A heuristic method for the supplier selection and order quantity allocation problem

Abstract

This paper addresses the so-called supplier-selection and order-quantity allocation problem. Because of the complexity of this of problem (e.g., non-linear, discontinuous cost function), a new heuristic method is proposed and tested. This heuristic method explores the search space in a short period of time to find cheaper solutions. In order to test the efficiency of the proposed heuristic, two metaheuristic algorithms are applied: particle swarm optimization (PSO) and differential evolution (DE). Additionally, two numerical examples were solved. In the first one, it is shown that the proposed heuristic performed best compared to other solutions previously published in the literature, both in terms of computational time and total cost. The complexity analysis found that in the worst case, the proposed heuristic executes on average 99.9% less numerical operations than PSO and DE. In the second numerical example, larger instances were studied. Our findings show that the proposed heuristic was able to find a feasible solution in 15 out 15 instances, while the PSO and the DE algorithms were unable to find a solution in 9 out of 15 instances. Therefore, the proposed heuristic does not just lead to lower total cost solutions, but it also performs a more exhaustive search in shorter computational times for larger instances of the problem. Finally, Wilcoxon and Kruskal-Wallis statistical tests demonstrate significant difference between the proposed heuristic and the PSO and DE; the proposed heuristic presented a lower median in most cases.