Fuzzy Integer Credibility Programming for Modeling and Solving Humanitarian Relief and Transportation Problem After the Crisis Under Uncertainty

Abstract

After the crisis, one of the most important goals of humanitarian logistics organizations is to transport essential goods to the affected areas as quickly as possible. To this end, decisions must be made on the supply of vehicles and their routing and scheduling. The problem of humanitarian aid transportation after the crisis is of particular importance because of the lack of vehicles, the uncertainty conditions, and the immediate and unpredictable changes. This paper deals with the issue of supply, routing and scheduling of vehicles in uncertain conditions with the aim of delivering the necessary goods within the specified time window to affected locations at the minimum cost. Accordingly, at first, the sources of uncertainty in the post-crisis transport and humanitarian relief problem are extracted, including uncertainties in the cost of using the vehicles, travel time and also fuzzy constraints. Then a fuzzy mixed integer programming model for the problem is proposed that simultaneously incorporates the fuzzy objective function, fuzzy constraints and fuzzy parameters. To achieve a sustainable strategy, fuzzy credibility programming approach has been proposed to deal with uncertainty and provide a solution that can find sustainable strategies against post-crisis environmental changes. The final model is implemented in AMPL optimization software and computational results are presented to evaluate the proposed model and method.

Keywords

• humanitarian relief and transportation
• vehicle routing problem
• vehicle scheduling problem
• fuzzy integer programming
• fuzzy credibility programming