Synchronization, cross-docking, and decoupling in supply chain networks

At any distribution centre (DC), the decision of whether to synchronise inbound and outbound flows for cross-docking, or to decouple these flows by maintaining inventory, has a significant impact on supply chain performance. Key drivers of this decision, in turn, are the sizes of the discrete lots that comprise the flows. Thus, we formulate an original optimisation model that determines order lot-sizing decisions to minimise, for given constant arc flows, the sum of ordering cost and pipeline inventory cost on arcs and buffer inventory at DCs. The model employs an average throughput as a surrogate to estimate buffer inventory at facilities at which synchronisation is not economical and therefore serves to decouple inbound and outbound flows. Perfect lot-for-lot matching of shipments would impose very restrictive constraints on supply chain operations, but equality of average throughput indicates an innovative, relaxed mode of synchronisation. This mode is practicable for cross-docking by means of bulk-breaking or consolidation of shipments. A heuristic approach based on the Lagrangian relaxation and subgradient optimisation is developed for the non-linear mixed-general integer optimisation model, which is illustrated by numerical examples and tested using a benchmark data set.