Accidents occur frequently, causing huge losses to enterprises and individuals. Safety investment is an important means to prevent accidents, but how much to invest is a dilemma. Previous studies have assumed that the demand of safety investment follows some probability distribution. In practice, the distribution information of safety investment is usually limited or difficult to obtain, i.e., it is unknown. To deal with this kind of problem without a probability distribution, we construct the measures of marginal accident loss (MAL) and marginal opportunity loss (MOL) from the perspective of demand uncertainty. Robust optimization technology is utilized to establish three robust optimization models, which are the absolute robust models (ARM), deviation robust models (DRM), and relative robust models (RRM). The results of numerical analysis show that MAL is positively correlated with safety investment and MOL is negatively correlated with the uncertainty of safety investment. The above robust optimization models in this study can be applied to different enterprise’s risk scenarios. ARM, DRM, and RRM are suitable for high- and nonhigh-risk industries and other industries, respectively.

中文翻译：

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无概率分布的安全投资决策问题：鲁棒优化方法

事故频发，给企业和个人造成巨大损失。安全投资是预防事故的重要手段，但如何投资却是一个难题。先前的研究假设安全投资的需求遵循某种概率分布。在实践中，安全投资的分配信息通常是有限的或难以获得的，即未知的。为了解决这种没有概率分布的问题，我们从需求不确定性的角度构造了边际事故损失（MAL）和边际机会损失（MOL）的度量。鲁棒优化技术被用于建立三个鲁棒优化模型，分别是绝对鲁棒模型（ARM），偏差鲁棒模型（DRM）和相对鲁棒模型（RRM）。数值分析结果表明，MAL与安全投资呈正相关，MOL与安全投资的不确定性呈负相关。本研究中的上述鲁棒优化模型可以应用于不同企业的风险场景。ARM，DRM和RRM分别适用于高风险和非高风险行业以及其他行业。