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An economic production quantity model with backlogging and imperfect rework process for uncertain demand

机译：经济生产数量模型，对不确定需求的返工过程

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摘要

This paper deals with a lot-sizing problem in the economic production quantity model with imperfect production processes and failure in repair where a Brownian motion process governs the inventory level variation. We assume that the unsatisfied demand is fully backlogged. In addition, we assume that all imperfect items produced are stocked separately and then reworked. Reworking and shortage costs are included in the proposed mathematical modelling and analysis. The aim of this research is to determine the optimal production lot size and backorder level such that the long-run total expected cost of the system is minimised. For the proposed model, we prove closed-form expressions for the inventory process and for the backlog costs. Moreover, a computer code using software package for the numerical work is furnished to derive the optimal solution. Some numerical examples and sensitivity analysis are provided to illustrate the validity of the proposed model.
机译：本文在经济生产数量模型中涉及具有不完美生产过程和修复失败的批量尺寸问题，以及布朗运动流程管理库存水平变化。我们假设不满意的需求完全积压。此外，我们假设产生的所有不完全物品都是单独库存，然后重新加工。建议的数学建模和分析中包含重新加工和短缺成本。该研究的目的是确定最佳的生产批量和延期级级，使得系统的长期总预期成本最小化。对于所提出的模型，我们证明了用于库存过程和积压成本的封闭式表达式。此外，提供了一种使用用于数值工作的软件包的计算机代码，提供了最佳解决方案。提供了一些数值例子和灵敏度分析以说明所提出的模型的有效性。

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