Integrated optimization of maintenance interventions and spare part selection for a partially observable multi-component system

Advanced technical systems are typically composed of multiple critical components whose failure cause a system failure. Often, it is not technically or economically possible to install sensors dedicated to each component, which means that the exact condition of each component cannot be monitored, but a system level failure or defect can be observed. The service provider then needs to implement a condition based maintenance policy that is based on partial information on the systems condition. Furthermore, when the service provider decides to service the system, (s)he also needs to decide which spare part(s) to bring along in order to avoid emergency shipments and part returns. We model this problem as an infinite horizon partially observable Markov decision process. In a set of numerical experiments, we first compare the optimal policy with preventive and corrective maintenance policies: The optimal policy leads on average to a 28% and 15% cost decrease, respectively. Second, we investigate the value of having full information, i.e., sensors dedicated to each component: This leads on average to a 13% cost decrease compared to the case with partial information. Interestingly, having full information is more valuable for cheaper, less reliable components than for more expensive, more reliable components

Optimising reorder intervals and order-up-to levels in guaranteed service supply chains

We consider the problem of determining the optimal reorder intervals R and order-up-to levels S in a multi-echelon supply chain system where all echelons are assumed to have fixed ordering costs and to operate with a (R, S) policy with stationary nested power-of-two reorder intervals. By using the guaranteed service approach to model the multi-echelon system facing a stochastic demand, we formulate the problem as a deterministic optimisation model in order to simultaneously determine the optimal R and S parameters as well as the guaranteed service times. The model is a non-linear integer programming (NLIP) problem with a non-convex and non-concave objective function including rational and square root terms. Then, we propose a sequential optimisation procedure (SOP) to obtain near-optimal solutions with reasonable computational time. The numerical study demonstrates that for a general acyclic multi-echelon system with randomly generated parameters, the SOP is able to obtain near-optimal solutions of about 0.46% optimality gap in average in a few seconds. Moreover, we propose an improved direct approach using a global optimiser, bounding the decision variables in the NLIP model and considering the SOP solution as an initial solution. Numerical examples illustrate that this reduces significantly the computational time

Optimising reorder intervals and order-up-to levels in guaranteed service supply chains

We consider the problem of determining the optimal reorder intervals R and order-up-to levels S in a multi-echelon supply chain system where all echelons are assumed to have fixed ordering costs and to operate with a (R, S) policy with stationary nested power-of-two reorder intervals. By using the guaranteed service approach to model the multi-echelon system facing a stochastic demand, we formulate the problem as a deterministic optimisation model in order to simultaneously determine the optimal R and S parameters as well as the guaranteed service times. The model is a non-linear integer programming (NLIP) problem with a non-convex and non-concave objective function including rational and square root terms. Then, we propose a sequential optimisation procedure (SOP) to obtain near-optimal solutions with reasonable computational time. The numerical study demonstrates that for a general acyclic multi-echelon system with randomly generated parameters, the SOP is able to obtain near-optimal solutions of about 0.46% optimality gap in average in a few seconds. Moreover, we propose an improved direct approach using a global optimiser, bounding the decision variables in the NLIP model and considering the SOP solution as an initial solution. Numerical examples illustrate that this reduces significantly the computational time

Optimizing usage and maintenance decisions for k-out-of-n systems of moving assets

We consider an integrated usage and maintenance optimization problem for a k-out-of-n system pertaining to a moving asset. The k-out-of-n systems are commonly utilized in practice to increase availability, where n denotes the total number of parallel and identical units and k the number of units required to be active for a functional system. Moving assets such as aircrafts, ships, and submarines are subject to different operating modes. Operating modes can dictate not only the number of system units that are needed to be active, but also where the moving asset physically is, and under which environmental conditions it operates. We use the intrinsic age concept to model the degradation process. The intrinsic age is analogous to an intrinsic clock which ticks on a different pace in different operating modes. In our problem setting, the number of active units, degradation rates of active and standby units, maintenance costs, and type of economic dependencies are functions of operating modes. In each operating mode, the decision maker should decide on the set of units to activate (usage decision) and the set of units to maintain (maintenance decision). Since the degradation rate differs for active and standby units, the units to be maintained depend on the units that have been activated, and vice versa. In order to minimize maintenance costs, usage and maintenance decisions should be jointly optimized. We formulate this problem as a Markov decision process and provide some structural properties of the optimal policy. Moreover, we assess the performance of usage policies that are commonly implemented for maritime systems. We show that the cost increase resulting from these policies is up to 27% for realistic settings. Our numerical experiments demonstrate the cases in which joint usage and maintenance optimization is more valuable

Integrated optimization of maintenance interventions and spare parts requirements for a partially observable multi-component system

We consider a multi-component system in which a condition parameter (e.g., vibration or temperature) is monitored. The outcome of monitoring indicates whether the system is functioning properly, defective, or has failed. However, the condition signal does not reveal which component in the system is defective or has failed. Maintenance is performed by a service provider who has specialized knowledge about the system. The maintenance service provider needs to infer the exact state of the system from the current condition signal and the past data, in order to decide when to visit the customer for maintenance and which spare parts to take along. We model this problem as a partially observable Markov decision process and propose a grid-based solution method to numerically obtain the optimal policy. We analyze the value of having better sensors in the system by considering a case where the maintenance service provider can fully observe the deterioration level of each component. The analysis results show that the positive impact of having full information on the components’ deterioration levels increases as the return cost for the components is getting higher. On the other hand, the positive impact of having full information on the components’ deterioration levels decreases when the ratio of the preventive and corrective maintenance costs is close to either 1 or 0. Additionally, we compare the optimal policy with the corrective and preventive maintenance policies in which the maintenance service provider brings all the components to the customer. The comparison results indicate that the positive impact of employing the optimal policy improves when the return costs for the components increases

Integrated maintenance and spare part optimization for moving assets

We consider an integrated maintenance and spare part optimization problem for a single critical component of a moving asset for which the degradation level is observable. Degradation is modeled as a function of the current operating mode, mostly dictated by the actual location of the moving asset. The spare part is stocked at the home base that the moving asset eventually visits. Alternatively, the spare part can be stocked on-board the moving asset to prevent costly expedited deliveries. The costs associated with spare part deliveries and part replacements depend on the operating mode. Our objective is to minimize the expected total discounted cost of spare part deliveries, part replacements, and inventory holding over an infinite planning horizon. We formulate the problem as a Markov decision process and characterize the structure of the optimal policy, which is shown to be a bi-threshold policy in each operating mode. Our numerical experiments show that the cost savings obtained by the integrated optimization of spare part inventory and part replacement decisions are significant. We also demonstrate the value of the integrated approach in a case study from the maritime sector

A survey of maintenance and service logistics management: classification and research agenda from a maritime sector perspective

Maintenance and service logistics support are required to ensure high availability and reliability for capital goods and typically represent a significant part of operating costs in capital-intensive industries. In this paper, we present a classification of the maintenance and service logistics literature considering the key characteristics of a particular sector as a guideline, i.e., the maritime sector. We discuss the applicability and the shortcomings of existing works and highlight the lessons learned from a maritime sector perspective. Finally, we identify the potential future research directions and suggest a research agenda. Most of the maritime sector characteristics presented in this paper are also valid for other capital-intensive industries. Therefore, a big part of this survey is relevant and functional for industries such as aircraft/aerospace, defense, and automotive

Maintenance optimization for a single wind turbine component under time-varying costs

In this paper, we introduce a new, single-component model for maintenance optimization under time-varying costs, specifically oriented at offshore wind turbine maintenance. We extend the standard age replacement policy (ARP), block replacement policy (BRP) and modified block replacement policy (MBRP) to address time-varying costs. We prove that an optimal maintenance policy under time-varying costs is a time-dependent ARP policy. Via a discretization of time, the optimal time-dependent ARP can be found using a linear programming formulation. We also present mixed integer linear programming models for parameter optimization of BRP and MBRP. We present a business case and apply our policies for maintenance planning of a wind turbine gearbox and show that we can achieve savings up-to 23%