A fuzzy bi-level programming approach to scarce drugs supply and ration planning problem under risk

Abstract

In this paper, a possibilistic bi-objective bi-level programming model is proposed to optimize the management of scarce drugs supply and rationing under difficult situations such as COVID-19 outbreak. Multiple followers and single leader exist in the proposed Stackelberg model in which the followers are divided into two groups, manufacturers and suppliers. The first group has priority over the latter. The competition between these two groups is addressed using a lexicographical procedure. Moreover, the interaction between the individuals in each group is incorporated through a normalized Nash equilibrium. To avoid the discriminative allocations, the disability-adjusted life years (DALY) index is employed to improve the rationing process. Due to the significance of uncertainty in such a problem, a novel risk-based possibilistic expected value approach is devised to control the mean and risk values of the objective functions. Finally, to validate the proposed solution method, the model is solved by applying Karush–Kuhn–Tucker (KKT) conditions and using the data extracted from a real case study. The results reveal the applicability and usefulness of the proposed possibilistic model compared to the conventional possibilistic approach