A parallel programming approach to the solution of the location-inventory and multi-echelon routing problem in the humanitarian supply chain

Abstract

Disasters around the world are becoming more frequent, diverse, complex and extremely challenging, causing millions of casualties and affecting both human development and available resources. Consequently, the present study addresses a multi-objective location, inventory and multi-scale routing (2E-LIRP) problem, which supports comprehensive decision making, so that the logistics network designer and manager can obtain adequate strategic planning in the face of uncertainty and the negative impact that an adverse event can generate. Moreover, the problem is formulated as an integer linear programming model, having as main objectives to minimize private logistics costs and maximize the welfare of the affected areas, considering dynamic demand, multiple products and heterogeneous fleet. Due to the computational complexity associated with the model, a new solution approach is proposed, based on the design of evolutionary metaheuristic algorithms; the first one, known as Non-dominated Sorting Genetic Algorithm version II (NSGA-II), the second one, Strength Pareto Evolutionary Algorithm version II (SPEA-II) and the third one, called Genetic Algorithm (GA), programmed in parallel and executed individually under a cooperative environment. Finally, the experimentation carried out on a test set, composed of twenty instances of varying complexity, allows inferring that the parallel-cooperative and purely parallel approach applied to NSGA-II, substantially improves the processing times and the number of non-dominated solutions, if compared to the results obtained by SPEA-II, designed under identical conditions. Moreover, by building a GA with these same characteristics, it improves up to 50% of the solutions, in terms of social costs (logistic and humanitarian costs), with computation times similar to its sequential counterpart.