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We consider a system with a finite lifespan and a single critical component that is subject to random failures. An age-based replacement policy is applied to preventively replace the component before its failure. The components used for replacement come from either a weak population or a strong population, referred to as population heterogeneity. However, the true population type is unknown to the decision maker. By considering that the decision maker has a belief on the probability of having a weak population, we build a partially observable Markov decision process model with the objective of minimizing the total cost over the lifespan of the system. The resulting optimal policy updates the belief variable in a Bayesian fashion by using the data obtained over the course of the system lifespan, and it denotes when to execute preventive replacement. It optimally balances the trade-off between the cost of learning the true population type (via deliberately delaying the preventive replacement time to better learn the population type) and the cost of maintenance activities. By addressing this so-called exploration-exploitation trade-off, we generate insights on the optimal policy and compare its performance with existing heuristic approaches from the literature. We also characterize a lower bound to the optimal cost, allowing us to determine the value of resolving the uncertainty on the population type.

This paper considers the problem of scheduling automated guided vehicles (AGVs) with battery constraints. Each transport request involves a soft time window, and the AGV fleet used to service those requests is heterogeneous with a diverse set of capabilities and travel costs. In contrast to the existing literature, each transport request may require different AGV material handling capabilities (such as lift loads, tow loads, or handle loads with a mounted robot arm), and the AGV batteries can be recharged partially under consideration of a critical battery threshold. The problem is to assign the transport and charging requests to AGVs, sequence the requests, and determine their starting times and the recharging durations of the AGVs with the objective of minimizing a weighted sum of the tardiness costs of transport requests and travel costs of AGVs. A mixed-integer linear programming model is formulated. We also propose a new matheuristic that makes use of an adaptive large neighborhood search algorithm and a linear program to solve industry-size instances. We illustrate the efficacy of our approach with an industry case study using real-world data.