{"title":"Optimal Batch Size and Process Setting in Light-Emitting Diode (LED) Coproduction Processes","authors":"Vashkar Ghosh, Anand Paul, Zhechao Yang, Lingjiong Zhu","doi":"10.1177/10591478241238975","DOIUrl":null,"url":null,"abstract":"This paper studies the challenges involved in production planning in coproduction systems, specifically the production of semiconductor chips for light-emitting diodes (LEDs). The production output in this industry is characterized by a stochastic distribution over the targeted production metric; thus the whole range of production is not suitable for a specific application. We formulate a novel stochastic profit optimization problem with random production output and random demand—based on information gleaned from interactions with a large integrated LED manufacturer—and determine the optimal production parameter setting and the batch size analytically; we solve the problem exactly in the special case of a single customer specification, and approximately in the case of an arbitrary number of customer specifications. We find that the optimal production setting depends on the sharpness of the density function governing the production output distribution and the range of parameter settings that are acceptable to customers. We show analytically that even under perfectly symmetric conditions, the optimal production setting is not necessarily symmetrically located with respect to the output range. We complement our analytical results with a Monte Carlo simulation of an augmented model with service level constraints. Our simulation results show that the approximate model that we develop serves as an excellent proxy for the intractable exact model, and illustrates the interplay between production output randomness, demand randomness, service levels, and production yield.","PeriodicalId":20623,"journal":{"name":"Production and Operations Management","volume":null,"pages":null},"PeriodicalIF":4.8000,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Production and Operations Management","FirstCategoryId":"91","ListUrlMain":"https://doi.org/10.1177/10591478241238975","RegionNum":3,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MANUFACTURING","Score":null,"Total":0}
引用次数: 0
Abstract
This paper studies the challenges involved in production planning in coproduction systems, specifically the production of semiconductor chips for light-emitting diodes (LEDs). The production output in this industry is characterized by a stochastic distribution over the targeted production metric; thus the whole range of production is not suitable for a specific application. We formulate a novel stochastic profit optimization problem with random production output and random demand—based on information gleaned from interactions with a large integrated LED manufacturer—and determine the optimal production parameter setting and the batch size analytically; we solve the problem exactly in the special case of a single customer specification, and approximately in the case of an arbitrary number of customer specifications. We find that the optimal production setting depends on the sharpness of the density function governing the production output distribution and the range of parameter settings that are acceptable to customers. We show analytically that even under perfectly symmetric conditions, the optimal production setting is not necessarily symmetrically located with respect to the output range. We complement our analytical results with a Monte Carlo simulation of an augmented model with service level constraints. Our simulation results show that the approximate model that we develop serves as an excellent proxy for the intractable exact model, and illustrates the interplay between production output randomness, demand randomness, service levels, and production yield.
本文研究了共同生产系统中生产规划所面临的挑战,特别是发光二极管(LED)半导体芯片的生产。该行业的生产产出具有目标生产指标随机分布的特点,因此整个生产范围并不适合特定应用。我们根据从与一家大型集成 LED 制造商的互动中收集到的信息,提出了一个具有随机产量和随机需求的新型随机利润优化问题,并通过分析确定了最佳生产参数设置和批量大小;我们精确地解决了单一客户规格的特殊情况,并近似地解决了任意数量客户规格的情况。我们发现,最佳生产设置取决于管理生产产出分布的密度函数的尖锐程度,以及客户可接受的参数设置范围。我们通过分析表明,即使在完全对称的条件下,最优生产设置也不一定与产出范围对称。我们通过对带有服务水平约束的增强模型进行蒙特卡罗模拟,对分析结果进行了补充。我们的模拟结果表明,我们开发的近似模型可以很好地替代难以解决的精确模型,并说明了产量随机性、需求随机性、服务水平和产量之间的相互作用。
期刊介绍:
The mission of Production and Operations Management is to serve as the flagship research journal in operations management in manufacturing and services. The journal publishes scientific research into the problems, interest, and concerns of managers who manage product and process design, operations, and supply chains. It covers all topics in product and process design, operations, and supply chain management and welcomes papers using any research paradigm.