Branch-and-price algorithms for large-scale mission-oriented maintenance planning problems

Abstract:

This paper presents an original segment age based approach for settling huge scope occasions of the joint particular support and repairperson task issue (JSM-RAP) for mission-situated frameworks in modern settings. Such frameworks perform successive missions isolated by planned limited length breaks during which a portion of their parts are defectively kept up with by repairpersons, meaning to expand framework unwavering quality in ensuing missions. The subsequent numerical model is computationally costly, in any event, for issues of moderate size. The proposed approach deteriorates the JSM-RAP into an expert issue and various subproblems that are tackled to produce support designs, i.e., sections. Two techniques are created to deal with the blended number nonlinear subproblems: a piecewise-straight estimate and a precise reformulation into blended number dramatic conic projects. Branch-and-value calculations are created by installing the segment age technique into a branch-and-bound tree to reestablish arrangement integrality and assurance its optimality. Moreover, we utilize an adjustment plan to speed up combination. Mathematical tests approve the proposed approach and exhibit its additional worth as far as calculation time and arrangement quality. Issue cases of extremely huge size, like genuine modern creation plants, are tackled productively. Results likewise show that rising the quantity of support levels gives greater adaptability to the enhancer to find blends of parts and upkeep activities that better utilize the restricted assets.

Introduction:

Numerous cutting edge frameworks work as indicated by substituting successions of missions and break periods during which upkeep activities are performed. Such multi-part frameworks are experienced in conventional assembling, creation and administration enterprises where gear, for example, creation lines, airplane, ships, and trucks work ceaselessly until they are interfered with to go through upkeep. New resources like automated independent vehicles and high level battle/guarded frameworks additionally display such examples. The specific support (SM) methodology presented by Rice et al. (1998) is especially appropriate for these mission-situated frameworks. To work on the capacity of such frameworks to effectively accomplish their resulting missions, support activities are completed on parts during the planned breaks. Restricted upkeep assets like time, financial plan, spare parts, and fix groups limit the number and levels of support exercises that can be performed before the following mission. The choice issue that involves choosing the parts to keep up with and the degree of support activities to do is known as the specific support issue (SMP). Moreover, when the chose support activities are to be performed by various repairpersons, possibly having different ability levels and expenses, the SMP that mutually decides the task of undertakings to repairpersons is alluded to as the joint specific upkeep and repairperson task issue (JSM-RAP) (Diallo et al., 2017, Diallo et al., 2019). The SMP and its variations have been applied to numerous modern frameworks like breeze turbines (O'Neil et al., 2022a, O'Neil et al., 2023), coal transport frameworks (Liu et al., 2009), machining lines in a motor shop (Zhu et al., 2011), armed force tanks (Sharma et al., 2017), atomic fuel creation frameworks (Zhao et al., 2019), airplanes turbine motor frameworks (Wang et al., 2019), and stream transmission frameworks (Liu et al., 2020).

Throughout the long term, different augmentations of the fundamental SMP with various frameworks structures, support strategies, asset constraints, demonstrating techniques, and arrangement calculations have been proposed to carry the models nearer to the real factors of modern and useful settings. The peruser is alluded to the new reviews by Al-Jabouri et al., 2022, Cao et al., 2018a, and Xu et al. (2015) for a definite record of the SMP writing. These expansions can commonly be bunched into four gatherings of attributes connected with the framework, upkeep, mission and numerical model. Framework attributes incorporate highlights, for example, framework level (single framework or armada of frameworks) (Schneider and Cassady, 2004, Schneider and Cassady, 2015, Khatab et al., 2020), framework state (double or multistate parts/frameworks) (Meng et al., 1999, Pandey et al., 2013a, Dao and Zuo, 2017a, Yin et al., 2023), and framework reliance (financial, underlying, or stochastic) (Xu et al., 2016, Dao and Zuo, 2017b, Shahraki et al., 2020). Support qualities allude to the traits connected with the execution of upkeep exercises. These properties like repairpersons' accessibility (adequate or restricted) (Diallo et al., 2017, Diallo et al., 2019, Chaabane et al., 2018), and the viability of activities did (great or defective support) (Khatab et al., 2008, Do et al., 2015, Khatab et al., 2018), can essentially influence upkeep choices and unwavering quality accomplished. Mission attributes incorporate elements, for example, mission types (single or multi-mission) (Zhang et al., 2019, Chaabane et al., 2020) and arranging skyline (limited or boundless) (Yu and Schneider, 2003, Maillart et al., 2009). Model attributes incorporate two principal qualities: advancement standards (e.g., dependability/accessibility boost or potentially cost/energy/discharges minimization) (Yu and Schneider, 2003, Hoai and Luong, 2006, Zhang et al., 2020), and boundary vulnerability and strength (Jiang and Liu, 2020a, Jiang and Liu, 2020b).

The fundamental test for most SMP models is that their details are challenging to settle ideally, particularly for modern size issues that would permit professionals to carry out and involve the SMP for their numerous frameworks and repairpersons. Rice (1999) demonstrated that the essential SMP is NP-hard, as are its expansions, suggesting that computational endeavors increment dramatically with issue size. Among the arrangement approaches proposed for the SMP are general heuristics (Khatab et al., 2007, Desire et al., 2009, Cao et al., 2018b, Ahadi and Sullivan, 2019, Galante et al., 2020), metaheuristics (e.g., hereditary calculation Dao et al., 2014, differential advancement Khatab et al., 2017, and reproduced strengthening Jiang and Liu, 2020b), careful arrangement draws near, (e.g., absolute specification Rice et al., 1998, search space decrease Rajagopalan and Cassady, 2006, profundity first inquiry calculations Cao et al., 2016, branch-and-bound-type techniques Xia et al., 2022, the two-stage approach Diallo et al., 2018), the maximum min approach (Schneider and Cassady, 2015), and AI (Liu et al., 2020, Kammoun et al., 2022, Hesabi et al., 2022, O'Neil et al., 2022a). Notwithstanding, enormous scope occasions of the issue, and specifically its JSM-RAP expansion, are as yet testing to address because of its combinatorial and nonlinear nature. In this manner, novel reformulations, approximations and arrangement techniques that can deal with genuine frameworks comprising of many parts are as yet required (Cao et al., 2018a, Diallo et al., 2019).

This paper proposes a clever methodology in view of segment age (CG) for settling huge scope occurrences of the JSM-RAP illustrative of genuine industry issues. The proposed approach is firmly connected with the two-stage approach created by Diallo et al. (2019) to address moderate-size occurrences of the issue with defective fix and various fix channels. The two-stage approach changes the JSM-RAP into a multi-layered numerous decision backpack issue (MdMCKP) by creating every single plausible mix (i.e., designs/sections) of parts, upkeep levels and repairpersons, and afterward tackling the MdMCKP to ideally choose a subset of examples that limit the all out support cost or expand the dependability for the following mission. Albeit this approach is demonstrated to be effective for little to-medium size occasions, its example age plot runs out of memory for modern size cases where the numerous parts, support levels and repairpersons monstrously increment the quantity of blends to investigate. Moreover, the MdMCKP is a paired number program (BIP) and is one of the most perplexing individuals from the Backpack Issue (KP) family, which is known to be NP-hard overall (Cacchiani et al., 2022). In this manner, a MdMCKP with an enormous number of parallel factors is very difficult to tackle to demonstrated optimality (Zia and Coit, 2010). Another extremely late example based approach for addressing the JSM-RAP is proposed by O'Neil et al. (2022b). Not at all like the two-stage approach of Diallo et al. (2019), which creates all possible examples at the start, they utilize a CG-based heuristic calculation in which the subproblems are tackled utilizing the hereditary calculation (GA). Since a metaheuristic is utilized to tackle the subproblems, no assurance about the nature of the got arrangement can be given, which is a significant restriction of their methodology.

 

Conclusions

 

In this paper, huge scope occasions of the joint particular upkeep and repairperson task issue for a series-equal framework are tended to. A segment age based approach that emphasizes between taking care of a confined expert issue to refresh the double multipliers and tackling different subproblems to create support designs is created.

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