Analysis of optimization models under different approaches to deal with uncertainty regarding pre-disaster planning in food bank supply chains

Purpose: Pre-positioning is a crucial choice in pre-disaster humanitarian logistics planning that consists of deciding in advance how much aid and where should it be located to enable effective and prompt operations in the case of an emergency. To support managers making such decisions, we propose four mathematical formulations that, considering the uncertainty on the demand to satisfy, seek to optimize aid prepositioning (before the event) and further distribution (after the event) in order to minimize unmet demand (MUD). The purpose of this paper is to evaluate and compare the performance of these formulations on a real case to discuss when and why should each approach be applied. Design/methodology/approach: The two first formulations adopt the cardinality-constrained (CC) approach to handle uncertainty. These formulations differ in their objective functions, the first formulation's objective seeks to MUD, whilst the second incorporates equity in the way that demand is satisfied. The two remaining formulations are scenario-based (SB) and as in the previous two formulations, seek to MUD with and without equity considerations, respectively. Findings: Applying our formulations to a case study, we compare the differences between the solutions produced by the proposed formulations and the solutions that would have been produced without uncertainty (perfect information) to have a better understanding of their performance and their behavior. A discussion of the strengths and weaknesses of each model is provided to help managers choose the model that best suits their needs. Originality/value: The formulations are applied to a case study where a food bank is faced with the arrival of a hurricane in Mexico. As far as our knowledge, it is the first work in literature to deal with humanitarian logistics under a cardinality-constrained approach.