number of components that\nwould be fully repaired by an optimal policy.\n