A supply chain is made up of three levels: a retailer, a manufacturer and a supplier. The members of this supply chain have recently realized the significant negative impact of the bullwhip effect on their supply chain. So$,$ they would like to quantify the bullwhip effect by comparing the variance of the customer orders to the retailer with the variance of the orders placed by the manufacturer to the supplier. Specifically, they select a typical product. The manufacturer$$s lead time to supply this product to the retailer is $6$ weeks, while the supplier$$s lead time to supply the same product to the manufacturer is $8$ weeks. All parties use a $12-$period moving average method to forecast the demand. The demand information is decentralized $($i$.$e$.,$ the retailer does not provide any demand information to the other supply chain members, thus the manufacturer and the supplier must estimate the mean demand based on the orders that they receive$).$

a$.$ Quantify the bullwhip effect $($i$.$e$.,$ how many times is the variance of demand placed by the manufacturer to the supplier larger than the variance of the demand placed by customers to the retailer?$)$

b$.$ To better cope with the bullwhip effect, the supply chain members decide to fully share demand information with each other. Quantify the bullwhip effect under this scenario.