Distribution network dynamics with correlated demands
The distribution network designs for two-level supply chains have been analysed using stochastic analytical methods. The market demands faced by multiple retailers are correlated. The correlated demand is modelled as a first order Vector Auto-Regressive process, which is used to represent the progression of and relationships in sets of time series of demand. All participants are assumed to operate an Order-Up-To policy with a Minimum Mean Squared Error forecasting. Inventory and capacity costs have been considered. Control engineering methods have been exploited to obtain the closed form expressions of the variances of the inventory levels and the order rates. The ratios of costs between the decentralised and centralised systems have been used to evaluate the economic performance of the consolidated distribution network. The variance expressions are the key components for the cost ratios. Insights about the system can also be obtained from the analysis of the variance expressions. The impacts of demand patterns, lead-times and the number of decentralised locations on the consolidation decision have been investigated. The results show that the auto-correlation and cross-correlation of the market demands highly affect the consolidation decisions. The Square Root Law for Inventory and Bullwhip has been proved to hold with certain demand correlations. Consolidation scenarios that are always attractive under a specific demand pattern and a set of constraints about the lead-times have been presented. The structural transition of the demand into orders placed onto higher echelons has been investigated. The result shows that higher echelons may not need the point-of-sales data as it is already contained in the order they receive from the retailers. Finally, the model has been validated by its application to real world data and has shown to be a useful tool for practitioners to investigate the dynamic behaviour and economic performance of the distribution network design.
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