Temporal and spatial considerations in maintenance planning

Maintenance spending is well-known to constitute a substantial part of total production and service costs. We focus on optimal planning of maintenance activities in several novel settings. In each setting, we formulate a mathematical optimization model using stochastic modeling techniques and establish the structural properties of the optimal policy through theoretical derivations. We provide additional policy insights using numerical observations and develop easy-to-implement and high-performing heuristic policies.Specifically, we first study an age-replacement setting (with minimal repair) in which the maintenance worker may be unpunctual. That is, the actual preventive replacement times may deviate from the prescribed replacement times in a probabilistic manner. We formulate a long-run expected cost-rate minimization model and compare the optimal solution and its performance to those when the unpunctual behavior is assumed to be either absent or independent of the prescribed replacement time.Next, we consider an age-replacement setting (without minimal repair) in which replacement costs are non-decreasing in system age. This assumption is motivated by factors such as decreasing salvage value or increasing costs associated with obtaining spare parts. We formulate a long-run expected cost-rate minimization model that captures this dependency and compare the optimal solution and its performance to those for the case in which replacement costs are assumed to be constant.Finally, we consider the problem of performing condition-based maintenance on a set of geographically distributed assets via a single maintenance resource that travels between the assets' locations. We use a graph representation to model possible geographical locations of the resource, including idling and asset locations and the links between them. We formulate a Markov decision process to dynamically obtain the optimal positioning of the maintenance resource and the optimal timing of the interventions that the resource performs.