Optimization and Simulation Studies of a Production System for Ventilators to Mitigate Challenges of COVID-19 Pandemic

Protocase公司是一家位于加拿大南部悉尼的制造公司，生产定制和设计的电子外壳和金属薄板部件。在新冠肺炎大流行到来后，Protocase决定制造呼吸机，以发挥作用，减轻这次大流行造成的挑战，包括拯救加拿大人生命的关键医疗设备短缺。这项研究的目标是模拟Protocase的供应链，并在采购和生产系统中存在不确定性的情况下，针对不同的生产场景进行模拟，以估计不同生产能力的产量。生产呼吸机所需的一些零部件将由Protocase生产，一些零部件将通过他们的供应链进口。 为了考虑与发货延迟相关的不确定性，将探索概率分布，以定义零部件到达生产系统的模式以及生产时间。考虑到对通风机的需求是不确定的，利用随机规划和排队论的方法对不确定系统进行分析，并应用混合整数线性规划方法得到最优解。考虑到零部件价格的不确定性，将考虑使用三角模糊数来表示成本。最后，我们使用了各种方法来解决整数线性规划问题，如割平面法、分枝定界法、松弛法和分解法。该项目完成后，鉴于其采购过程和生产系统中的不确定性，Protocase将能够就其资源的最佳分配做出明智的决定，以在一段时间间隔内生产不同数量的呼吸机。该项目的成果不仅将帮助Protocase在缓解全球和国家大流行的挑战方面发挥关键作用，而且还将使加拿大通过成为关键设备的潜在供应商而产生全球影响，这也可以为加拿大带来经济利益。

Protocase Incorporated is a manufacturing company in Sydney, NS Canada that produces custom-made and designed electronic enclosures and sheet metal components. After the arrival of the COVID-19 pandemic, Protocase decided to manufacture ventilators to play a role in mitigating the challenges caused by this pandemic including the shortage of vital medical equipment to save Canadians' lives. The goal of this study is to simulate Protocase's supply chain and conduct simulations for different production scenarios, given the uncertainties in the procurement and production systems, to estimate outputs for different production capacities. Some parts that are needed to produce a ventilator will be produced by Protocase, and some parts will be imported through their supply chain. To consider the uncertainty associated with delay in shipments, probability distributions will be explored to define the arrival pattern of the components to the production system as well as the production time. Given that the demand for ventilators is uncertain, methods of stochastic programming and queueing theory will be used to analyse the uncertain system and mixed integer linear programming will be applied to obtain optimal solutions. Triangle fuzzy numbers will be considered to present costs given the uncertainty in components' prices. Finally, we use various methods to solve the integer linear programming problems, such as cutting plane, Branch-and-Bound, relaxation and decomposition methods. Upon the completion of this project, Protocase will be able to make informed decisions about optimal allocation of their resources to produce different number of ventilators in a time interval given the uncertainties in their procurement process and production system. The outcome of this project not only will help Protocase play a crucial role in mitigating the challenges of a global and national pandemic, but also will enable Canada to have a global impact by becoming a potential supplier for a vital equipment which can also bring economic benefits to Canada.