Nonlinear goal programming models quantifying the bullwhip effect in supply chain based on ARIMA parameters

In less than half a century, the supply chain management (SCM) imposed itself as a strategic expertise. Today, it lands a new era, more complex, and must be the synonymous of competitive advantage. The supply chain has essentially served as a link between customers and products, producers and suppliers. The generation of the new supply chain (SC) should be evolutionary, and should be adjusted quickly to the rise or the decrease of the various customers' demands. Several problems of the supply chain are superimposed such as the amplification of the demand, also called the bullwhip effect (BWE). This latter is a distortion in the market demand when this demand propagates from enterprise to enterprise. Finally, at the end of the chain, the supplier of raw materials receives completely uncertain commands. Our research aims to reduce, or even eliminate, the bullwhip effect in two respects – namely increase of the stock level and reduction of the service given back to customers. The solution that we propose to the bullwhip rests on, firstly, the use of the preference functions based on a statistical chronological series analysis (Box and Jenkins method) in order to construct the different models such as demand, stock level, and the order quantity. Secondly, the integration of the decision maker preference in the demand forecast and inventory management processes.