The Multi-Vehicle Cyclic Inventory Routing Problem: Formulation and a Metaheuristic Approach

This paper presents a new variant of the Multi-Vehicle Cyclic Inventory Routing Problem (MV-CIRP) which aims to determine a subset of customers to be visited, the appropriate number of vehicles used, and the corresponding cycle time and route sequence, such that the total cost (e.g. transportation, inventory, and rewards) is minimized. The MV-CIRP is formulated as a mixed-integer nonlinear programming model. We propose a Simulated Annealing (SA) based algorithm to solve the problem. SA is first tested on the available benchmark Single-Vehicle CIRP (SV-CIRP) instances and compared to the state-of-the-art algorithms. SA is then tested on the benchmark MV-CIRP instances and compared to optimization solver and a standard Iterated Local Search (MV-ILS) approach. Experimental results show that SA is able to obtain 9 new best known solutions when solving the SV-CIRP instances and outperforms both the optimization solver and the MV-ILS when solving the MV-CIRP instances. Furthermore, insights in the complexity of the MV-CIRP are discussed and illustrated.