Institute of Transportation, MOTC

       This paper is developed based on a real-world decision scenario that an industrial gas company that applies the Vendor Managed Inventory model and supplies liquid oxygen with a self-operated heterogeneous vehicle fleet to hospitals in nearby cities. To solve this problem, this paper proposes a novel Joint Replenishment and Heterogeneous Vehicle Routing Problem with Cyclical Schedule and formulates it as a non-linear mixed-integer linear programming problem which simultaneously determines the length of the planning cycle (PC), the length of the replenishment cycle and the dates of replenishment for each customer and the vehicle routes of each day within PC, such that the average daily operation cost within PC, including inventory holding cost, setup cost, transportation cost, and overtime labor cost, is minimized. A solution method based on Genetic algorithm, embedded with an innovative encoding and decoding mechanism and local search operators, is then proposed, and the hash function is adopted to avoid repetitive fitness evaluation for identical solutions. In the fitness evaluation and selection process, linear ranking normalization and elitism strategy are included to improve solution quality. Mechanism experiments verified that the hash function could decrease the computation time significantly, and the elitism strategy contributes to decreasing cost. Numerical experiments verified that the hash function could decrease the computation time significantly, and demonstrated that the proposed solution method can effectively solve the problem under different lengths of PC and number of customers. The method is also shown to be effective in determining whether the company should expand the storage capacity of a customer whose demand increases. Sensitivity analysis of the vehicle fleet composition shows that deploying a mixed fleet can reduce the daily operating cost.