Instructions: In this assignment you will explore some issues related to capacity analysis and the supply chain for The Great DVD.

1. You've gotten some complaints about the performance of your server. So, you need to think about capacity issues.

   
   

   1. Suppose you have one page on your site and only one user of your site. You can choose to have all of your graphic images at the top of the page or they can be uniformly distributed throughout the page (recall that each image is handled with an individual HTTP request). Will this have an impact on performance? Why or why not? (Be explicit.)

      
      

   2. Now suppose that you have more than one user (but still one page). Will the expected service time depend on the design of the page? Why or why not? (Be explicit.)

      
      

   
   

2. People renting movies often also want to buy batteries for their portable DVD players. Fortunately, all DVD players use AA batteries and there is a battery supplier moments away from the airport. Let:

   
   

   

   Assume that the demand rate is known and constant, that there are no back orders, that there are no lead times (i.e., you receive the order immediately after you place it), and that you have no capacity constraints. In this case, you will let your inventory level fall to zero before you place an order. Hence, your inventory at a particular time (after time 0) is given by:

   

   
   

   1. Let the average inventory over the cycle be given by:

      
      

      

      Show that:

      

      [HINT: You (should) know that . So, just substitute and integrate.]

      
      

   2. Explain (in words) why:

      
      

   3. Show (by minimizing G with respect to Q) that the optimal order size is given by:

      
      

   4. Explain how electronic commerce technology might effect the optimal order size. (Specifically, differentiate the expression for the optimal order size with respect to each of the paramters that e-commerce technology might have an impact on.)

You may use any books or notes at your disposal, but you should work entirely on your own.