Heuristic algorithm based on reduce and optimize approach for a selective and periodic inventory routing problem in a waste vegetable oil collection environment

This paper develops a general heuristic algorithm to solve the selective and periodic inventory routing problem (SPIRP) in a waste vegetable oil collection environment. In the past, the SPIRP has been formulated and solved via a valid set of inequalities and an adaptive large-neighborhood search algorithm. The proposed algorithm is based on a reduce and optimize approach (ROA) and a new inequality. The ROA always solves the problem using a small feasible subset containing a near-optimal solution. Two available sets of benchmark instances are tested and solved: (a) in the first set with 36 instances, the new algorithm improves the reported solution in 94.44% of the instances; (b) in the second set with 54 instances, the results show that the proposed algorithm finds a better solution than the previously published ones in 92.59% of the cases. In a third set composed of 24 very large instances, the proposed heuristic algorithm always finds better solutions than the CPLEX MIP solver. Finally, the computational results show that the proposed algorithm obtains, on average, a solution within 1.99%, 2.86%, and 7.41% of optimality for the first, second, and third set of instances, respectively. Also, the computational experiments show that the heuristic algorithm is effective and efficient in instances with up to 300 source nodes.