An iterated local search algorithm for the single-vehicle cyclic inventory routing problem

The single-vehicle cyclic inventory routing problem (SV-CIRP) is concerned with a repeated distribution of a product from a single depot to a selected subset of retailers having stable demands. If a retailer is selected for replenishment, the supplier collects a retailer-related fixed reward. The objective is to determine the subset of retailers to cyclically replenish, the quantities to be delivered to each, and to design the vehicle delivery routes so that the expected total distribution and inventory cost is minimized while the total collected rewards from the selected retailers is maximized. The resulting distribution plan must prevent stockouts from occurring at each retailer. The underlying optimization problem for this SV-CIRP is formulated as a mixed-integer program with linear constraints and a nonlinear objective function. In this paper, an iterated local search algorithm (ILS) is developed to solve the SV-CIRP. The proposed approach is tested on some randomly generated problems and the obtained results are compared with the results from an efficient insertion heuristic approach. Computational results show that the proposed iterated local search algorithm is more competitive and superior to the known heuristic approaches for the single-vehicle cyclic inventory routing problem