Real-time integrated production-scheduling and maintenance-planning in a flexible job shop with machine deterioration and condition-based maintenance
Introduction
In the context of production decisions, the term “real-time” refers to the system’s instantaneous reaction to disruptions and unforeseen events without interrupting the production processes [1]. A reaction can include assigning an operation to a different machine, delaying or accelerating an operation, rerouting a job, or shifting the starting time of a maintenance activity [[1], [2], [3], [4]]. An event can be an order cancellation, a due date change, the arrival of a new order, a random machine breakdown, or a shortage of material [[1], [2], [3], [4]]. Real-time optimization models are in high demand in practice, as manufacturing systems are highly dynamic and subject to unexpected events and disruptions. Real-time optimization models can help manufacturing systems react and adapt to such events and requirements by continuously updating disrupted plans/schedules using real-time information about the status of the machines and operations on their shop floors. The availability of this real-time data is achieved by adopting innovative manufacturing technologies, such as Industry 4.0 [[5], [6], [7], [8]]. With Industry 4.0 concepts, such as the internet of things (IoT), cyber-physical systems (CPSs), detailed information about machines, orders (or jobs), operations, equipment, work-in-progress (WIP), inventory, and shipments can be collected in real-time. These concepts can also be integrated into the company’s enterprise resource planning/material requirements planning/computerized maintenance management (ERP/MRP/CMM) system, making all the information mentioned earlier instantly available for decision making. This level of real-time connectivity will empower Industry 4.0-based manufacturing systems to utilize real-time updates to manage, monitor, and control their operations. This includes production scheduling and maintenance planning, which are two of the core components of any manufacturing process. For more details about how such technologies (i.e., Industry 4.0 concepts, such as IoT and CPS) can be utilized for shop floor real-time data collection, processing, and analysis, readers are referred to [9]. In this paper, we intend to focus on utilizing real-time data to jointly optimize production schedules and maintenance plans in a dynamic and stochastic flexible job shop production environment. The flexible job shop scheduling problem (FJSSP) is a classical combinational optimization problem in real-world manufacturing systems. FJSSP is a generalization of the job shop and parallel machine scheduling problems [10]. In FJSSP, each job has a predetermined number of operations to be processed by more than one machine (i.e., alternative routings are allowed). As a result, FJSSP should deal with two problems: the machine assignment problem (which determines the best machine for each operation) and the sequencing problem (which searches for the best sequences for processing the jobs on each machine). FJSSP seeks to find an optimal assignment and sequence by optimizing a single (e.g., makespan [11]) or multi-objective (makespan and maintenance costs [12]) function. FJSSP is proved to be strongly NP-hard due to its complexity [13,14].
Although several studies have been dedicated to flexible job shop scheduling, most of these studies assumed that the production environment is static (i.e., all required data is available at time zero and is not subject to change with time) and machines are always available for production (i.e., never break or goes under planned maintenance). However, production environments are highly dynamic in practice, and changes such as new job arrivals [[15], [16], [17]], variable processing times [18], and due date changes [19] are expected during production. Also, machines are certainly subject to aging, deterioration, and some unavailability intervals due to scheduled preventive maintenance (PM) activities [12,20,21] as well as random machine breakdowns [15,22,23], which lead to corrective maintenance (CM) activities. PM activities can be broadly classified into two types: time-based maintenance (TBM) or condition-based maintenance (CBM). TBM tasks are performed in predetermined periods and are conducted to delay the deterioration (of machines or equipment) leading to failures and reduced production efficiency [20]. TBM assumes that a machine’s (or equipment’s) failure behavior under normal use can be estimated using historical failure data [24]. CBM tasks are performed based on information that is collected using condition monitoring. CBM actions are initiated only when there is evidence of unusual behaviors of machinery. CBM is supposed to avoid unnecessary maintenance tasks and therefore reduces maintenance costs [25]. CBM assumes that the existing indicative prognostic parameters can be detected, and the possibility of machine’s (or equipment’s) failure can be determined before its actual occurrence. Prognostic parameters indicate prospective issues and early defects that cause a machine (or a component) to depart from its expected performance level. Aging and deterioration of machines (or equipment) are common maintenance issues, among the main reasons for reduced production efficiency [26,27]. A trend analysis of the machine (or equipment) condition data can also reveal the degradation tendency of crucial components [28]. If all these issues and disruptions (e.g., aging, deterioration, random breakdowns, maintenance activities, new job arrivals, and due date changes) are neglected during production planning, they will result in production losses as well as a reduction in production efficiency and machines (or equipment) service life. Hence, integrating maintenance planning (by addressing aging, deterioration, and different maintenance activities) into flexible job shop scheduling with real-time dynamics will reduce maintenance and production costs and keep manufacturing systems competent, reliable, competitive, and efficient.
Although several researchers have addressed the issue of integrating maintenance planning and production scheduling, their studies did not address real-time dynamics and the proposed models considered TBM activities (e.g., [12,21,29,30]), TBM activities with fixed time intervals (e.g., [31]), different TBM activities in diverse intervals (e.g., [32]), opportunistic maintenance (e.g., [33]), or noncyclical TBM activities (e.g., [34]). Even for studies that addressed machine deterioration and CBM in flexible job shops, simulation-based optimization models (e.g., [20,35]), decomposition methods (e.g., [27,36]), and machine-learning-based health indicator models (e.g., [37]) were proposed, no closed-form formulation was developed before for machines reliability (including deterioration, random breakdown, minimal repairs, and CBM) and its impacts on machine condition, processing times, and maintenance costs. As a result, this work aims to solve the joint optimization problem of production schedules and CBM plans in a flexible job shop with real-time dynamics (which can be denoted as ). The issues and disruptions addressed in this paper are new job arrivals, due date changes, machines deterioration, random machine breakdowns, minimal repairs, and CBM actions. This new problem is solved by minimizing the expected total system cost including the expected total tardiness cost and the expected total maintenance costs. Due to the complexity of this new problem, this paper proposes the design and application of a metaheuristic-based approach to solve the problem. The genetic algorithm (GA) has been successfully applied to tackle combinatorial optimization problems [38]. Compared with the other metaheuristics, GA has more flexibility and does not need to embed knowledge [38]. Besides, GA has been successfully applied to tackle several production scheduling problems including flexible job shop scheduling [11,15,39]. Hence, we apply and adapt a modified version of a hybrid GA (denoted hereafter as ) for the problem under investigation (more details about the proposed are provided in Section 4.4). Apart from determining operations assignments and sequences, this new problem needs to determine optimal CBM plans, and update created plans and schedules when needed (i.e., upon new job arrivals, due date changes, machines breakdowns, or CBM) using real-time updates. Thus, and to put it succinctly, the contribution of this paper can be summarized in the following two points:
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The formulation of the new problem (i.e., the joint optimization of production scheduling and maintenance planning in a flexible job shop with new job arrivals, due date changes, machines deterioration, random machine breakdowns, minimal repairs, and CBM interventions) – (see Section 3 and Appendix A). To do that, we first modeled the reliability of machines as a multi-state system using continuous-time Markov chains. Then, a matrix-based approach is introduced to formulate the effects of machines’ deterioration, random breakdowns, and maintenance activities (both minimal repairs and CBM) on the processing times and the associated maintenance and production costs. Finally, the developed formulations are integrated into a mixed-integer programming model to jointly optimize production schedules and CBM plans by minimizing the expected total system cost, including the expected total cost of tardiness and the expected total maintenance cost.
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The development of a proactive-reactive scheduling approach based on a modified hybrid GA (see Section 4). A hybrid rescheduling policy is included (see Section 4.2 for more details). A problem-specific solution representation, repair, and evaluation are embedded into the proposed . Finally, a new mechanism for generating updated solutions (i.e., production schedules and maintenance plans) is included in the proposed metaheuristic (see Section 4.4 for more details). The proposed approach can be utilized as a real-time optimization-based system to generate integrated plans and reacts to several production disruptions, including new job arrivals, random breakdowns, due date changes, minimal repairs, and CBM activities.
Several computational experiments are performed to test the performance of the developed model and algorithm, and also to investigate the following research questions:
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RQ1: As frequent updates are to be conducted, is the quality of the initial plans still essential for the quality of the realized (i.e., final) plans?
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RQ2: What is the best rescheduling policy (i.e., course of action) to deal with each of the newly addressed events (due date changes, minimal repairs, and CBM)?
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RQ3: As decisions are required in real-time, what is the effect of reaction (or rescheduling) times on the efficiency of the generated plans?
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RQ4: Despite the general belief that decision-making with real-time information will result in better decisions, to what extent can the availability of real-time information enhance the integrated decisions (in terms of total expected costs)?
The test instances are generated based on well-known benchmarks by including the new parameters of our problem (more details are provided in Section 5.1). The test instances are grouped into three sets: a calibration set (20 calibration instances) to tune the algorithm and find the best parameter setting, a pre-evaluation set (400 test instances) to test the performance of the proposed , and a scenario-based set (1800 test instances) to test the performance of the proposed -based proactive-reactive scheduling approach and to answer the considered research questions. The results of the conducted computational study indicate that the proposed outperforms a set of three heuristics (LFOH, LAPH, and LFO-LAP, which are developed by [15]) and two well-known metaheuristics (a hybrid GA proposed by [40] and a teaching-learning-based optimization (TLBO) proposed by [41]) in all instances. The results also show that the proposed -based proactive-reactive scheduling approach outperforms the commonly used approach in practice (i.e., the right-shift policy), and allows for about 27 % of cost-saving on average. Furthermore, additional cost-saving of about 30 % is achieved when the limits for rescheduling times are increased from 30 to 90 s. In addition, the results suggest several policies (i.e., courses of action) for each the newly addressed issues in this investigation (i.e., due date changes, minimal repairs, and CBM) based on the conducted experiments and the obtained results for different scenarios and strategies.
This paper is structured as follows: a summary of the related literature is presented in Section 2. In Section 3, the new problem is described and formulated. The proposed -based proactive-reactive scheduling approach is presented in Section 4. Details of the conducted computational study are addressed in Section 5. Finally, conclusions and directions for future research are presented in Section 6.
Section snippets
Related work
As the focus of this paper is on the joint optimization of production scheduling and maintenance planning in a flexible job shop with real-time dynamics, including new job arrivals, due date changes, machine deterioration, random machine breakdowns, minimal repairs, and CBM, the first sub-section reviews the current state-of-the-art on production scheduling with real-time dynamics (i.e., dynamic scheduling, rescheduling, or real-time scheduling) with a slight focus on flexible job shop
Problem description and formulation
In this section, we discuss the requirements, characteristics, and assumptions of the considered problem. The integrated optimization of production scheduling and maintenance planning in a flexible job shop production system using real-time information is addressed in this paper.
Flexible job shops are generalized versions of job shops such that for each operation; there is a set of available candidate machines to process it [10]. Therefore, compared to classical job shops, there are two
Proposed integrated real-time optimization-based system
The proposed integrated real-time optimization-based system is presented in Fig. 4. This system works in both modes (offline and online) and utilizes an integrated planning (i.e., maintenance-planning and production scheduling) module. The offline mode is triggered at time zero to generate the integrated baseline plans using the integrated maintenance-planning and production scheduling module. This mode requires initial information about the machines and the jobs (or orders), which can be
Computational study
In this section, details about the computational study are provided. All the developed codes are written in MATLAB and run on a PC with an Intel® Core™ i5 CPU processor at 3.10 GHz and 10 GB RAM.
Discussion
Considering the importance of production scheduling, maintenance panning, and real-time dynamics, in this paper, we addressed these aspects in a well-known complicated production environment, the flexible job shop. In addition, several issues that could be of high interest in real-world settings were considered, which are new job arrivals, due date changes, random machine breakdowns, machine deterioration, minimal repairs, and CBM. An integrated mixed integer programming model was proposed to
Conclusions and future work
This paper investigates the integration of production scheduling and maintenance planning in the context of Industry 4.0 (i.e., under real-time settings). The considered production layout is a flexible job shop in which machines are not identical and are subject to deterioration, random breakdowns, minimal repairs, and condition-based maintenance. New formulations are introduced to model each machine's condition and the effects on the processing times and the associated maintenance and
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The funding for this research was provided by the Canada Research Chairs (CRC) program. This work is also supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada through the Discovery Grant (#RGPIN-2017-04434).
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