A cyclic policy for the loading of multiple products on a vehicle with different compartment sizes

In this paper, we address a multi-product loading problem in which a vehicle (a truck or a ship) is used to transfer multiple products. The product demands are different but stationary over time. The vehicle consists of compartments of different sizes and each compartment can contain only one product type during each shipment. No shortages are permitted, and we assume that the inventory holding cost is significantly lower than the delivery cost. The objective is to minimize the setup rate, that is, the number of deliveries per time unit. A cyclic policy is shown to be optimal, and a heuristic algorithm is developed to determine the cycle length as well as the assignments of products to the compartments during each of the requisite number of shipments made during that cycle. A comparison of the solutions obtained by the proposed algorithm with the optimal solutions (or a bound) indicate that the algorithm provides solutions with optimal setup rates in most of the problem instances considered and, when not optimal, the setup rates of these solutions are close to optimal values.