Maintenance Optimization Problem Research Articles

Distributionally robust CVaR optimization for refinery integrated production–maintenance scheduling under uncertainty

In the petroleum refining industry, efficient production planning and maintenance scheduling are crucial for economic performance and operational efficiency. Moreover, the production processes face significant uncertainties stemming from market fluctuations and equipment failures. However, traditional optimization methods often treat production and maintenance independently and neglect the risk management associated with uncertainties in the production process, leading to unreliable plans and suboptimal execution. To address these issues, this paper proposes an innovative data-driven distributionally robust conditional value-at-risk (DRCVaR) method to tackle the integrated production–maintenance optimization problem under crude oil price uncertainty. By constructing confidence sets with L2 norm constraints based on historical data, our approach directly links the model’s conservatism to the amount of available data, effectively managing risk. In addition, we propose robust linear transformation to simplify the min–max nonlinear problem into a conic constraint problem, enhancing solution efficiency and ensuring better operational stability. Refinery case studies demonstrate that the proposed DRCVaR consistently achieves a practical and acceptable solution, significantly outperforming state-of-the-art approaches.

A novel TD3 for solving multi-level imperfect maintenance optimization problem

Abstract As we all know, multi-level imperfect maintenance strategy is usually more effective than single-level maintenance strategy for the actual production machines. At the same time, in the previous multi-level maintenance strategies, the majority of maintenance models only consider the constant maintenance thresholds, while variable maintenance thresholds are usually ignored. Under these contexts, a novel multi-level imperfect maintenance model with variable preventive maintenance (PM) thresholds, variable overhaul maintenance (OM) thresholds and variable number of PMs in each OM cycle is established. In order to deal with the concerned problem, a novel twin delayed deep deterministic policy gradient (TD3) algorithm that is a kind of reinforcement learning is designed, renamed as NTD3. Finally, through numerical simulation, we can find that (1) the average improvements between the proposed maintenance strategy and other three traditional strategies in the average cost rate (ACR) are 11.50%, 595.91% and 5.16%, respectively; and (2) the average improvement between the proposed NTD3 and other random search method is 5.53%. Thus, the effectiveness of the proposed maintenance strategy and the superiority of proposed NTD3 are all demonstrated.

Towards equitable infrastructure asset management: Scour maintenance strategy for aging bridge systems in flood-prone zones using deep reinforcement learning

Bridges play a critical role in transportation networks; however, they are vulnerable to deterioration, aging, and degradation, especially in the face of climate change and extreme weather events such as floodings. Furthermore, bridges can significantly affect social vulnerability; their damage or destruction can isolate communities, inhibit emergency responses, and disrupt essential services. Maintaining critical bridges in a cost-effective and sustainable manner is crucial to ensure their longevity and protect vulnerable communities. To address the maintenance optimization problem of bridge systems considering the effects of time deterioration, flood degradation, and social vulnerability, this study proposes a deep reinforcement learning algorithm to optimally allocate resources to bridges that are at expected cost of failure due to scour. The algorithm considers the effects of flood degradation with different return periods and is trained using a Markov Decision Process as the environment. The study conducts four flood simulation scenarios using Geographic Information System data. The findings suggest that the deep reinforcement learning algorithm proposes a sequence of repair actions that outperforms the status quo, currently employed by bridge managers. The significance of this study lies in its valuable insights for cities worldwide on how to effectively optimize their limited resources for the maintenance and rehabilitation of critical infrastructure systems to decrease portfolio cost and increase social equity.

Optimal Preventive Maintenance Scheduling of Multi State System. A Comparative Study of Different Meta-heuristic Algorithms

This work presents a comparative study of different meta-heuristic algorithms which are commonly used in the literature, such as Genetic Algorithms, Particle Swarm Optimization, Artificial Bee Colony and Grey Wolf Optimizer. These algorithms are applied to solve a multi-state system maintenance optimization problem considering time and system availability constraints. The objective is to find the optimal inspection and maintenance intervals for each component of the system in order to minimize the preventive maintenance cost of overall the system. The performances of the algorithms are compared using different metrics, regarding the quality and stability of the results and the speed of convergence, in order to determine the most efficient algorithms.

Deep reinforcement learning for maintenance optimization of multi-component production systems considering quality and production plan

In this article, the maintenance optimization of multi-component production systems is investigated by considering quality and production plan. On the one hand, the downtime determined by the production plan provides opportunities for reducing maintenance costs; on the other hand, the deterioration of product quality induced by poor health state leads to extra loss. The coupled relations between production plan, quality, and maintenance, as well as the dependence between multiple components, pose challenges for maintenance optimization. To overcome these challenges, a novel decision model and a deep reinforcement learning-based solving method are proposed. Specifically, in addition to the degradation states of all components, the remaining time of the current batch related to the production plan is also treated as the system state, and the quality loss related to the degradation states is added to the reward function. The deep Q-network algorithm is employed, solving the maintenance optimization problem that considers quality and production plan. The effectiveness of the proposed method is validated by a numerical experiment.

A machine learning framework for explainable knowledge mining and production, maintenance, and quality control optimization in flexible circular manufacturing systems

In the present study, we employed multiple decision tree algorithms to categorize cases and reflect the most efficient policies constructed by a reinforcement learning algorithm. These approaches treated a complex production, maintenance, and quality control optimization problem within a degrading manufacturing and remanufacturing system. The decision trees’ nodes represent the independent variables, while the trees’ leaves represent the set of function values. The reinforcement learning method revealed all optimization parameters and best policies, which were employed as the training sample for the tree algorithms. After constructing every decision tree, each resulting decision rule was used to solve the optimization problem, and its performance was assessed. Additionally, we performed a sensitivity analysis to determine if the pruning level impacts the objective function value and, generally, the effectiveness of the proposed approach.

Dynamic inspection and maintenance scheduling for multi-state systems under time-varying demand: Proximal policy optimization

Inspection and maintenance activities are effective ways to reveal and restore the health conditions of many industrial systems, respectively. Most extant works on inspection and maintenance optimization problems have assumed that systems operate under a time-invariant demand. Such a simplified assumption is oftentimes violated by a changeable market environment, seasonal factors, and even unexpected emergencies. In this article, with the aim of minimizing the expected total cost associated with inspections, maintenance, and unsupplied demand, a dynamic inspection and maintenance scheduling model is proposed for Multi-State Systems (MSSs) under a time-varying demand. Non-periodic inspections are performed on the components of an MSS and imperfect maintenance actions are dynamically scheduled based on the inspection results. By introducing the concept of decision epochs, the resulting inspection and maintenance scheduling problem is formulated as a Markov Decision Process (MDP). The Deep Reinforcement Learning (DRL) method with a Proximal Policy Optimization (PPO) algorithm is customized to cope with the “curse of dimensionality” of the resulting sequential decision problem. As an extra input feature for the agent, the category of decision epochs is formulated to improve the effectiveness of the customized DRL method. A six-component MSS, along with a multi-state coal transportation system, is given to demonstrate the effectiveness of the proposed method.

Determining the optimal production–maintenance policy of a parallel production system with stochastically interacted yield and deterioration

In this paper, we study the integrated production–maintenance optimization problem of a multi-component deteriorating machine. The deterioration of each component is described by a discrete-time Markov chain with finite state space. To meet a constant demand, production planning is scheduled based on the system deterioration and the inventory level. We consider the mutual dependence between the production and the system deterioration. For each component, its deterioration transition probabilities depends on its own characteristics and its production quantity. Production yield is stochastically decreasing with the system deterioration. Maintenance is scheduled immediately if at least one component failure occurs. Otherwise, the decision-maker need to determine whether to schedule a preventive maintenance or to continue producing. We formulate the problem into a Markov decision process framework. The total discounted costs including the production costs, maintenance costs and holding/backlogging costs in the infinite horizon is obtained. Some structural properties of the optimal policy with respect to the machine condition, the inventory level are presented under mild conditions. The proposed model is further examined by a numerical example, where the properties of the production and maintenance planning and the corresponding cost are investigated. It can provide theoretical reference in managing the production and maintenance problems in multiple production lines.

A Deficiency of the Weighted Sample Average Approximation (wSAA) Framework: Unveiling the Gap between Data-Driven Policies and Oracles

This paper critically examines the weighted sample average approximation (wSAA) framework, a widely used approach in prescriptive analytics for managing uncertain optimization problems featuring non-linear objectives. Our research pinpoints a key deficiency of the wSAA framework: when data samples are limited, the minimum relative regret—the discrepancy between the expected optimal profit realized by an oracle aware of the genuine distribution, and the maximum expected out-of-sample profit garnered by the data-driven policy, normalized by the former profit—can approach towards one. To validate this assertion, we scrutinize two distinct contextual stochastic optimization problems—the production decision-making problem and the ship maintenance optimization problem—within the wSAA framework. Our study exposes a potential deficiency of the wSAA framework: its decision performance markedly deviates from the full-information optimal solution under limited data samples. This finding offers valuable insights to both researchers and practitioners employing the wSAA framework.

A closed-loop maintenance strategy for offshore wind farms: Incorporating dynamic wind farm states and uncertainty-awareness in decision-making

The determination of maintenance strategies is subject to complexity and uncertainty arising from variable offshore wind farm states and inaccuracies in model parameters. The most common method in the existing studies is to adopt an open-loop approach to optimize a maintenance strategy. However, this approach lacks the ability to capture periodic operational state of the wind farm and the awareness of eliminating uncertainty. Consequently, the determined strategy is inadequate to instruct maintenance activities, inducing excessive revenue losses. In this paper, a closed-loop maintenance strategy optimization method is proposed for decision-makers to identify a more profitable manner of wind farm maintenance management. The life-cycle maintenance optimization problem is decomposed into a sequence of sub-optimization problems covering multiple time periods by using a rolling-horizon approach. Each sub-optimization problem is intentionally designed based on the monitored state of the wind farm and the available reliability, availability, and maintainability (RAM) database. Meanwhile, the decision maker consciously mitigates the parameter uncertainty in the maintenance model gradually by updating the current database. Compared to conventional strategies covering the entire lifetime of wind farms, the proposed maintenance strategy is periodically adjusted to provide a series of sub-strategies. The proposed approach was applied in a simulation experiment, a generic small-scale offshore wind farm, to assess its performance. Computational results show that adapting maintenance strategies based on the current state of the wind farm can reduce revenue losses in comparison to conventional open-loop strategies. In addition, the benefits of updating the RAM database in decreasing revenue losses is revealed.

On the multi-period combined maintenance and routing optimisation problem

This paper focuses on the combined maintenance and routing optimisation problem in a multi-period environment that consists of scheduling maintenance operations for a set of geographically distributed machines, subject to non-deterministic failures with a set of technicians that perform preventive maintenance and corrective operations. This study uses a two-step approach based on column generation. The first step consists of a maintenance model that determines the optimal time until the next preventive maintenance operation, and each machine’s maintenance frequency while minimising the total expected maintenance costs. The second step involves a routing model that assigns and schedules maintenance operations for each technician over the planning horizon while minimising the routing and maintenance costs. We formulate the second step problem as a periodic vehicle routing problem and to solve it, we propose a column generation approach. The master problem is a set partitioning formulation that indicates which machines must be visited in the planning horizon. This decomposition has two auxiliary problems: the first one is an elementary shortest-path problem to find a feasible path for each period and the second one finds a set of visiting periods for each machine. Our approach balances the maintenance cost, routing cost, and failure probabilities.

Condition-based Maintenance Optimization for Gamma Deteriorating Systems under Performance-based Contracting

With the further development of service-oriented, performance-based contracting (PBC) has been widely adopted in industry and manufacturing. However, maintenance optimization problems under PBC have not received enough attention. To further extend the scope of PBC’s application in the field of maintenance optimization, we investigate the condition-based maintenance (CBM) optimization for gamma deteriorating systems under PBC. Considering the repairable single-component system subject to the gamma degradation process, this paper proposes a CBM optimization model to maximize the profit and improve system performance at a relatively low cost under PBC. In the proposed CBM model, the first inspection interval has been considered in order to reduce the inspection frequency and the cost rate. Then, a particle swarm algorithm (PSO) and related solution procedure are presented to solve the multiple decision variables in our proposed model. In the end, a numerical example is provided so as to demonstrate the superiority of the presented model. By comparing the proposed policy with the conventional ones, the superiority of our proposed policy is proved, which can bring more profits to providers and improve performance. Sensitivity analysis is conducted in order to research the effect of corrective maintenance cost and time required for corrective maintenance on optimization policy. A comparative study is given to illustrate the necessity of distinguishing the first inspection interval or not.

Multi-stage preventive maintenance optimization with thresholds of reliability

This paper studies the problem of multi-stage preventive maintenance (PM) optimization on the basis of reliability thresholds. According to the change rule of product's failure rate and by means of setting the reliability thresholds, the replacement cycle is divided into three maintenance stages, they are: (1) Stage I: do not carry out PM; (2) Stage II: carry out periodic PM; (3) Stage III: carry out sequential PM. In each stage, the failures are restored with minimal repair. Age reduction factor and quasi-renewal coefficient are adopted to derive the recursive relations of failure rate function in each stage. A multi-stage PM optimization model is established based on the reliability thresholds, with the aim to minimize the equipment's expected cost rate. Taking the gearbox, rotor and bearing of wind turbine as an example, a case study is conducted to illustrate the effectiveness of the proposed method.

Discrete Model for a Multi-Objective Maintenance Optimization Problem of Safety Systems

The aim of this article was to solve a multi-objective maintenance optimization problem by minimizing both unavailability and cost through the use of an optimal maintenance strategy. The problem took into account three different system designs upon which the objective functions are dependent, and the time to start preventive maintenance (PM) was used as a decision variable. This variable was optimized for all system components using a discrete maintenance model that allows for the specification of several discrete values of the decision variable in advance to find the optimal one. The optimization problem was solved using innovative computing methodology and newly updated software in MATLAB, which was used to quantify the unavailability of a complex system represented through a directed acyclic graph. A cost model was also developed to compute the cost of different maintenance configurations, and the optimal configuration was found. The results for a selected real system (a real fluid injection system adopted from references) showed that unavailability was less sensitive to variations in maintenance configurations, while cost variations were more noticeable in relation to different maintenance configurations. Applying PM, the increasing value of the decision variable increased cost because it led to more frequent corrective maintenance (CM) actions, and recovery times due to CM were more expensive than recovery times due to PM.

Maintenance analysis of a partial observable K-out-of-N system with load sharing units

In this paper, we consider the inspection and maintenance optimization of a K-out-of- N load-sharing system that operates in a deteriorating working condition. The failure rate of each component depends on its load-sharing and the system working condition. During the operation, the system working condition can be deteriorated from the healthy state to the abnormal state. Both the states of the components and the system working environment are hidden. To ensure the system safety, periodical inspection is implemeted, upon which, two-folds of information can be obtained: the state of each component and the partial revealed information corresponding to the state of the working condition. A maintenance policy is proposed based on the observations. The policy is assessed by the total expected discounted maintenance cost in the long-run horizon. We cast the problem into a partially observable Markov decision process framework. We utilize the value iteration algorithm to solve the inspection and maintenance optimization problem. Sensitivity analyses through numerical examples are carried out. A case study of a parallel system with electric motors is examined to show the applicability of the proposed model.

Selective maintenance of multi‐state systems with the repairperson fatigue effect and stochastic break duration

AbstractSystems in the industry are often required to execute a sequence of missions, and the state of the multi‐state systems may deteriorate with the increasing of running time. To improve the system reliability of the next mission, selective maintenance is applied in the limited break. Due to the fatigue effect, the work rate of the repairperson decays with time. However, the existing selective maintenance studies do not consider the impact of fatigue effect on work rate, which leads to underestimating the duration of maintenance actions and overestimating the system reliability. To overcome the above problems, a new selective maintenance model for multi‐state systems is developed to maximize the system reliability of the next mission. First, the decay process of the work rate of a repairperson is described as a piecewise continuous decreasing exponential function of working time. Next, a homogenous discrete‐state continuous‐time Markov process is used to describe the performance capacity degradation of components. Considering the stochastic break duration, based on the state probability distribution of each component obtained by the Markov model, the universal generation function (UGF) method is applied to evaluate the multi‐state system reliability. Then, taking the selected maintenance actions and maintenance priority as decision variables, the resulting selective maintenance optimization problem is solved by a tailored genetic algorithm. Finally, two computational experiments are carried out to demonstrate the effectiveness of the proposed method.

A decomposition method by interaction prediction for the optimization of maintenance scheduling

Optimizing maintenance scheduling is a major issue to improve the performance of hydropower plants. We study a system of several physical components of the same family: either a set of turbines, a set of transformers or a set of generators. The components share a common stock of spare parts and experience random failures that occur according to known failure distributions. We seek a deterministic preventive maintenance strategy that minimizes an expected cost depending on maintenance and forced outages of the system. The Auxiliary Problem Principle is used to decompose the original large-scale optimization problem into a sequence of independent subproblems of smaller dimension while ensuring their coordination. Each subproblem consists in optimizing the maintenance on a single component. Decomposition-coordination techniques are based on variational techniques but the maintenance optimization problem is a mixed-integer problem. Therefore, we relax the dynamics and the cost functions of the system. The resulting algorithm iteratively solves the subproblems on the relaxed system with a blackbox method and coordinates the components. Relaxation parameters have an important influence on the optimization and must be appropriately chosen. An admissible maintenance strategy is then derived from the resolution of the relaxed problem. We apply the decomposition algorithm on a system with 80 components. It outperforms the reference blackbox method applied directly on the original problem.

A condition-based maintenance model considering multiple maintenance effects on the dependent failure processes

Maintenance is generally assumed to play a positive role, however, in reality, it is also common that maintenance actions have negative impacts. In this paper, a condition-based maintenance model for repairable systems subject to dependent failure processes (soft failure due to system degradation and hard failure due to random shocks) is proposed. It is a unified model with strong compatibility. The effects of maintenance actions with negative or positive effects incurred by inspection, preventive maintenance and corrective maintenance are all considered. In order to show the effects of maintenance actions intuitively, a vector space spanned by the degradation level, deteriorate rate and hard failure threshold is constructed. It can easily show the complex and multiple effects between maintenance impacts. Finally, the model is used to deal with high-voltage transmission lines’ maintenance optimization problem. The results show that the model is feasible and can be applied in the field of maintenance optimization.

Opportunistic perfect preventive maintenance policy in presence of masked data

In this paper, the maintenance optimization problem of multi-component system is considered. It is assumed that the exact cause of system failure might be masked. That is, the exact cause of failure is unknown, and we only know that it belongs to a set called mask set. Both opportunistic perfect preventive maintenance (OPPM) and perfect corrective maintenance are considered. Threshold of OPPM and inter-inspection interval are considered as decision parameters which are optimized using long-run cost rate criteria. The applicability of the proposed maintenance policy is investigated using an illustrative example.

Optimizing imperfect preventive maintenance in multi-component repairable systems under [formula omitted]-dependent competing risks

Existing maintenance optimization models for single-component repairable systems are extensively studied. However, maintenance optimization in multicomponent reparable systems (MCRS) is still a challenging problem, especially when dealing with stochastic dependent (s-dependent) competing risks between components. This paper develops a novel reliability-centered maintenance optimization model for MCRS operating under s-dependent competing risks. The s-dependency is captured by the joint reliability function constructed using Copula method and unknown parameters are estimated by maximum likelihood estimations (MLE). Maintenance strategies are carried out both at components and system levels. At components level, a preventive maintenance (PM) is performed whenever the reliability of the MCRS reaches a given threshold. PM actions are imperfect and modeled using the hybrid hazard rate approach. At system level, the whole system is preventively replaced after a certain number of PM cycles. The objective of the proposed maintenance strategies is to determine the optimal reliability threshold together with the optimal number of PM cycles that minimize the total expected maintenance cost rate in the infinite time horizon. The optimality conditions of the resulting maintenance optimization problem are formally discussed via two propositions. A case study that investigates a ball screw mechanism with multiple components is provided to validate the proposed approaches.