Robust optimization in relation to a basic safety investment model with imprecise probabilities

Consider the following basic model in economic safety analysis: a firm is willing to invest an amount x in safety measures to avoid an accident A which, in the case of occurrence, leads to a loss of size L. The probability of an accident is a function of x. The optimal value of x is determined by minimizing the expected costs. In the present paper we study this model (and an extended version of it) in an applied risk/safety management setting, which allows for imprecise probabilities for the accident probabilities. The imprecision reflects the fact that the knowledge basis for assigning the probabilities is poor and based on many assumptions, and also that there are different knowledge bases among relevant experts and stakeholders. The purpose of the paper is to present and discuss a set-up for the precise formulation of this type of problems and show how they can be solved. We demonstrate in the paper how an optimal investment level x can be determined under different sets of situations and conditions, including one where a tolerability limit is defined for the accident probability. The main conclusion of the paper is that the robust optimization methods could in practice provide useful decision support but should be supplemented with sensitivity analyses showing the optimal investment levels for various parameter values followed by qualitative analyses providing arguments supporting the different parameter values. (C) 2013 Elsevier Ltd. All rights reserved.