运筹与管理2026，Vol.35Issue(1)：68-74,7.DOI:10.12005/orms.2026.0010
产出不确定下考虑再制造的混合生产计划鲁棒优化
Robust Optimization for Lot-sizing Problems with Remanufacturing under Yield Uncertainty
摘要
Abstract
Yield uncertainty is caused by production defects in the manufacturing process.Due to factors such as the environment,machine failure and worker proficiency,the actual output of the production system often devi-ates from the planned output.In order to provide products that meet customer quantity and quality requirements and minimize operating costs,manufacturing companies need to decide the production batch size for each cycle.Although enterprises strive to achieve zero production defects,production defects are unavoidable in the manufac-turing process,which requires enterprises to formulate production plans under the condition of accepting produc-tion defects.Additionally,China's"14th Five-Year Plan for Green Development in Industry"has put forward a series of goals,including reducing carbon dioxide emissions per unit of industrial added value by 18％by 2025 and achieving remarkable results in the green and low-carbon transformation of industrial production methods by 2025.Attaining these goals will contribute to the green and low-carbon transformation of China's industrial production,significantly improving energy and resource efficiency and comprehensively enhancing the level of green manufacturing.Moreover,remanufacturing as a kind of low carbon production mode,can help enterprises to increase profits and achieve energy conservation and emission reduction.This paper studies the production planning problem of a non-static multi-cycle single project under a hybrid production system that considers remanufacturing,aiming to achieve the lowest total operating cost within the planning cycle under the conditions of time-varying production costs.Therefore,in order to ensure the stability and green sustainable development of the production system,it is necessary to study the robust optimization for lot-sizing problems with remanufacturing under yield uncertainty.The research on the issue of hybrid production planning considering yield uncertainty with remanufacturing serves a dual purpose.Firstly,it offers theoretical guidance for manufacturing enterprises to judiciously organize production under yield uncertainty,thereby enhancing the stability of the production system.Secondly,through remanufacturing,it can enhance the green manufacturing level of the production system and reduce resource consumption. First,this paper develops a kind of the robust optimization model under yield uncertainty to minimize the total operating cost of production system and satisfy the constraints of inventory cost and shortage cost under the most pessimistic yield condition.To efficiently solve this,the nonlinear robust optimization model is then trans-formed into an equivalent mixed-integer linear programming model according to the problem characteristics.Finally,the effectiveness of the model is verified by a real auto parts production case and a large number of randomly generated instances. The experimental results show that:(1)To assess the advantages of robust strategies in dealing with variations in actual yield conditions,Monte Carlo simulations are conducted for each example.Each scenario is simulated 10000 times to obtain the results for expected cost and worst-case cost.Compared with the traditional model,the robust model can provide a robust production strategy for decision makers under uncertain scenarios.The average pessimistic cost decreases by 11.77％,and the gap between target cost and expected cost decreases from 7.63％to-9.88％.(2)According to the experimental requirements,we classify the quantity of returned products,startup costs and returns disposal costs to explore the preference for robust production planning strate-gies under different circumstances.Compared with other parameters,setup cost is highly correlated with solving efficiency,and the correlation coefficient between them is 0.999.Expanding the scale of the experiment further corroborate the findings of the small-scale experiment.(3)We analyze the cost structure of robust production planning strategies under different stockout cost conditions.Simultaneously,we study the production level and inventory level of robust strategies to further understand their performance in response to yield uncertainty.Decision makers can refer to the robust strategy of reducing production frequency and increasing inventory to cope with yield uncertainty.The numerical experiments and case studies prove that the robust optimization model proposed in this paper can provide decision makers with production planning strategies under output uncertainty.In hybrid production systems,robust strategies help decision-makers develop effective production plans under the condition of accepting production defects.On the other hand,through the research on remanufacturing production methods,the green manufacturing level of the production system is fully improved,resource utilization efficiency is improved,and greater social benefits are achieved. Future research directions can be developed from the following two aspects:(1)The description of the hybrid production system in this article is based on a single product.In future research,the hybrid production system can be further considered in terms of different output rates of multiple products,and the robust optimiza-tion problem of multi-product production planning considering remanufacturing under output uncertainty can be studied.(2)Uncertain conditions can be extended to include demand uncertainty or return uncertainty,so that the research on this issue can be closer to reality and include a variety of scenarios.关键词
生产计划/再制造/联合生产/鲁棒优化/产出不确定Key words
lot-sizing/remanufacturing/joint set-up/robust optimization/yield uncertainty分类
管理科学引用本文复制引用
吴鹏,杨丽清..产出不确定下考虑再制造的混合生产计划鲁棒优化[J].运筹与管理,2026,35(1):68-74,7.基金项目
国家社会科学基金资助项目(22BGL272) （22BGL272）
教育部人文社会科学研究一般项目(21YJA630096) （21YJA630096）
福建省"雏鹰计划"青年拔尖人才项目(0470-00472214) （0470-00472214）
福建省自然科学基金面上项目(2022J01075) （2022J01075）
