A dual sourcing inventory model for modal split transport: Structural properties and optimal solution

Shifting freight volumes from road to rail transport increases the economic performances of freight logistics. However, compared to road transport, rail transport generally lacks the flexibility in delivery quantity and frequency, and exhibits economies of scale in its shipment volume. This often leads to high inventory levels in the destination after deliveries. We generalize the tailored base-surge dual sourcing inventory model by introducing a fixed cost in rail transport, adding an extra decision in its delivery frequency, and relaxing the assumption of the base stock control of road transport, to support firms’ modal split transport optimization. The objective is to optimize the controls of the two transport modes and the corresponding inventory management at the destination, which minimize the combined average transport and inventory costs per period in the steady state. Using stochastic dynamic programming, we find that when the delivery quantity and frequency of rail transport is fixed, the optimal shipment volume via the road transport indeed follows a base stock control. This allows to solve the relevant Bellman equation via an efficient policy iteration approach. We also find that the total cost is convex in the delivery quantity of rail transport, and a bi-section search can be applied. Finally, we analyze the sensitivity and robustness of our model using values suggested by a consumer goods firm.