This paper addresses a case study regarding inventory models for acquiring liquefied petroleum gas (LPG) cylinders. This is an industrial challenge that was proposed at an European Study Group with Industry, by a Portuguese energy company, for which the LPG cylinder is the main asset of its LPG business. Due to the importance of this asset, an acquisition plan must be defined in order to determine the amount of LPG cylinders to acquire, and when to acquire them, in order to optimize the investment. As cylinders are returned and refilled, the reverse logistic flows of these assets must be considered. As the classical inventory models are not suitable for this case study, three new inventory models, which account for the return of LPG cylinders, are proposed in this work. The first proposed model considers deterministic constant demand and continuous returns of LPG cylinders, with discrete replenishment from the supplier. The second model is similar, but for the case when the returned cylinders cover for the demand. A third model is also proposed considering that both the demand and the returns are stochastic in nature and the replenishment from the supplier is discrete. The three models address different scenarios that the company is either currently facing or is expecting to occur in the near future.

中文翻译：

---

带有反向物流的库存模型，用于液化石油气公司的资产收购

本文介绍了有关用于获取液化石油气（LPG）气瓶的库存模型的案例研究。葡萄牙能源公司在欧洲工业研究小组提出的一项工业挑战中，LPG钢瓶是其LPG业务的主要资产。由于该资产的重要性，必须定义一个购买计划，以确定要购买的LPG气瓶的数量以及何时购买它们，以优化投资。归还钢瓶并重新装瓶时，必须考虑这些资产的逆向物流流程。由于经典的清单模型不适合此案例研究，因此在这项工作中提出了三种新的清单模型，这些模型说明了液化石油气钢瓶的返还。第一个提出的模型考虑了确定性的恒定需求和液化石油气钢瓶的连续收益，以及供应商的离散补给。第二个模型是相似的，但是对于返回的气缸满足需求的情况。考虑到需求和回报本质上都是随机的并且供应商的补给是离散的，提出了第三种模型。这三种模型解决了公司当前面临或预计在不久的将来发生的不同情况。考虑到需求和回报本质上都是随机的并且供应商的补给是离散的，还提出了第三种模型。这三种模型解决了公司当前面临或预计在不久的将来发生的不同情况。考虑到需求和回报本质上都是随机的并且供应商的补给是离散的，还提出了第三种模型。这三种模型解决了公司当前面临或预计在不久的将来发生的不同情况。