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

Protocase Incorporated是一家位于加拿大悉尼的制造公司，生产定制和设计的电子外壳和钣金组件。在2019冠状病毒病大流行到来后，Protocase决定生产呼吸机，以缓解这场大流行带来的挑战，包括挽救加拿大人生命的重要医疗设备短缺。本研究的目标是模拟Protocase的供应链，并对不同的生产场景进行模拟，考虑到采购和生产系统的不确定性，以估计不同生产能力的产出。生产呼吸机所需的部分零部件将由Protocase生产，部分零部件将通过其供应链进口。

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.