Random Breakdowns Research Articles

Checkpointing models for tasks of different types

A server subject to random breakdowns and repairs offers services to incoming jobs whose lengths are highly variable. A checkpointing policy is in operation, aiming to protect against possibly lengthy recovery periods by backing up the current state at periodic checkpoints. The problem of how to choose a checkpointing interval to optimise performance is addressed by analysing a general queueing model which includes breakdowns, repairs, back-ups and recoveries. Exact solutions are obtained under both Markovian and non-Markovian assumptions. Numerical experiments illustrate the conditions where checkpoints are useful and where they are not, and, in the former case, quantify the achievable benefits.

Flexible job shop scheduling with stochastic machine breakdowns by an improved tuna swarm optimization algorithm

In job-shop production environments, machine breakdowns are a significant factor in reducing productivity. Existing approaches seldom consider algorithm improvement and rescheduling scheme design in an integrated manner, and lack stability considerations. This paper addresses the flexible job shop scheduling problem with random machine breakdowns, aiming to produce a stable rescheduling scheme that minimizes a combined index of maximum completion time and stability. The paper innovatively applies the tuna swarm optimization algorithm to the flexible job shop scheduling problem, proposing an efficient and superior improved version called the genetic chaos levy nonlinear tuna swarm optimization (GCLNTSO) algorithm. Three stability metrics are designed to guide the generation of efficient and stable rescheduling schemes. A rescheduling scheme is proposed that combines right-shift rescheduling with complete rescheduling. The proposed scheme is benchmarked against Brandymalter and Kacem’s problems, and compared with other algorithms from the literature. The results demonstrate that the GCLNTSO algorithm outperforms other algorithms in terms of both performance and stability.

Robust job shop scheduling with machine unavailability due to random breakdowns and condition-based maintenance

This paper presents a novel solution approach for a variant of the job shop scheduling problem with machine unavailability due to both condition-based preventive maintenance and corrective maintenance following random breakdowns. We first provide an exact mathematical formulation of the problem under simplifying assumptions, namely that the number of breakdowns for each job position on each machine is known, the degradation rates are fixed, and the preventive and corrective maintenance durations are deterministic parameters. Moreover, to handle the more realistic case of stochastic machine degradation, random breakdowns, and uncertain maintenance durations, a simulation-optimisation algorithm is proposed. The real makespan function is first approximated using multiple surrogate measures, which are optimised through independent genetic algorithms. Then, the fittest solutions obtained from these surrogate measures are simulated, and the best among them is added to an elite list, which is included in the genetic algorithms' populations for the next iteration. Schedule robustness is ensured by using an objective function that consists of the weighted average of the expected makespan and its 90th percentile. Furthermore, to reduce the likelihood of falling into a local optimum, a stopping criterion based on simulated annealing is implemented. Numerical experimentation on extended benchmark instances confirmed the validity of the mathematical formulation and the favourable performance of the proposed simulation-optimisation algorithm in terms of computational time and solution quality.

A two-step scheduling and rescheduling framework for integrated production and usage-based maintenance planning under TOU electricity tariffs: A case study of the tile industry

The primary motivation of this study is to provide an easily implementable and cost-effective solution for reducing energy expenses, improving slurry quality, mitigating system instability due to random breakdowns, and minimizing maintenance frequencies in the ball mills of the tile industry. To achieve this goal, a two-step framework is proposed which can also be applied to parallel machines in make-to-order environments. The first step integrates the usage-based maintenance and production scheduling under time-of-use (TOU) electricity prices and involves a mixed integer linear programming (MILP) model with buffer time insertion to handle unpredictable machine unavailability. The second step suggests a combination of model-based and manual reactive policies for rescheduling. Compared to its non-energy-aware counterpart, the proposed model shows a 22% improvement in energy costs and a 4% increase in energy savings. Additionally, the usage-based maintenance strategy reduces maintenance frequencies by more than 50% compared to the time-based one. By integrating TOU-based production scheduling with usage-based maintenance scheduling, we offer three advantages for energy-intensive industries: 1) increased scheduling flexibility to shift production to low-tariff periods, 2) the ability to schedule maintenance operations during idle time resulting from production shifts, and 3) reduced maintenance frequencies for machines with extended idle times through a usage-based maintenance strategy. The proposed approach performs best when machines exhibit significant differences in energy consumption rates and have high total idle times. However, implementing it for bottleneck machines does not lead to notable improvements in energy-related indicators.

Minimizing the makespan for the two-machine flow shop scheduling problem with random breakdown

AbstractThis paper studies a two-machine flow shop scheduling problem with availability constraints due to a breakdown on the first machine. The starting time of the breakdown is considered stochastic and follows a known probability distribution. A service-level constraint is introduced to model the guarantee with which the obtained schedule takes into account the stochastic nature of the breakdown’s starting time. The objective is to find a solution that minimizes the makespan while satisfying the desired service level. The studied problem is strongly NP-hard. We develop two mixed integer linear models that linearize the non-linear model. Using interval modeling of the breakdown, we propose lower bounds and a valid inequality that are used to strengthen both models. When the lower bounds and the valid inequality are applied, the performance of both models is greatly improved by reducing the gap and reaching optimality for more instances. We also introduced two heuristics that exploit the proposed interval modeling. The computational results indicate that both models are able to reach optimality for the 10-job instances. Moreover, the comparisons results between both models with the two heuristics showed their effectiveness.

A semi-empirical algorithm for determining the impulse characteristics of gas-insulated two-electrode systems in the vicinity of Paschen minimum with and without taking into account the spark channel thermoionization time

The impulse characteristic represents the response of the gas insulation to the impulse load. There is no rational way to determine it, since it must include all pulse shapes and all probability quantiles of a random breakdown event. Near Paschen minimum is the operating point of gas surge arresters. For this reason, the results presented in this paper are important for the coordination of insulation at the low-voltage level. The semi-empirical algorithm derived in this paper is simple and allows obtaining impulse characteristics based on a small number of measurements. The paper presents two variants of the derived algorithm. One with and one without taking into account the thermoionization time of the streamer channel. Both variants were experimentally verified in well-controlled laboratory conditions and good results were obtained from the point of view of engineering practice. Of course, the algorithm which includes the thermoionization time of the spark channel gave more exact results. However, even in that case, an improvement can be made by observing the thermoionization process as a stochastic phenomenon. In this sense, suggestions for further improvement of the proposed algorithm are given.

Large Energy Capacitive High-Entropy Lead-Free Ferroelectrics

HighlightsUltrahigh energy storage density of ~ 13.8 J cm−3 and large efficiency of ~ 82.4% are achieved in high-entropy lead-free relaxor ferroelectrics via high-entropy strategy, realizing nearly ten times growth.Outstanding energy storage properties are attributed to the enhanced random field and breakdown field, decreased nanodomain sizes, strong multiple local distortions coexisting in-phase and anti-phase oxygen octahedron tilts.Evolution of energy storage performance and domain structure with the increase in configuration entropy is systematically revealed for the first time.

Reinforcement learning and stochastic dynamic programming for jointly scheduling jobs and preventive maintenance on a single machine to minimise earliness-tardiness

This paper addresses the problem of stochastic jointly scheduling of resumable jobs and preventive maintenance on a single machine, subject to random breakdowns, to minimise the earliness-tardiness cost. The main objective is to investigate using trending machine learning-based methods compared to stochastic optimisation approaches. We propose two different methods from both fields as we solve the same problem firstly with a stochastic dynamic programming model in an approximation way, then with an attention-based deep reinforcement learning model. We conduct a detailed experimental study according to solution quality, run time, and robustness to analyse their performances compared to those of an existing approach in the literature as a baseline. Both algorithms outperform the baseline. Moreover, the machine learning-based algorithm outperforms the stochastic dynamic programming-based heuristic as we report up to 30.5% saving in total cost, a reduction of computational time from 67 min to less than 1 s on big instances, and a better robustness. These facts highlight clearly its potential for solving such problems.

Evaluation of the Robustness for Integrated Production Scheduling and Maintenance Planning Problem

In this paper, we consider the surrogate measures of robustness for the integration of production scheduling and preventive maintenance planning problem with stochastic machine failures. First, the influence of two categories of maintenance on operation completion time is analyzed. Since it does not come with an exact solution, a novel measure algorithm for evaluating two types of robustness simultaneously is proposed, based on the internal relationships among the scheduling structure, the number and sequence of preventive maintenance activities, the probability and downtime of failures, and the expected completion time of operation. Extensive experiments are conducted on 19 benchmark problems with random machine breakdowns. Experimental results first show that the correlation between our algorithm and Monte Carlo simulation in two robustness indicators is above 99%, and the former computes much faster than the latter. A thorough comparison is made with the other three surrogate robustness measures, which further proves the accuracy of our algorithm. Additional experiments also confirm the benefits by integrating preventive maintenance.

Transitive Reduction Approach to Large-Scale Parallel Machine Rescheduling Problem With Controllable Processing Times, Precedence Constraints and Random Machine Breakdown

This paper studied a novel parallel machine rescheduling problem with controllable processing times under machine breakdown and precedence constraints. This problem is strongly <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {NP}$ </tex-math></inline-formula> -hard, and we modeled it as a mixed-integer problem (MIP). The primal problem is decomposed into the discrete subproblem and the continuous one. We treat the discrete with the dispatching rule and analyze the continuous in the terms of mathematical programming. Pros and cons from the analysis lead us to implement the commercial solver. The proposed method is capable of efficiency and nonzero initial state. We introduce transitive reduction to cull the redundant constraints out of its directed acyclic graph (DAG) representation. Transitive reduction extends the efficiency from the dispatching rule to the solver. The proposed method can do the predictive scheduling and pick up the partial solution left by the machine breakdown in the reactive session. As a result, the complete method solves the rescheduling problem with efficiency, and allows for large cases. At last, the computational results showed that this technique significantly brought down the time and RAM consumption in using the solver. This technique allows the scheduler to solve big instances with computational economy and efficiency.

Mathematical modelling of breakdowns with soft failures and explicit analytical expressions of an &lt;i&gt;M&lt;/i&gt;/&lt;i&gt;M&lt;/i&gt;/1 queue's transient state probabilities

In the last decade, the increasing usage of digital electronics and software has given rise to a new form of failure occurrence known as soft failure. Soft failure is not the same as catastrophic failure. Catastrophic failure removes all waiting customers, including those receiving service, and the system enters the repair state, whereas soft failure does not require the removal of customers and instead requires the customer to wait for the server reactivation because repair can be accomplished by simply rebooting the system. A new approach for categorising and analysing these events is necessary to characterise and distinguish soft failures from hardware catastrophic failures. As a result, this paper considers a single server queueing model with soft failure. The system is prone to random breakdowns while providing service to the customer. When a system malfunctions, repair work begins right away. During the repair period, new customers are not permitted to join the system. For the first time, the transient state probabilities of an M/M/1 queue with soft failures are computed explicitly. Some performance metrics, such as availability and reliability, are derived. Numerical examples are also provided to demonstrate the effect of parameters.

Impact of Preventive Maintenance and Machine Breakdown on Performance of Stochastic Flexible Job Shop Scheduling with Setup Time

Real-time scheduling problems increase the practical implementation of the manufacturing system. In this study, using a single objective performance measure i.e., Number of Tardy Jobs (NTJ), the influence of 5 input constraints, i.e., reliability level (R_L), percentage of machine failure (%McF), mean time to repair for random machine breakdown (MTR_RMcB), due date tightness factor (Ғ), and routing flexibility level (R_FL) were evaluated for considered stochastic Flexible Job Shop Scheduling Problem (FJSSP). The study integrated reliability-centered preventive maintenance (PMRC) and random machine breakdown (RMcB) environment with sequence-dependent setup time in the considered problem. A statistical response surface methodology was used to assesses NTJ. A second-order regression model was obtained to compute correlation between input constraints and NOTJ at 95% confidence level. The results demonstrate that main effects of R_L, %McF, Ғ, and R_FL; the interaction effects of R_L and Ғ, %McF and R_FL, MTR_RMcB and R­_FL, and Ғ and R_FL; and quadratic effects of Ғ and R_FL, have significant impact on NTJ performance measure. Ғ has emerged as the major factor affecting NTJ. The confirmatory data demonstrate that error is less than 5%, confirming model can be used for future computations. Further, the novelties of the work are shown by the fact that it takes into account the uncertainties in the scheduling issue, as well as the dynamic tasks arrival environment. The aforementioned findings will assist production managers in planning and scheduling flexible job shops in order to satisfy customer demand on time.

On Connectivity of Conditional Configuration Graphs under Destruction

Configuration graphs with node degrees being independent identically distributed random variables following the power-law distribution with a shift are studied. We consider conditional graphs that consist of only one connected component. Computer simulations are used to study how the connectivity of such graphs changes under the two types of destruction processes: the “target attack” and the “random breakdown”. We propose models for the dependence of the probability of graph connectivity destruction on the graph size, the node degree distribution parameter, and the number of deleted nodes.

Optimum utilization of on-demand manufacturing and laser polishing in existence of supply disruption risk

3D printing has moved from being a rapid prototyping tool to an additive manufacturing method within the last decade. Additive manufacturing can satisfy the need in dire situations where spare parts distribution is an issue but access to a 3D printer is much more likely and rapid than access to original parts. Managing inventories of spare parts can be tackled with more ease thanks to the reduced part types with additive manufacturing. While quality (in terms of reliability) of additively manufactured spare parts in terms of mechanical properties seem to be lower than original parts (particularly due to the inherent staircase appearance and the corresponding stress concentration zones that can lead to premature fatigue failure), use of post-processing subtractive techniques to correct such surface irregularities are found to improve reliability. While each process adds another layer of complexity to the cost minimization problem, demand uncertainty and risk of supply disruption represent the modern global problems faced recently. The problem tackled in this study is the joint optimization of the supply reliability considering the effect of laser polishing parameters and the demand uncertainty. In this problem, a condition of random breakdowns of identical products is considered. Also, the original supplier of machine components is subject to exogenous disruptions, such as strikes, raw material scarcity, or the COVID-19 pandemic. As a result, the optimum control policy with the right cost parameters was shown via numerical experiments originated from mathematical analyses. This optimality can be critical in managing the system in the best possible way, particularly during times of unforeseen circumstances such as pandemics.

Planning and scheduling of a parallel-machine production system subject to disruptions and physical distancing

Abstract This paper aims to quantify the effects of production disruptions (PDs) and physical distancing constraints due to the pandemic in a parallel-machine production environment. The machines are non-identical and are utilized for producing a finite set of jobs (parts) in a plastic injection moulding production. The production process is subjected to random production downtime disruptions. A mixed-integer linear programming (MILP) model is developed for optimizing the joint production plan and schedule, which maximizes the production’s total benefit. The model is utilized to plan and schedule a set of 17 machines in a Canadian manufacturing company. To explore the effects of physical distancing and PDs on the production’s total net profit, four different scenarios for normal operation and production during the pandemic, with and without production downtimes, are considered. A genetic algorithm is utilized to solve the model. The results show that considering machines’ random breakdowns and physical distancing individually reduces the total profit of the production by 71.58 and 57.98%, respectively; while their joint effect results in a 88.54% reduction in the annual net profit.

An Imperfect Inventory Model for Multi-Warehouses Under Different Discount Policies With Shortages

A multi-warehouse inventory model with shortage has been developed where demand is taken as deterministic. In reality, during production, if the machine works for a long time there may be a random breakdown and the system shifts from controlled to out of the controlled situation, in this time production system produces defective items. The retailer offers an all-unit quantity discount on the selling price of the item who in return gets a quantity-based discount on the purchase price of the item. The motive of this model is to study a multi-warehouse model for imperfect items under a quantity-based discount, where the defectives can be screened and then can be sold in a single batch where the decision variables are set as optimal ordering quantity and optimal shortage quantity, to maximize the total profit of the retailer. A solution procedure is given to find the optimal solution and a numerical example is given to illustrate this study. Sensitivity analysis is also performed to study the effect of the changes in parameter values on the optimal solution.

Energy consumption control in the two-machine Bernoulli serial production line with setup and idleness

In recent years, the topic of sustainable manufacturing system design with energy saving features has received increasing attention. For a typical production line setting, the machines are subject to random breakdown and restart besides blockage and starvation, and they are usually connected via buffer areas with finite capacity. In the present study, the energy consumption of the serial production line with two Bernoulli machines is considered, with an aim to minimise the total energy consumption under a desired production rate. The energy consumption of the two-machine system is composed of the energy needed to setup, to remain idle, and for actual manufacturing. In order to minimise the total energy expenditure, a nonlinear fractional polynomial optimisation model is constructed, which is first converted to a nonlinear polynomial optimisation problem. Then the property of the total energy cost is analysed via the sum of squares (SOS) method. To speed up the solving process, a new heuristic approach named energy consumption saving (ECS) algorithm is proposed considering the monotonicity and local optimality of the energy cost function. Finally, by presenting optimal configurations of the production line with different throughputs, buffer capacities, and energy parameters, a simulation-based study is performed to validate the SOS and ECS algorithms.

Robust job-shop scheduling under deterministic and stochastic unavailability constraints due to preventive and corrective maintenance

This paper presents a modeling and solution approach for a robust job-shop scheduling problem (JSP) under deterministic and stochastic machine unavailability caused, respectively, by planned preventive maintenance (PM) and unplanned corrective maintenance (CM) following random breakdowns. The goal is to optimize the sequence of jobs and run-based planned preventive maintenance tasks in a robust manner while considering the degradation of machines over time. The time to failure for each machine is assumed to follow a Weibull distribution. The robust objective function to be minimized is a weighted sum of the expected values of the makespan and the gross positive deviation between the actual and planned start times of the jobs, as proxies for quality robustness and solution robustness, respectively. Two metaheuristic algorithms that aim at providing a good balance between performance quality and solution robustness are developed. In both algorithms, the “true” makespan objective function (with both PM and CM) is approximated using three surrogate measures. Genetic algorithm (GA) is first used to optimize the surrogate functions, then the fittest solutions from the three oracles are simulated with random breakdown scenarios and the best among them is introduced as an elite member in the next GA iteration. The first algorithm terminates as soon as the solution obtained is worse than the best know solution or when the maximum number of iterations is reached, whereas the second algorithm applies a rule inspired by Simulated Annealing for termination. Numerical experimentation on benchmark instances from the literature showed excellent performance of the proposed algorithms in terms of average marginal improvement and runtime. These results show that the proposed framework can generate high-quality robust job shop schedules under deterministic and stochastic machine unavailability constraints. Moreover, the sensitivity analysis results recommended some key insights and directions for future research.

Rescheduling Plan Optimization of Underground Mine Haulage Equipment Based on Random Breakdown Simulation

Due to production space and operating environment requirements, mine production equipment often breaks down, seriously affecting the mine’s production schedule. To ensure the smooth completion of the haulage operation plan under abnormal conditions, a model of the haulage equipment rescheduling plan based on the random simulation of equipment breakdowns is established in this paper. The model aims to accomplish both the maximum completion rate of the original mining plan and the minimum fluctuation of the ore grade during the rescheduling period. This model is optimized by improving the wolf colony algorithm and changing the location update formula of the individuals in the wolf colony. Then, the optimal model solution can be used to optimize the rescheduling of the haulage plan by considering equipment breakdowns. The application of the proposed method in an underground mine revealed that the completion rate of the mine’s daily mining plan reached 83.40% without increasing the amount of equipment, while the ore quality remained stable. Moreover, the improved optimization algorithm converged quickly and was characterized by high robustness.

Joint determination of purchasing and production lot sizes in an unreliable production system

This paper discusses a production-inventory system under random machine breakdown. Holding safety stock is the common way to mitigate the effect of random machine breakdown on shortages that may occur during machine repair time. Since holding safety stock can be costly, especially for expensive products, this paper investigates an alternative strategy in which it is assumed that the production manager can purchase the same products from a supplier in order to meet the demands that may be lost due to the depletion of the inventory after the machine breakdown. The supplier has known lead-time and reliability with the quality assured products. Despite holding safety stock, purchasing occurs only when the machine breakdown happens. The question is about the optimal amount of production and purchasing lot sizes to minimize the total expected costs. The optimality of the model is investigated when failure and repair time follow an exponential distribution, and a computational algorithm for finding the optimal lot sizes is presented. A comparison between the purchasing strategy and holding safety stock is performed through a sensitivity analysis regarding some effective parameters. This study shows using the purchasing strategy when holding or production cost rises is more beneficial than holding safety stock.