A novel multi-stage possibilistic stochastic programming approach (with an application in relief distribution planning)

Abstract

In this paper, a novel multi-stage possibilistic stochastic programming (MSPSP) approach is developed. At the early stages, there is little information on how to pursue MSPSP the optimal decision, while in the course of time, new series of information become unfolded, which further necessitate the model to be updated. Compared to other competent uncertainty programming approaches (i.e. the classical two-stage stochastic programming (TSSP) and multi-stage stochastic programming (MSSP), and enhanced versions of TSSP and MSSP approaches), the proposed MSPSP method relaxes the subjectively setting the deterministic occurrence probabilities and allows possible perturbation in their values as fuzzy probabilities. It further enables these values to be updated so that the updated values do not conflict with each other and their summation does not exceed one. Also, given the existence of several sources of uncertainty and the deep level of uncertainty in the early stages, the scenario dependent variables at such stages are treated as random fuzzy variables. Finally, it takes into account the effect of unfolded information in an on-going fashion in the course of time. Applicability of the proposed approach is tested on a real case study for the post-disaster relief distribution planning in Tehran. Finally, useful managerial insights are provided through conducting several sensitivity analyses.