Inverse Optimization Method for Safety Resource Allocation and Inferring Cost Coefficient Based on a Benchmark

Abstract

Due to cost-push inflation, the trade-off between safety costs and risk prevention (safety) has become difficult worldwide. Most companies experience the difficulty of safety cost overruns and allocate safety resource inefficiently. In this paper, a forward model maximizing safety input is formulated. Because there is a wide range of variation of safety resource cost coefficient parameters, it is hard to determine safety resource cost coefficients in the forward model, to make the decisions on which types of safety resources are allocated to which potentially risky locations with what prices, and to ensure total input is as close to the benchmark as possible. Taking allocation, themes, resources, and cost coefficient parameters as new decision variables, the inverse optimization model is formulated based on a bi-level model. With consideration of quaternion decision, bi-level programming, and NP-hard problem, based on the comparison of exact penalty algorithm and an improved PSO algorithm, in which the inertia weight is adaptively changing with the number of iterations, the PSO is suitable for solving the specific inverse model. Numerical experiments demonstrated the effectiveness of the PSO algorithm, proving that it can allocate the right amount and types of safety resources with the right prices at the right places.