An approximation approach to a trade-off among efficiency, efficacy, and balance for relief pre-positioning in disaster management

•Designing a multi-mode-route humanitarian relief logistics network.•Introducing a new utility level for delivered RCs in disaster management.•Proposing new efficacy and balance measures based on the utility level.•Applying a new integrated separable programming-MCDM approach.•Investigating a real case to prove the applicability of the proposed approach. This work develops a multi-objective, two-stage stochastic, non-linear, and mixed-integer mathematical model for relief pre-positioning in disaster management. Improved imbalance and efficacy measures are incorporated into the model based on a new utility level of the delivered relief commodities. This model considers the usage possibility of a set of alternative routes for each of the applied transportation modes and consequently improves the network reliability. An integrated separable programming-augmented ε-constraint approach is proposed to address the problem. The best Pareto-optimal solution is selected by PROMETHEE-II. The theoretical improvements of the presented approach are validated by experiments and a real case study.