Unavailability Constraints Research Articles

Metaheuristic Algorithms for Related Parallel Machines Scheduling Problem with Availability and Periodical Unavailability Constraints

Metaheuristic Algorithms for Related Parallel Machines Scheduling Problem with Availability and Periodical Unavailability Constraints

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.

Auxiliary resource planning in a flexible flow shop scheduling problem considering stage skipping

This paper investigates a flexible flow shop scheduling problem wherein there are some unrelated parallel machines with different technology levels in the first stage. Some of these machines are multifunctional that can do several processes on jobs. Therefore, the jobs assigned to these machines do not require processing in some of the next stages. Although the majority of the traditional scheduling problems deal with machines as the only resource, there are usually unavailability constraints to auxiliary resources such as labor, tools, pallets, industrial robots, and so on. This challenge with inspiration from a spring manufacturing plant is tackled in the considered problem with machine eligibility and sequence-dependent setup times. This problem is described with a numeric example, and its parameters and decision variables are defined. Then, to formulate the problem, a mixed-integer linear programming model is developed to minimize the makespan and determine the number of required auxiliary resources. Then the genetic algorithm is calibrated for all aforementioned features of the problem at hand as the main solution approach. Furthermore, two other well-known metaheuristics i.e., simulated annealing and enhanced particle swarm optimization are modified and employed for computational comparisons. The result shows that the proposed algorithm provides accurate results regarding the number of required auxiliary resources to achieve the minimum makespan. Moreover, supplementary analysis is presented considering practical constraints such as budget and desired efficiency of machines. The result indicates that the solution approach could provide proper alternatives for managers in various conditions.

Model of Production System Evaluation with the Influence of FDM Machine Reliability and Process-Dependent Product Quality.

This paper investigates the Job Shop Scheduling Problem (JSSP) with FDM (Fused Deposition Modeling) machine unavailability constraints due to Predictive Maintenance (PdM) tasks, under the objective of minimizing the makespan, total tardiness and machine idle time. The Ant-Colony Optimization (ACO) algorithm is elaborated to deal with the JSSP. The reliability characteristics of the critical machine (FDM) influence the product as well as the production system quality. PdM periods are estimated based on historical data on failure-free times of the FDM machine components and deviations from the standards established for the key process parameters: infill density, layer thickness and extruder temperature. The standards for the key process parameters are identified based on investigation of the mechanical properties of printed elements. The impact of failure time and the number of nonstandard measurements of parameters on the quality of the Job Shop System (JSS) are observed. Failure rate of the FDM machine is corrected with the probability of a stoppage in the future period due to the “outlier” in measurements of any key parameters of the additive process. The quality robustness of production schedules increases with the disturbance-free operation of the FDM up to the peak value. After reaching the peak value the quality robustness decreases. The original issue of this paper is a model of scheduling production and maintenance tasks in a job shop system with an FDM machine as a bottleneck using ACO. Additionally, an original FDM-reliability model is also proposed. The model is based on weighted p-moving averages of the observed number of deviations from the norms, established for key process parameters such as fill density, layer thickness and extruder temperature.

Offloading Data through Unmanned Aerial Vehicles: A Dependability Evaluation

Applications in the Internet of Things (IoT) context continuously generate large amounts of data. The data must be processed and monitored to allow rapid decision making. However, the wireless connection that links such devices to remote servers can lead to data loss. Thus, new forms of a connection must be explored to ensure the system’s availability and reliability as a whole. Unmanned aerial vehicles (UAVs) are becoming increasingly empowered in terms of processing power and autonomy. UAVs can be used as a bridge between IoT devices and remote servers, such as edge or cloud computing. UAVs can collect data from mobile devices and process them, if possible. If there is no processing power in the UAV, the data are sent and processed on servers at the edge or in the cloud. Data offloading throughout UAVs is a reality today, but one with many challenges, mainly due to unavailability constraints. This work proposes stochastic Petri net (SPN) models and reliability block diagrams (RBDs) to evaluate a distributed architecture, with UAVs focusing on the system’s availability and reliability. Among the various existing methodologies, stochastic Petri nets (SPN) provide models that represent complex systems with different characteristics. UAVs are used to route data from IoT devices to the edge or the cloud through a base station. The base station receives data from UAVs and retransmits them to the cloud. The data are processed in the cloud, and the responses are returned to the IoT devices. A sensitivity analysis through Design of Experiments (DoE) showed key points of improvement for the base model, which was enhanced. A numerical analysis indicated the components with the most significant impact on availability. For example, the cloud proved to be a very relevant component for the availability of the architecture. The final results could prove the effectiveness of improving the base model. The present work can help system architects develop distributed architectures with more optimized UAVs and low evaluation costs.

Integrated Scheduling of Tasks and Preventive Maintenance Periods in a Parallel Machine Environment With Single Robot Server

In this study, the objective of minimizing makespan has been considered for a scheduling problem of identical parallel machines with a single server and unavailability constraints. The unavailability constraints correspond to preventive maintenance periods. In this study, the jobs and the maintenance periods are scheduled simultaneously. This scheduling problem has a wide range of potential application areas in the manufacturing environment. In addition, the studied problem is a challenging one from theoretical point of view, due to its NP-Hardness. To conduct the study, a lower bound ( LB ) for the problem, and three metaheuristics namely Simulated Annealing ( SA ), Tabu Search ( TS ), and Genetic Algorithm ( GA ) have been proposed. The best parameters settings of the proposed algorithms were conducted using pilot runs with a Taguchi design. The algorithms performance has been assessed by using a set of test problems generated randomly. These test problems are based on a literature benchmark. The size of the instances, or number of jobs, were up to 500. Along with the performance analysis of the proposed algorithms, the effect of varying processing times and unavailability periods on the performance of the proposed algorithms is studied. The present work provides strong evidence of the efficiency and the performance of the proposed algorithms.

Scheduling Two Identical Parallel Machines Subjected to Release Times, Delivery Times and Unavailability Constraints

This paper proposes a genetic algorithm (GA) for scheduling two identical parallel machines subjected to release times and delivery times, where the machines are periodically unavailable. To make the problem more practical, we assumed that the machines are undergoing periodic maintenance rather than making them always available. The objective is to minimize the makespan (Cmax). A lower bound (LB) of the makespan for the considered problem was proposed. The GA performance was evaluated in terms of the relative percentage deviation (RPD) (the relative distance to the LB) and central processing unit (CPU) time. Response surface methodology (RSM) was used to optimize the GA parameters, namely, population size, crossover probability, mutation probability, mutation ratio, and pressure selection, which simultaneously minimize the RPD and CPU time. The optimized settings of the GA parameters were used to further analyze the scheduling problem. Factorial design of the scheduling problem input variables, namely, processing times, release times, delivery times, availability and unavailability periods, and number of jobs, was used to evaluate their effects on the RPD and CPU time. The results showed that increasing the release time intervals, decreasing the availability periods, and increasing the number of jobs increase the RPD and CPU time and make the problem very difficult to reach the LB.

A note on scheduling on uniform parallel machines with unavailability constraints

We show by counterexample that the binary integer quadratic programming model proposed by Kaabi and Harrath [2019. “Scheduling on Uniform Parallel Machines with Periodic Unavailability Constraints.” International Journal of Production Research 57: 216–227] is incorrect. We fix this model and propose two linear ones.

Modeling and Solving Scheduling Problem with m Uniform Parallel Machines Subject to Unavailability Constraints

The problem investigated in this paper is scheduling on uniform parallel machines, taking into account that machines can be periodically unavailable during the planning horizon. The objective is to determine planning for job processing so that the makespan is minimal. The problem is known to be NP-hard. A new quadratic model was developed. Because of the limitation of the aforementioned model in terms of problem sizes, a novel algorithm was developed to tackle big-sized instances. This consists of mainly two phases. The first phase generates schedules using a modified Largest Processing Time ( L P T )-based procedure. Then, theses schedules are subject to further improvement during the second phase. This improvement is obtained by simultaneously applying pairwise job interchanges between machines. The proposed algorithm and the quadratic model were implemented and tested on variously sized problems. Computational results showed that the developed quadratic model could optimally solve small- to medium-sized problem instances. However, the proposed algorithm was able to optimally solve large-sized problems in a reasonable time.

Single-machine common due date total earliness/tardiness scheduling with machine unavailability

Research on non-regular performance measures is at best scarce in the deterministic machine scheduling literature with machine unavailability constraints. Moreover, almost all existing works in this area assume either that processing on jobs interrupted by an interval of machine unavailability may be resumed without any additional setup/processing or that all prior processing is lost. In this work, we intend to partially fill these gaps by studying the problem of scheduling a single machine so as to minimize the total deviation of the job completion times from an unrestrictive common due date when one or several fixed intervals of unavailability are present in the planning horizon. We also put serious effort into investigating models with semi-resumable jobs so that processing on a job interrupted by an interval of machine unavailability may later be resumed at the expense of some extra processing time. The conventional assumptions regarding resumability are also taken into account. Several interesting cases are identified and explored, depending on the resumability scheme and the location of the interval of machine unavailability with respect to the common due date. The focus of analysis is on structural properties and drawing the boundary between polynomially solvable and $$\mathcal {NP}$$ -complete cases. Pseudo-polynomial dynamic programming algorithms are devised for $$\mathcal {NP}$$ -complete variants in the ordinary sense.

Scheduling on uniform parallel machines with periodic unavailability constraints

Scheduling problems under unavailability constraints has become a popular research topic in the last few years. Despite it’s important application in the real world, the uniform parallel machine scheduling problem was the least studied due to its complexity. In this paper, we investigated the uniform parallel machine scheduling problem under deterministic availability constraints. Each machine is subject to one unavailability period. Different versions of the problem regarding the type of jobs (identical and non-identical) and the performance measures (the total completion times and the makespan) were studied. For the case of identical jobs and for both performance measures, we developed linear programming models and optimal algorithms to provide a solution to the problem. For the case of non-identical jobs, we proved that the problem is NP-hard and propose a quadratic program. Because, this later cannot solve problems with very large number of jobs and machines, a heuristic was developed to find near optimal solutions to the problem especially with very large number of jobs and machines. The computational results showed that the heuristic’s performance is very high regardless the dimensions of problem instances.

Flexibility-based multi-objective approach for machines selection in reconfigurable manufacturing system (RMS) design under unavailability constraints

The reconfigurable manufacturing system (RMS) is a recent manufacturing paradigm driven by the high responsiveness and performance efficiencies. In such system, machines, material handling units or machines components can be added, modified, removed or interchanged as needed. Hence, the design of RMS is based on reconfigurable machines capabilities and product specification. This paper addresses the problem of machines selections for RMS design under unavailability constraints and aims to develop an approach to ensure the best process plan according to the customised flexibility required to produce all parts of a given product. More specifically, we develop a flexibility-based multi-objective approach using an adapted version of the well-known non-dominated sorting genetic algorithm to select adequate machines from a set of candidate (potential) ones, in order to ensure the best responsiveness of the designed system in case of unavailability of one of the selected machines. The responsiveness is based on the flexibility of the designed system and a generated process plan, which guarantees the management of machines unavailability. It is defined as the ability and the capacity to adapt the process plan in response to machines unavailability. Two objectives are considered, respectively, the maximisation of the flexibility index of the system and the minimisation of the total completion time. To choose the best solution in the Pareto front, a multi-objective decision-making method called technique for order of preference by similarity to ideal solution is used. To demonstrate the applicability of the proposed approach, a simple example is presented and the numerical results are analysed.

An approximation solution for scheduling problem in single machine under unavailability constraints

An approximation solution for scheduling problem in single machine under unavailability constraints

The “Dual-Ants Colony”: A novel hybrid approach for the flexible job shop scheduling problem with preventive maintenance

Due to their importance in the fields of both manufacturing industries and operations research, production scheduling and maintenance planning have received considerable attention both in academia and in industry. This paper investigates the Flexible Job Shop Scheduling Problem (FJSSP) with machine unavailability constraints due to Preventive Maintenance (PM) activities, under the objective of minimizing the makespan. We propose two new formulations: the first one in the form of a Mixed Integer Nonlinear Program (MINLP) and the second corresponding to a bi-level disjunctive/conjunctive graph. To deal with this variant FJSSP with PMs (FJSSP/PM), we develop the “Dual-Ants Colony” (DAC), a novel hybrid Ant Colony Optimization (ACO) approach with dynamic history, based on an ants system with dual activities. This optimization provides an effective integration of a local search and a set of dispatching rules. Three regular performance measures are also implemented. To show the efficiency of the DAC algorithm, computational experiments are carried out on a large range of well-known benchmarks from the literature and others newly generated. We address first the classical JSSP case, then the flexible FJSSP for partial flexibility. Finally, we study the case with preventive maintenance based on well-chosen PM periods. Obtained results demonstrate the viability and performance of the proposed approach, especially for the FJSSP/PM.

A single-machine scheduling problem with multiple unavailability constraints: A mathematical model and an enhanced variable neighborhood search approach

AbstractThis research focuses on a scheduling problem with multiple unavailability periods and distinct due dates. The objective is to minimize the sum of maximum earliness and tardiness of jobs. In order to optimize the problem exactly a mathematical model is proposed. However due to computational difficulties for large instances of the considered problem a modified variable neighborhood search (VNS) is developed. In basic VNS, the searching process to achieve to global optimum or near global optimum solution is totally random, and it is known as one of the weaknesses of this algorithm. To tackle this weakness, a VNS algorithm is combined with a knowledge module. In the proposed VNS, knowledge module extracts the knowledge of good solution and save them in memory and feed it back to the algorithm during the search process. Computational results show that the proposed algorithm is efficient and effective.Highlights A scheduling problem with multiple unavailability is proposed and formulated. A knowledge-based variable neighborhood search algorithm is proposed. Extensive computational tests confirm the good capability of the proposed model and algorithm.

Overhanging approximal restoration: Clinical and radiography features at Tarogong Public Health Service Indonesia

Introduction: Overhanging approximal restoration may causes gingival inflammation, periodontal tissue destruction, decreases alveolar bone height, and caries reccurence. Overhanging restoration can be detected clinically and by radiography image. Overhang restorations can occur due to the poor filling procedures, one of which is the limitation of supporting tools. Restoration of teeth done in Puskesmas often found unavailability constraints supporting tools so that in cases of approximal caries often experience overhang. The aim of this study was to evaluate the incidence of overhanging proximal restoration at Tarogong Public Health Centre in Garut Regency West Java Indonesia. Methods: This study was a descriptive cross sectional for the incidence on patient with overhanging approximal restoration who visited at Dental Unit Tarogong Public Health Center in Garut Regency. Intraoral clinical examination was conducted to examine visually and by tactile for the overhang restoration. Periapical radiography examination was taken and became supporting examination. Results: Collected data were 43 cases of overhanging approximal restoration from total 57 patients. The incidence of overhanging approximal restoration were 75,4. Conclusion: The conclusion of this study by radiography was the incidence of overhanging restoration was 75.4 which showed that overhanging restoration approksimal more than good restoration aproksimal at Tarogong Public Health Centre in Garut Regency West Java Indonesia.

High-multiplicity scheduling on one machine with forbidden start and completion times

We are interested in a single machine scheduling problem where jobs can neither start nor end on some specified instants, and the aim is to minimize the makespan. This problem models the situation where an additional resource, subject to unavailability constraints, is required to start and to finish a job. We consider in this paper the high-multiplicity version of the problem, when the input is given using a compact encoding. We present a polynomial time algorithm for large diversity instances (when the number of different processing times is greater than the number of forbidden instants). We also show that this problem is fixed-parameter tractable when the number of forbidden instants is fixed, regardless of jobs characteristics.

A hybrid genetic algorithm for non-permutation flow shop scheduling problems with unavailability constraints

This article deals with the non-permutation flow shop scheduling problems with non-availability intervals. Specifically, two kinds of unavailability constraints are investigated and the jobs are non-resumable in both cases. In the first case, the non-availability intervals are periodically fixed and known in advance. In the second case, the intervals are flexible and the machines’ continuous working time cannot exceed a maximum allowed time. Two mixed binary integer programming models are provided for deriving the optimal schedules, respectively. The problems of minimising makespan in such flow shops are proved Non-deterministic Polynomial-time hard in strong sense. Then a hybrid incremental genetic algorithm (HIGA) that combines an incremental evolution strategy framework, a local refinement and a population diversity supervision scheme is proposed to solve the large-sized problems efficiently. The numerical experiments under different problem parameters’ settings indicate that the HIGA can achieve quite satisfactory performance compared with genetic algorithm and a constructive heuristic based on Nawaz, Enscore, Ham.

Heuristics for the identical machine scheduling problem with preventive maintenances

In this paper, two mixed integer programming models integrating production scheduling and preventive maintenances are proposed to derive the optimal solutions for the identical machine scheduling problem with unavailability constraints. In the first model, the maintenance activities are performed periodically and the objective is to minimize the makespan. In the second model, the maintenance activities are flexible and the machines’ continuous working time cannot exceed a maximum allowed time T; the objective is to minimize the total completion time of jobs. For the first problem, we propose a heuristic longest batch time (LBT) and prove that the worst case error bound of LBT is 2. For the second problem, we develop a heuristic modified smallest processing time (MSPT) based on some properties of the optimal solutions. Computational experiments show that both of the heuristics are effective and efficient compared with the results obtained by CPLEX and the other algorithms.

Algorithm for Manufacturing Planning Under Unavailability Constraints

Production scheduling is a major issue in industrial engineering because of its impact on optimization of profits the use of resources. This paper proposes an algorithm for optimizing a production scheduling model under production and maintenance constraints. This work is an extension of resources management algorithm developped by Ezzeddine et al. [6] to an industrial application purpose. A numerical example is illustrated in the last section of this paper.