LORA（Level Of Repair Analysis，修理级别分析）是一种系统性的分析方法，它以经济性或非经济性因素为依据，确定装备中待分析产品需要进行维修活动的最佳级别，广泛应用于飞机、船舶等。对于经济性分析，最早于90年代由美国L. Barros,   R.J. Basten等人建立了0-1规划模型，国内西北工业大学、电子科大和一些装备研究院所的研究者进行过相关研究。但这个模型求解太难了，大家都陆续转向联合优化问题，经济性分析模型的求解被长期搁置而成为冷门，同样也限制了修理级别分析的实际应用。

    模型的求解是此领域待解决的基础性问题。一些人使用lingo和cplex等软件求解模型，但结果却不尽人意。近期Deng和Qiao等人在Computers & Industrial Engineering（IF=7.9，工程技术大类一区top）上发表文章，称其提出一种原创的0-1规划模型求解方法，让LORA的落地成为可能。

    作者在2019年尝试通过启发式算法来求解经济性模型，首次完整给出了算法的收敛曲线和求解结果，相关结果发表于当年的航空学报上。经过长期思考提出了一种解码算法，实现去约束的目的，大大提高了求解性能。论文首次给出了可行解的准确数目计算公式，同时还建立考虑维修时间的多目标模型并完成求解。这是修理级别经济性分析领域十多年来最精彩的工作之一，论文非常详细，附录中还给出了关键的程序代码，我已经按流程复现出其中的主要结果。

    作者希望能与业内同行开展合作，通过数学和计算机工具持续提升对这一问题的求解能力，帮助降低各类装备每年所产生的昂贵维修或维护成本。

《A novel unconstrained methodology for economic analysis of the level of repair with a case study of a multi-indenture and multi-echelon repair network》

附件（Attachment）：

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航空学报-article-2.pdf-Download 

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Repair Level Analysis Latest Progress 2024

LORA（Level Of Repair Analysis）is a systematic analysis method that determines the optimal level of maintenance activities for equipment based on economic or non-economic factors. It is widely used in aircraft, ships, and other equipment. In terms of economic analysis, the 0-1 programming model was first established by L. Barros, R.J. Basten and others in the United States in the 1990s. Researchers from Northwestern Polytechnical University, Electronic Science and Technology University, and some equipment research institutes in China have conducted related studies. However, solving this model was too difficult so researchers gradually turned to joint optimization problems instead. The solution to the economic analysis model has been long neglected and has become a niche area which also limits the practical application of Level Of Repair Analysis. The solution of the model is a fundamental problem to be solved in this field. Some people use software such as lingo and cplex to solve models but with unsatisfactory results. Recently, Deng and Qiao published an article in Computers & Industrial Engineering (IF=7.9) proposing an original solution method for 0-1 programming models making it possible for LORA to be implemented. In 2019, authors attempted to solve the economic model using heuristic algorithms providing complete convergence curves and solutions for their algorithm for the first time which were published in that year's Journal of Aeronautics. After long-term consideration they proposed a decoding algorithm achieving unconstrained purposes significantly improving performance during solving process. The paper provided accurate calculation formulas for feasible solutions while establishing multi-objective models considering maintenance time completing its resolution. This work represents one of most remarkable achievements within more than ten years regarding economical aspect analysis within repair level domain; key program codes are also included within appendix section. Authors hope to collaborate with industry peers continuously enhancing problem-solving capabilities through mathematical tools aiming at reducing expensive annual maintenance costs generated by various types of equipment.

《A novel unconstrained methodology for economic analysis of the level of repair with a case study of a multi-indenture and multi-echelon repair network》

Abstract

The multi-indenture and multi-echelon economic analysis of repair levels is commonly modelled as a constrained 0–1 programming problem. However, with the increase in the scale of the decision variables, the proportion of feasible solutions in the solution space sharply decreases, posing a challenge for traditional solution methods. In this paper, the transformation of the initial problem into an unconstrained integer programming problem is demonstrated. Specifically, the total number of feasible decisions can be solved analytically through a decision flow method, and a bijective relationship between decision sequence numbers and feasible decisions is established using a mixed-radix system, converting the optimization variables to feasible decision sequence numbers; in this way, the initial problem becomes unconstrained. The advantages of this approach include the following: (1) All the solutions in the transformed solution space are feasible, which significantly improves the efficiency of the solution and reduces the dimensionality of the decision variables; and (2) the proposed model is highly flexible in terms of considering additional variables, such as decision time, transportation modes, and repair locations. Furthermore, the sequence numbers of each feasible solution are transformed into binary sequences, and the binary particle swarm optimizer (BPSO) algorithm can be employed to solve the model. The proposed methodology is applied to the case of a three-indenture and three-echelon repair network considering multiple fault modes, and the results are compared with those of previous studies. The results validate the rationality and substantial advantages of the proposed methodology for economic analysis in terms of computational speed and convergence performance.