Operation Process Rebuilding (OPR)-Oriented ... - IEEE Xplore

IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING, VOL. 14, NO. 1, JANUARY 2017

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Operation Process Rebuilding (OPR)-Oriented Maintenance Policy for Changeable System Structures Tang-Bin Xia, Member, IEEE, Xin-Yang Tao, and Li-Feng Xi Abstract— Considering the operation process rebuilding (OPR) of manufacturing/operation systems, we propose a dynamic interactive bilevel maintenance methodology to satisfy rapid market changes. Predictive maintenance (PdM) intervals at the machine level are dynamically scheduled by a multiobjective model for each diverse machine. A system-level opportunistic maintenance (OM) policy is proposed to facilitate PdM optimizations according to OPR activities. This novel OPR-OM policy utilizes a variable maintenance time window to construct optimal maintenance schedules that are suitable for changeable system structures. The results obtained by applying this methodology at Shanghai Port indicate that the proposed methodology can help a port transportation system to achieve rapid responses to OPR activities, which can significantly improve system efficiency and economy. Note to Practitioners—The majority of existing maintenance strategies focus on fixed system structures, which scarcely consider changeable system structures derived from operation process rebuilding (OPR). Thus, this paper, which is motivated by this problem, attempts to satisfy flexible needs in a keenly competitive market. This paper proposes a bilevel maintenance methodology that is integrated with OPR to achieve costeffective and fast-responding system-level maintenance optimizations. Implementation of the proposed methodology involves the following basic steps: 1) collect individual machine condition data; 2) prepare machine-level maintenance schedules according to a multiobjective model (maintenance cost rate, machine availability, and operation profit rate); and 3) utilize a variable maintenance time window to optimize system-level maintenance according to OPR activities. The bilevel methodology can be easily modified according to practical requirements, i.e., other decision-making objectives at the machine level and the maintenance time window range at the system level. Index Terms— Dynamic decision making, operation process rebuilding (OPR), opportunistic maintenance (OM), predictive maintenance (PdM), variable maintenance time window (VMTW). Manuscript received August 8, 2016; revised September 12, 2016 and October 10, 2016; accepted October 13, 2016. Date of publication November 9, 2016; date of current version January 4, 2017. This paper was recommended for publication by Associate Editor A. E. Smith and Editor L. Shi upon evaluation of the reviewers’ comments. This work was supported in part by the China Postdoctoral Science Foundation under Grant 2014M561465, in part by the National Natural Science Foundation of China under Grant 51505288, Grant 71301176, and Grant 51475289, in part by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China under Grant 51421092, and in part by the Programme of Introducing Talents of Discipline to Universities under Grant B06012. (Corresponding author: Xin-Yang Tao.) The authors are with the State Key Laboratory of Mechanical System and Vibration, Department of Industrial Engineering, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TASE.2016.2618767

I. I NTRODUCTION

I

N THE manufacturing industry, manufacturing enterprises (such as General Motors) utilize manufacturing systems to output products, such as different types of cars, whereas operation enterprises (such as Shanghai International Port Company) run operation systems to provide services, such as port transportation services. These manufacturing/operation systems are usually composed of many diverse machines. With changeable market requirements, the randomness of manufacturing/operation orders (variable product requirements or service demands) and the specificity of diverse products/freights pose formidable challenges to industrial manufacturing/operation enterprises. To withstand competition in the market, the enterprises have focused on the efficiency of operation process rebuilding (OPR), which is an important and useful management method that is derived from business process reengineering. Based on OPR, changeable system structures are utilized to effectively adjust and rebuild the operating process to satisfy multiple diverse requirements and small batch orders, quickly respond to market changes and achieve the target of flexible manufacturing. If port transportation systems are employed as an example, the randomness in the arrival times of the freights and the diversity in the types of freights they handle may require different configurations of port machines. However, this rebuilding of a system structure will create difficulties in maintaining the excellent condition of an entire system and its diverse machines. Port systems need proper maintenance due to their changeable system structures, which is necessitated by OPR activities. Shanghai Port is one of the largest ports in the world with a container throughput of 36.537 million TEU (20-ft equivalent unit) and a cargo throughput of 719 million tons in 2015. To address vast operational requirements and to overcome instability, which is likely caused by machine failure, Shanghai Port requires capacity expansion, machine replacement, and machine upgrading with included sequential OPR activities. These OPR activities create changeable system structures and require a dynamic maintenance methodology. During the past several decades, maintenance models, policies, and methodologies have served an important role in manufacturing/operation systems. A comprehensive maintenance methodology can effectively improve system efficiency, reduce maintenance costs, and ensure production safety. OPR activities in changeable system structures introduce new challenges in dynamic maintenance decision making. The literature primarily focuses on a system’s rebuilding

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Fig. 1.


Framework of the interactive bilevel maintenance methodology.

mechanism [1], [2] and does not consider a corresponding maintenance methodology to support the system’s rebuilding mechanism. As additional manufacturing/operation systems have opted for changeable system structures, this paper proposes an interactive bilevel maintenance methodology that involves OPR. Each machine requires a distinctive schedule of maintenance action, which is referred to as predictive maintenance (PdM), depending on real-time monitored conditions, to prevent possible failure. Based on machine-level PdM schedules, OPR-oriented opportunistic maintenance (OM) is developed as an advanced maintenance policy for multiunit systems to optimize PdM actions according to a changeable system structure and machine relevance. Utilization of the PdM action for one machine as a simultaneous maintenance opportunity for others helps in maintenance optimization, which can ensure total maintenance (TM) cost savings and improve system availability [3]. Note that the existing OM policies are primarily applied for static system structures (parallel, series, series– parallel, and k-out-of-n systems). Thus, changeable system structures, which are necessitated by OPR activities, will create new challenges for system-level OM scheduling. Therefore, an improved dynamic OM policy that considers diverse OPR activities is needed. This paper develops a dynamic maintenance methodology for manufacturing/operation systems that experience sequential OPR activities. First, a machine-level multiobjective PdM method is proposed. Imperfect maintenance effects are applied to simulate machine degradations, considering maintenance cost, machine availability, and profit rate as the objectives for establishing the PdM scheduling model. Then, based on machine-level PdM outputs, we propose a dynamic OM policy for systems with OPR activities, which is referred to as OPR-OM. The basic concepts of an OPR-OM policy are as follows. 1) Separate maintenance actions for parallel machines, and combined maintenance actions for series machines to prevent unnecessary system downtime.

2) Utilize a variable maintenance time window (VMTW) to achieve PdM separation, make combination decisions, and achieve a significant reduction in the complexity of the calculations. 3) Optimize the VMTW values, and program the corresponding dynamic maintenance schedules when there is a new OPR activity to achieve seamless PdM decision making. The framework of this interactive bilevel maintenance methodology for changeable system structures is shown in Fig. 1. The left part of Fig. 1 shows a typical port transportation system, which is composed of several cranes on the shore side and automatic guided vehicles (AGVs) for transportation and transtainers on the port side. A container from the ship is taken through a crane (C1, C2, or C3), an AGV (A1, A2, A3, or A4) and a transtainer (T1, T2, or T3) to reach the yard. This system may experience diverse OPR activities, as shown in the right part of the figure, where the maintenance methodology for changeable system structures is developed. At the machine level, PdM intervals are dynamically scheduled by the multiobjective model for each individual machine, whereas imperfect maintenance effects are considered. Necessitated by sequential OPR activities (OPR1 and OPR2), these outputs are pulled to support the system-level policy for changeable system structures (Structures 1–3). After the real-time OPR-OM maintenance optimizations at the system level, the results will be fed back to the machine-level PdM scheduling. In this decision-making manner, this bilevel maintenance methodology can make dynamic decisions on more suitable, effective, and economical system-level maintenance optimizations, which ensure a system’s operating stability and economy when the system is faced with diverse OPR activities. The remainder of this paper is organized as follows. Section II briefly reviews the literature on OPR and maintenance policies. Section III proposes the machine-level multiobjective PdM method. Section IV discusses the development of

XIA et al.: OPR-ORIENTED MAINTENANCE POLICY FOR CHANGEABLE SYSTEM STRUCTURES

the dynamic OPR-OM policy for the entire system, based on machine-level PdM outputs. Section V reports and discusses the numerical results of OPR-OM from a port transportation system. Finally, Section VI presents the conclusions from this paper and suggestions for future studies. In this paper, “maintenance interval” refers to single machines, particularly the time duration of the manufacturing/ operation among PdM actions, which is determined by the machine-level PdM model. “Maintenance cycle” relates to the entire system, which is defined as an OM cycle. By the end of this cycle, OM may have been jointly performed by some machines and is determined by the system-level OPR-OM policy. “Maintenance schedule” refers to the outcome of the proposed bilevel methodology. II. L ITERATURE R EVIEW In recent years, additional studies have focused on OPR, whereas operations management has been extended in numerous fields. As the central part of operations management, OPR has gained increased attention from both academia and the manufacturing industry [4]–[6]. Gunasekaran and Ngai [7] analyzed the future of operations management by considering the significance of changes in the market and society and attempted to develop a framework for new methodologies and tactics. Wang et al. [8] discussed the limitations of a current supply chain operations reference model and provided a mapping technique to integrate operation process modification in a supply chain setting. Bevilacqua et al. [9] presented a case study in which OPR was applied in emergency management to minimize downtime, deficiencies, illnesses, and consequent time losses. However, few studies address the influence of OPR activities on maintenance schedules due to the complexity of scheduling OM with changeable system structures. Existing maintenance studies are primarily devoted to constant systems. At the failure detecting and simulation level, some valuable research on networked infrastructure modeling and failure cascading has been published [10], [11]. Hong et al. [12] introduced a preprocessing model of the bearing using wavelet packet-empirical mode decomposition for feature extraction and self-organization mapping for a condition assessment of the performance degradation. Some researchers investigated valuable maintenance methods for a single machine at the machine level [13], [14]. Jin and Mechehoul [15] proposed a condition-based maintenance program to reduce the device testing cost by utilizing tester’s self-diagnostic data and devise an optimization algorithm to determine the best maintenance policy. Xia et al. [16] integrated the multiple attribute value theory and imperfect maintenance into an improved sequential preventive maintenance model for energy systems that are subject to degradation. At the system level, some researchers examined important system-level maintenance policies for static system structures [17], [18]. Okogbaa et al. [19] developed an optimal intervention policy for series systems that analyzes system failure and searches for optimal maintenance schedules. Xia et al. [20] developed an OM model for series–parallel systems and proposed a maintenance time window to simplify calculations. Sun and Li [21] considered

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stochastic factor and buffer utilization for investigating opportunity estimation for real-time energy control of typical multimachine manufacturing systems, without sacrificing the system throughput. Chang et al. [22] developed a systematic method for shutting down equipment when performing maintenance in an automotive assembly environment. Gu et al. [23] investigated hidden opportunities for performing proper maintenance tasks during production time without production losses and developed a passive maintenance opportunity window method. Ni et al. [24] investigated extra hidden opportunities for PMs during production time without violating the system throughput requirement. You et al. [25] proposed an updated sequential PdM policy to decide a real-time maintenance schedule for a continuously monitored degrading system that can minimize maintenance cost rates in the long term. Jia [26] conducted a valuable study of the OM of an asset composed of multiple nonidentical life-limited components with both economic dependence and structural dependence. Due to the specific characteristics of manufacturing/ operation systems that experience sequential OPR activities, machine failure usually causes serious accidents and substantial damage to staff safety and adversely impacts operating costs and system efficiency. Thus, maintenance methodologies serve an important role in multiunit systems. Researchers have begun combined research on industrial practices and maintenance policies [27]. Dekker et al. [28] proposed an analytical model with a control approach to devise the optimal port expansion methodology by balancing the investment cost for the port against the congestion cost for the users. Jiang et al. [29] developed a container yard storage methodology for improving land utilization and operation efficiency in a transshipment hub port. Yang et al. [30] designed three maintenance levels by failure probabilities at intervention, including preventive, necessary, and mandatory maintenance, and proposed the optimal maintenance methodology for a port project with a long life span. Li et al. [31] established a maintenance cost model that considers both operation and user costs and applied it to optimize maintenance methodology for port structures. Talley et al. [32] provided a novel and unique methodology for evaluating the effectiveness of the performance of individual port services by utilizing the concept of port service chains. The literature review reveals that the existing methodologies primarily focus on static system structures and only slightly address changeable system structures. In practice, sequential OPR activities not only influence the operations of port transportation systems but also produce challenges in systemlevel maintenance decision making. To address this problem, this paper proposes an interactive bilevel maintenance methodology that includes the machine-level multiobjective PdM method and a system-level OPR-OM optimization policy for changeable system structures of manufacturing/operation systems. III. M ACHINE -L EVEL M ULTIOBJECTIVE PdM M ETHOD A port transportation system (as an operation system) typically consists of different types of machines, such as cranes, AGVs, and transtainers. The system may experience sequential

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OPR activities when diverse machines in the corresponding system structures have individual characteristic deteriorations. To present the machine-level multiobjective model, two types of maintenance actions are considered: 1) PdM action at the end of each maintenance interval, which can improve a machine’s reliability but not to the level of a new machine and 2) minimal repairs during PdM intervals for unscheduled breakdowns, which cannot improve a machine’s reliability but enables the machine to continue to work. In this section, we apply improvement factors to model the imperfect maintenance effects of PdM actions and introduce the multiobjective method to dynamically output PdM intervals for supporting the system-level OM optimizations. A. Imperfect Maintenance Modeling For the machine-level multiobjective PdM method, three types of improvement factors are applied to model the imperfect maintenance effects: 1) the recursion decline factor to reflect the maintenance effect on the machine total serving time; 2) the failure rate increasing factor to reflect the maintenance effect on the machine reliability changing rate; 3) the environment factor to reflect the external environment effect on the machine reliability. Thus, the imperfect maintenance effect can reflect the fact that a machine can improve but will not perform as well as the new machine after PdM action. Machine deteriorations can be accurately modeled by integrating maintenance actions with the external environment. Thus, the machine failure rate function can be defined as f (i+1) j (t) = ε j b j f i j (t + a j Ti j ) t ∈ (0, T(i+1) j )

(1)

where f (t) denotes the machine failure rate function, j is the index of the machine, i denotes the index of the PdM intervals, and T is the machine working duration between PdM actions. The recursion decline factor 0 < ai < 1 shows that each imperfect PM causes this machine’s initial failure rate to become λi (ai Ti ) for the next cycle. The failure rate increasing factor bi > 1 indicates that an imperfect PM magnifies the failure rate due to the deterioration process. The environment factor εi j > 1 reflects that the machine health is affected by external factors, such as temperature, humidity, and climate. These factors can be extracted and predicted based on historical maintenance data and online monitoring information for each machine [33]. Actual machine characteristic monitoring of data is discrete; thus, (1) can be expressed as a j Ti j f (i+1) j (k) = ε j b j f i j k + t T(i+1) j (2) × for k = 0, 1, 2 . . . , t where t is the characteristic detection period. B. Multiobjective Method After modeling the imperfect maintenance effect, we apply the maintenance cost rate, machine availability, and profit rate as decision-making objectives to obtain the machine-level

PdM intervals. Because diverse local objectives require the attention of different enterprise managers, a comprehensive PdM decision-making model that can integrate multiple objectives into a whole target or focus on one objective by adjusting the impact factors of these objectives is needed. First, the maintenance cost rate objective can be expressed as T CPMi j + CMRi j 0 i j f i j (t)dt (3) Ci j = T Ti j + TPMi j + TMRi j 0 i j f i j (t)dt where Ci j denotes the maintenance cost rate in the i th PdM interval for machine j , CPMi j is the cost of a PdM action, CMRi j denotes the cost of a minimal repair action, TPMi j is the duration of PdM action, and TMRi j represents the duration T of a minimal repair action. 0 i j f i j (t)dt refers to the expected failure frequency during this PM interval. Thus, the optimal maintenance cost rate Ci∗j can be obtained by dCi j = 0. (4) d Ti j T Second, the machine availability objective is expressed as Ti j Ai j = (5) T Ti j + TPMi j + TMRi j 0 i j f i j (t)dt where Ai j is the availability in the i th PdM interval for machine j . The optimal machine availability A∗i j can be obtained by d Ai j = 0. (6) dT ij T

Third, the machine profit rate objective is expressed as T POi j Ti j − PPMi j · TPMi j − PMRi j · TMRi j 0 i j fi j (t)dt Pi j = T Ti j + TPMi j + TMRi j 0 i j f i j (t)dt (7) where Pi j denotes the profit rate in the i th PdM interval for machine j , POi j is the profit rate of machine operation, PPMi j is the profit loss rate of PdM action, and PMRi j is the profit loss rate of minimal repair action. The optimal machine profit rate Pi∗j can be obtained by d Pi j = 0. (8) d Ti j T Then, Ci∗j , A∗i j , and Pi∗j can be obtained by solving (4), (6), and (8). To obtain the optimal PdM intervals, the multiobjective model is developed as Oi j = −w1

Ci j Ai j Pi j + w2 ∗ + w3 ∗ ∗ Ci j Ai j Pi j

(9)

where w1 , w2 , and w3 are the impact factors of each objective (w1 + w2 + w3 = 1), and Oi j is the global objective. Because the preference is a minimum maintenance cost rate, a negative sign is employed. By maximizing (9), the machine-level PdM intervals Ti j can be dynamically calculated. Thus, the PdM intervals for each machine (crane, AGV, and transtainer) in the port transportation system can be calculated to support


Fig. 2.

143

Illustration of the machine-level multiobjective PdM method.

the system-level OPR-OM policy. The machine-level multiobjective PdM method is shown in Fig. 2. Based on machine state monitoring and imperfect maintenance effect factors (including the recursion decline factor, the failure rate increasing factor, and the environment factor), we employ a multiobjective model (decision objectives, including cost, availability, and profit) to obtain the machine-level maintenance schedule. These machine-level PdM intervals are employed as the inputs of the system-level maintenance optimization, whereas the system-level maintenance ORP-OM results are also returned to the machine-level PdM scheduling. IV. S YSTEM -L EVEL OPR-OM O PTIMIZATION P OLICY Changeable system structures of a manufacturing/operation system can be adjusted according to sequential OPR activities, which include machine replacement, upgradation, and addition. These changes in system structures introduce difficulties for the system-level maintenance policy. In this section, based on machine-level PdM schedules, a system-level dynamic OPR-OM policy is proposed by utilizing VMTWs. The VMTW method is developed to establish real-time systemlevel OPR-OM schedules for sequential changeable structures. VMTWn is a dynamic maintenance time window that changes according to each OPR. For diverse system structures caused by different OPR activities, variable widths of VMTWn are defined as the criteria to separate the PdM actions in parallel subsystems and combine the PdM actions in series subsystems by utilizing PdM opportunities for nonfailed machines. The machines can be connected even in changeable series–parallel structures. For the series subsystem, a PdM action indicates a cessation in transport; in the parallel subsystem, simultaneous PdM actions stop the entire system. This paper proposes a

dynamic maintenance methodology to improve system availability and reduce TM cost. This system-level OPR-OM policy applies the machinelevel PdM intervals as the inputs at system level. First, after each OPR activity, which is caused by diverse freight requirements, the system structure is adjusted. The parallel subsystems and the series subsystems of the port transportation system simultaneously change. These subsystems form the basis for optimizing the VMTW. The new system can be effectively analyzed at the system level, and the optimal OM schedules (PdM optimizations) for this system structure can be dynamically calculated. Second, we introduce the concept of maintenance time window, where several machines’ PdM actions can be combined to reduce unnecessary system downtime [34]. In this paper, an improved VMTW that differs from the traditional fixed maintenance time window (FMTW) is proposed to address diverse OPR activities. A new optimal VMTWn is researched after each OPR activity, where n is the OPR index. By applying the VMTW method in making system-level OM schedules (PdM optimizations), we can avoid computation complexity and achieve the targeted objectives of quick maintenance response and dynamic optimization decision making. Third, simultaneous PdM actions of all machines in a parallel subsystem can cause a breakdown of the entire system. To ensure the availability of the entire system, this policy separates these PdM actions as follows: If existing TPMi j > Ti j − Ti j > 0 (i = 1 to I ) for all j = 1 to (J − 1) then Ti j = Ti j + VMTWn (i = 1 to I ).

(10)

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For a parallel subsystem, j is the first machine that reaches its PdM interval in the maintenance cycle i , and I is the expected number of TM cycles for the system structure; j = (1 to (J − 1)) represents other machines in the same subsystem, and J is the number of total machines in the subsystem; i is the PdM interval index of machine j , and I is its expected number of total PdM intervals for the system structure. The same policy is separately executed for each parallel subsystems, according to (10). For example, in a parallel subsystem that consists of the machines j1, j2, and j3, j1 reaches its PdM interval at time 20 in this cycle, and its PdM duration is 5. If both j2 s and j3 s expected PdM time point is between time 20 and time (20+5), the entire system will be forced to shut down. To avoid this situation, both j2 s and j3 s PdM actions should be delayed by a time period of VMTWn . Thus, in the parallel subsystem, the simultaneous PdM actions of all machines can be avoided and the availability of the entire system can be improved. Fourth, for the series subsystem, each machine’s PdM action stops the subsystem and provides a maintenance opportunity for other machines. To save maintenance costs and improve the availability of the entire system, the policy combines these PdM actions by If existing Ti j − Ti j < VMTWn (i = 1 to I , j = 1 to (J − 1)) then Ti j = Ti j − Ti j + Ti j (i = i to I ), Ti j = Ti j . (11) For the series subsystem, j is the first machine that reaches its PdM interval in the maintenance cycle i , and I is the expected number of TM cycles for the system structure; j = (1 to (J − 1)) represents other machines in the same subsystem, and J is the number of total machines in the subsystem; i is the PdM interval index of machine j , and I is its expected number of total PdM intervals for the system structure. The same policy is separately executed for all series subsystems according to (11). For example, in a series subsystem that consists of j1, j2, and j3, j1 reaches its PdM interval at time 20 in this cycle. If j2 s or j3 s expected PdM time point is between time 20 and time (20 + VMTWn ), these two PdM actions can be combined to improve the entire system’s availability. j2 s or j3 s PdM actions should be advanced to the same time point as j1 s time point. Thus, the PdM actions in series subsystems can be effectively combined to reduce the TM cost and improve the system-level availability. Because different VMTWn s may cause different system OM schedules, the TM cost is used to evaluate the schedules and achieve the optimal VMTWn . The maintenance cost of machine j in OM cycle i can be defined as ⎧ CB j · TPMi max , (Down) ⎪ ⎪ ⎪ Ti j ⎨ CPMi j + CMRi j 0 f i j (t)dt (12) CCi j = ⎪ + CB j · TPMi max , (OM) ⎪ ⎪ ⎩ 0, (Work on) where CCi j is the maintenance cost of machine j in OM cycle i , which has three situations: “Down” indicates

Fig. 3.

Flowchart of the system-level dynamic OPR-OM policy.

no OM on machine j in this cycle but it has to stop; “OM” indicates that machine j has performed OM in this cycle; “Work on” indicates no OM on machine j in this cycle but it continues to works. CB j represents the breakdown cost rate of machine j , TPMi max is the maximal PdM duration of this OM cycle, and Ti j is the machine j ’s new maintenance interval when it acts in this OM cycle. Therefore, the system TM cost can be obtained by TCCi =

J

CCi j

(13)

TCCi

(14)

j =1

STCCn =

I

i=1

where TCCi is the TM cost of all machines in OM cycle i , and STCCn is the system TM cost in all OM cycles between two OPR activities. By calculating MIN(STCCn ), the optimal maintenance time window VMTWn and the corresponding OM schedules (PdM optimizations) for the system can be obtained. The flowchart of the proposed system-level OPR-OM policy is shown in Fig. 3. V. A PPLICATION R ESULTS AND D ISCUSSION To validate the effectiveness of the proposed methodology, the port transportation system of Shanghai Port has been employed as an example. This manufacturing/operation system is designed with changeable series–parallel structures that consist of three types of machines (cranes, AGVs, and transtainer). Due to the changing cargo and machine updating, the port transportation system experiences sequential OPR activities. This paper chooses the decision horizon of 3000 h


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TABLE I M AINTENANCE PARAMETERS OF E ACH M ACHINE

Fig. 4.

OPR activities (decision horizon is 3000 h).

for implementing the OPR-OM policy, whose OPR activities and corresponding structure changes are shown in Fig. 4. A. Machine-Level PdM Results In machine-level PdM modeling, the Weibull distribution has been employed to express a machine hazard rate’s evolution, which is extensively applied in mechanical engineering and electronic engineering [35]. Its equipment reliability is expressed a f 1 j (t) = r j

t r j −1 r

η jj

, (r j > 1, η j > 0)

(15)

where r j is the shape parameter and η j is the scale parameter. These parameters and the other maintenance parameters can be collected from the machines’ practical operating data. A comprehensive list of the maintenance parameters of each machine is presented in Table I. The specific data are derived from Shanghai Port’s actual operation machines and simulations. According to practical plant investigations, the machines’ maintenance parameters are relatively stable in one decision horizon (significantly longer than the maintenance intervals); therefore, they are assumed to be constant in this paper. According to the multiobjective PdM method in Section III, the machine-level maintenance schedules can be obtained cycle by cycle. In this case study, the weights of each objective are set according to the port operation enterprise as follows: maintenance cost (w1 = 0.4), machine availability (w2 = 0.3), and profit rate (w3 = 0.3). This machine-level model is an

open method to which other objectives can be added and the weights changed by decision makers, depending on the practical situation. Visual basic has been employed to program and calculate the PdM intervals. The results are presented in Table II. The results enable the following observations. 1) Different machines have different PdM intervals due to their individual characteristics, which is more practical in manufacturing/operation systems. 2) When the maintenance and environment effects are considered, each of machine’s maintenance intervals gradually decreases, which indicates that additional maintenance actions are required to maintain the machines in excellent condition. B. System-Level OPR-OM Results Based on machine-level PdM schedules, the system-level OPR-OM schedules can be established to optimize the machine-level results from the perspective of the entire system by considering OPR activities. As shown in Fig. 4, the system experiences two OPR activities in the decision horizon (3000 h): the first OPR occurs at t = 1000 (h), and the second OPR occurs at t = 2200 (h). The results of the systemlevel dynamic OPR-OM schedules are shown in Table III. This paper calculates the optimal maintenance time window for each system structure and presents the corresponding OM schedules (PdM optimizations): “D” indicate no OM on this machine but it has to stop; “OM” indicates that the machine has performed an OM (a PdM action) at this time; “W” indicates no OM on this machine and it continues to work, and “–” indicates that the machine is not available in this maintenance cycle. The optimal maintenance time windows (VMTWn ) are obtained by (14). From the system-level OPR-OM maintenance schedules, different system structures have different optimal maintenance time windows. The optimal maintenance time window can ensure the lowest TM cost for a specific system structure, as discussed in Section V-C. After OPR2, the system has

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TABLE II R ESULTS OF M ACHINE -L EVEL PdM I NTERVALS (T)

TABLE III R ESULTS OF S YSTEM -L EVEL DYNAMIC OPR-OM S CHEDULES

a larger maintenance time window and has performed more OM (PdM actions) than the initial system, or after OPR1. This is because the system structure determines the systemlevel maintenance results. Because the system has more series subsystems after OPR2, OM can significantly reduce the machine breakdown cost and TM cost. C. Effectiveness of the OPR-OM Policy To verify the effectiveness of the proposed OPR-OM policy (VMTW), three traditional OM methodologies are considered for comparison: 1) the first methodology applies individual maintenance (IM) to each machine in the system; 2) the second methodology simultaneously applies TM to every machine; and 3) the third methodology applies the FMTW in the entire decision horizon where even the system structure changes. Considering the TM cost in the entire decision horizon as the decision-making objective, the results of the comparison are shown in Fig. 5. During the decision horizon (3000 h), the TM cost of this OPR-OM policy (VMTW with VMTW1 = 50 h, VMTW2 = 70 h, and VMTW3 = 400 h) has the lowest cost at U.S. $757 633, which is significantly less than the cost of the three traditional methodologies. The OPR-OM policy achieves a maintenance cost savings of 19.17%, 21.85%, and 14.72% compared with the cost of IM, TM, and FMTW = 50 h, respectively. These results establish the effectiveness of the

Fig. 5.

TM cost of different methodologies (decision horizon is 3000 h).

OPR-OM policy in terms of system-level maintenance cost savings. In general, this interactive bilevel maintenance methodology, which is based on a machine-level multiobjective PdM model and a system-level dynamic OPR-OM policy, facilitates the creation of maintenance schedules for manufacturing/operation systems, decreases a system’s TM cost, and enables rapid response to OPR activities and structural changes. Whenever an OPR activity is caused by the changing market, this methodology applies the VMTW to program optimal PdM schedules for the manufacturing/operation system


with a new system structure. It not only ensures a quick response to diverse OPR activities but also establishes the most economical system-level OM schedules. VI. C ONCLUSION In this paper, a novel interactive bilevel maintenance methodology is proposed for manufacturing/operating systems by handling sequential OPR activities. This methodology is aimed at making dynamic decisions according to diverse changes in a system’s structure to ensure system operating efficiency and economy. Maintenance cost, machine availability, and machine profit are considered as the objectives for obtaining machine-level PdM schedules. Depending on the system structures after OPR activities, this methodology can dynamically prepare the most suitable OM schedules by utilizing VMTW to reduce system-level computational complexity and TM cost. Numerical results from Shanghai Port indicate that the bilevel methodology can quickly and effectively program maintenance schedules for manufacturing/operating systems with sequential OPR activities (including machine replacement, machine upgradation, system expansion, and structural changes). Compared with traditional maintenance methodologies, the proposed methodology can achieve substantially higher savings in maintenance cost. Therefore, we can conclude that the proposed maintenance methodology is valid for designing fast, efficient, and economical maintenance schedules for manufacturing/operating systems with OPR activities. The proposed maintenance methodology needs improvement via additional studies. For example, some additional production factors, such as system availability and product delivery cycles, should be employed as objectives to evaluate the obtained system-level maintenance schedules. This paper assumes that a sufficient number of maintenance techniques and machine spare parts exist, which may not be valid in all situations. Therefore, how system-level maintenance schedules can be obtained with limited availability of techniques and spare parts should be investigated. In this paper, the VMTW is a dynamic time window that will change according to each real-time reconfiguration. We would consider changing the VMTW even in the same system configuration if we could handle the increasing scheduling complexity. The joint optimization of time for OPR and the VMTW is another interesting question that warrants future examination. R EFERENCES [1] Y. Koren and M. Shpitalni, “Design of reconfigurable manufacturing systems,” J. Manuf. Syst., vol. 29, no. 4, pp. 130–141, 2010. [2] S. Si, G. Levitin, H. Dui, and S. Sun, “Importance analysis for reconfigurable systems,” Rel. Eng. Syst. Safe, vol. 126, no. 6, pp. 72–80, 2014. [3] T. Xia, X. Jin, L. Xi, and J. Ni, “Production-driven opportunistic maintenance for batch production based on MAM–APB scheduling,” Eur. J. Oper. Res., vol. 240, no. 3, pp. 781–790, 2015. [4] S. Chopra, W. Lovejoy, and C. Yano, “Five decades of operations management and the prospects ahead,” Manage. Sci., vol. 50, no. 1, pp. 8–14, 2004. [5] L. G. Sprague, “Evolution of the field of operations management,” J. Oper. Manag., vol. 25, no. 2, pp. 219–238, 2007. [6] N. V. Herzog, S. Tonchia, and A. Polajnar, “Linkages between manufacturing strategy, benchmarking, performance measurement and business process reengineering,” Comput. Ind. Eng., vol. 57, no. 3, pp. 963–975, 2009.

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Xin-Yang Tao received the B.S. degree in mechanical engineering from Tongji University, Shanghai, China. He is currently pursuing the Ph.D. degree in industrial engineering from Shanghai Jiao Tong University, Shanghai. His current research interests include intelligent maintenance systems, machine reliability modeling, maintenance strategy making, and system maintenance scheduling.

Li-Feng Xi received the B.S. degree from the University of Science and Technology of China, Hefei, China, in 1989, the M.S. degree from Chinese Academy of Sciences, Xi’an, China, in 1992, and the Ph.D. degree from Shanghai Jiao Tong University, Shanghai, China, in 1995, all in mechanical engineering. He is currently the Dean of the School of Mechanical Engineering, Shanghai Jiao Tong University. His current research interests include quality and reliability engineering, theory and method of production system planning and design, and precision manufacturing of autoengine.