Safety Investment Decision Problem without Probability Distribution: A Robust Optimization Approach

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.