Dynamic supply network design: integrating inventory and transportation modelling

Supply network design involves making decisions about the number and location of physical distribution facilities and the transportation network required to support them. Supply chain design methodologies appearing in the academic literature can be broadly classified as: deterministic, stochastic or dynamic. Stochastic approaches employ probability density functions to model demand and inventory decisions. In practice this work is normally undertaken once the physical supply network has been decided. Dynamic supply chain design employs control theory to understand the effect of time delays and feedback paths on system behaviour. However, as both stochastic and dynamic approaches are normally applied after the physical network has been decided, then the potential of these methods is constrained. In this paper we will present a new method for integrating deterministic, stochastic and dynamic approaches to supply chain design, which we will illustrate by means of a simple example. Maister (1976) has shown that as a distribution network is consolidated the inventory required obeys the square root law. This knowledge was recently supplemented by that fact that the capacity of the distribution centres also obeys the same square root law. This conclusion was reached via control theory analysis of a divergent supply chain (Ratanachote and Disney, 2008). Here we extend this approach to consider the effect of transportation lead-times and costs on the distribution network design.