Effective local search approaches for the single-vehicle cyclic inventory routing problem

The single-vehicle cyclic inventory routing problem (SV-CIRP) is concerned with a cyclic distribution of a product from a single depot to a selected subset of retailers facing stable demands. If a retailer is selected for replenishment, the supplier collects a retailer-related reward. The objective is to select a subset of retailers to replenish, quantities to be delivered to each, and design delivery routes that minimise the expected total distribution and inventory costs while maximising the total collected rewards. The resulting distribution plan must prevent stockouts from occurring at each retailer. The underlying optimisation model for the SV-CIRP is formulated as a mixed integer program with linear constraints and a nonlinear objective function. An effective iterated local search based algorithm is developed to solve the problem. Various instances are generated to test the proposed algorithm. Numerical results show that it is very competitive and can find good quality solutions for the SV-CIRP in reasonable computational time