Inventory theory and mode choice in freight transport: the case of the simultaneous use of two transport modes on one shipper-receiver relationship

Understanding mode choice is a central issue of freight transport microeconomics and modelling. In order to estimate quantitatively the probable reaction of the transport system to an economic change or to a transport policy, it is necessary to model the preferences of shippers (and/or receivers) as regards transport modes. Many efforts have been made to do so; they are generally based on a utility function taking as its arguments the characteristics of the transport alternatives, such as travel time, cost, reliability, etc. (the abstract mode approach). Although this proves efficient for econometric purposes, it does not make explicit why a given shipper would prefer a certain mode rather than another. It is now widely accepted that the preferences of shippers stem from their own logistic imperatives: they have to provide their own customers with a given level of service, and simultaneously keep their logistic costs low; this dictates the design of their supply chains, their transport organisation, and, in particular, the transport modes they opt for. However there are still little microeconomic models representing explicitly this relationship tying freight transport demand to logistics. A possible direction to develop such models is to import methods from inventory theory. Inventory theory models are generally intended to support shippers managing supply chains on a daily or strategic basis; as such, they are designed to hold under restrictive conditions. However, they can prove useful in freight transport economics. Recently, some models of inventory theory have been analysed from a microeconomic perspective to yield both theoretical and econometric insights on the behaviour of shippers. In this paper the authors explore another opportunity offered by inventory theory. Using an extension of the news vendor inventory model, the authors show that under certain circumstances, a shipper should use two transport modes simultaneously for a unique commodity flow directed to a unique receiver. This type of organisation is observed in reality, especially for goods which are expensive to carry, but for which delivery disruption is unacceptable and supply chain reactivity primordial. However it is, to the authors' knowledge, inconsistent with classic microeconomic models of mode choice. Technically, the model consists of an extension of the single commodity, single inventory periodic review model with backlogging and strictly positive travel time. The shipper has the possibility to send, at each time period, one shipment via a slow and inexpensive transport mode, and another shipment via a fast but expensive transport mode. At each time period, the shipper has to decide of the size of these two shipments, depending on the inventory at destination, the demand at destination, the pipeline inventory, and the cost parameters. This is a complicated problem of operations research. Instead of deriving an optimal policy, the authors analyse a simple heuristic: the shipper sends shipments of fixed size with the slow mode, and adapts to the demand at destination with the fast mode. The equations describing the dynamics of the supply chain are stated, the notion of "excess inventory at destination" which plays a pivotal role in the analysis of the model, is introduced. Then, the equilibrium behaviour of the supply chain is analysed by simulation. The properties of this supply chain under this policy are examined from a microeconomic perspective; in particular, the optimal mode share of the shipper is derived and interpreted microeconomically. Also, the willingness of the shipper to pay for a reduction of the travel times of each mode are derived, and compared. The model is applied to a case study, which illustrates in which case it is optimal for the shipper to use two modes simultaneously instead of one; in such a case, the elasticities of the mode share to the characteristics of each transport mode is computed. In the particular example presented in the paper, it is shown that this mode share is much more sensitive to parameters concerning the logistics of the shippers than to the cost and speed of the transport modes.