Institute of Transportation, MOTC

       This study investigates a novel extension of the multi-commodity joint replenishment problem (mJRP), namely simultaneous multi-commodity joint replenishment problem and heterogeneous vehicle routing problem under cyclic schedules (mJRP-HVRP-CS), which is initiated by the Vendor Managed Inventory (VMI) model adopted by a paint importer who replenishes multiple products for its customers under a cyclic interval. The problem is formulated as a mixed integer nonlinear programming model to determine an optimal replenishment plan (including the length of the planning horizon of the replenishment plan, the interval and the day of replenishment for each commodity of each customer, and the vehicle deployment and routing plan of each day in the planning horizon) which minimizes the average daily total cost, which is the sum of the inventory holding cost, setup cost, transportation cost, and overtime labor cost. The plan is executed by a mix fleet of self-owned and outsourced vehicles and constrained by a list of practical considerations including customer storage capacity, fleet capacity, and maximum working time. As the problem is combinatorially complex, this study proposes a solution method based on simulated annealing algorithm (SAA) to handle it. It incorporates tabu list and hash table in the process of local search to avoid short-term repeated search and repeated solution evaluation respectively. An elite list is also incorporated to guarantee the solution quality under limited computational budget. Numerical experiments demonstrate that the proposed SAA can achieve a solution which has a 12% cost saving compared with the case that all commodities are replenished daily. The mechanism experiments reveal that hash table and elite list can significantly reduce the computation time whereas the tabu list can improve the stability of solution quality. Finally, this study shows that the computation time of the SAA is quadratic, but not exponentially, proportional to both the number of customers and the number of items per customer, which demonstrates the practicality of the proposed SAA in solving large-scale instances within reasonable time.