he book Designing and Managing the Supply Chain. The above listed equations can be found on pages 86-87 of the same book.The following is an example of how equation there is used:Assume that the average demand for belts is 90 units (this would be calculated using equation one), and that the lead-time is one period. In other words, the order is placed and received all in the same period. It takes one period to receive the order. This means that the average demand during the lead-time period is 1*90 = 90. This is the first part of equation three. Next assume that the standard deviation associated with the 90 unit average is 12 units (this would be calculated using equation two), and that the small franchise wants to satisfy 95% of all demand. To ensure this service level, the small franchise must order an additional 12*1.65*(1^.5) = 19.8 (the z-score of 1.65 was taken form Appendix A of Operations Management for MBAs ). This is the second part of equation three.The small franchise must therefore order 90+19.8 = 109.8 units.Because the small franchise doesnt know the exactly how many belts it will need, it must attempt to predict the demand ahead of time so that they can place the order and receive the belts by the time they are actually needed. Now that we have a firm grasp on how demand is estimated by the franchise, lets look at how this impacts the Orem Studio. The first step in doing so is to quantify the variance of the order placed by Orem, Qt, relative to the variance of customer demand, Dt, for any given period, t. In other words, we are looking for the variance of orders placed by the Orem Studio to the belt manufacturer relative to the variance of the demand faced by the franchise (Chen, p. 437). It can then be shown that the variance in Q relative to the variance in D is: (4)The mathematical proof of this expression can be found on page 438 of the article entitled Quantifying the Bullwhip Effect in a Simple Supply C...
