Question 1: Consider two departments in a company which have very similar photocopying needs and are located in adjacent office space. Both departments are getting ready to replace the aging photocopiers in their separate copying rooms. The options available to them are: Option 1: Buy two new model X copiers and operate them in separate, independent copying rooms each dedicated to one department. Option 2: Buy two model X copiers and operate them in a joint copying room, which serves both departments. Option 3: Buy one new model Y copier with the exact same features as the model X, but with twice the speed and operate it in a joint copying room. During discussions between the two departments, some concerns have been expressed about the responsiveness of a busy copying room serving twice as many customers. You are asked to apply waiting time analysis to provide additional input into the purchasing decision. In your analysis, assume that each department generates copying jobs at a rate of 9 per hour, and that the time to complete a job averages 6 minutes on the model X and 3 minutes on the model Y. You may assume that the coefficient of variation of the time between arrivals and the service times are both 1, i.e., CVa = 1 and CVp = 1. (a) Evaluate the average flow time of jobs under these three options? (Flow time includes waiting time as well as processing time, i.e., flow time = waiting time + processing time) (b) What other factors you would consider in determining between these three options.

Question 2: Brookline Bakery is a commercial baker that sells baked goods such as cookies and muffins to a number of coffee houses and snack. Flour is an ingredient to many of their products so they use it at a fairly constant rate. They currently follow a policy of ordering 16,000 pounds every four weeks. (That is equivalent to 20 days since Chicagoland Sweets operates 5 days per week and roughly 250 days per year.) Their supplier sells flour in 50-pound bags at a price of $20 per bag. Brooklines management estimates that it cost $64 every time that they place an order for flour. Their cost of inventory is 25% per year. a) What are Brookline annual inventory related costs (both holding and ordering) under their current policy? What are their inventory costs per unit sold (i.e., total inventory cost divided by the demand rate)? Can you suggest a better policy? Brookline has signed on a number of new accounts. Management estimates that they will need twice as much flour per week. The purchasing manager likes the simplicity of ordering once every four weeks and has suggested sticking to that schedule and just ordering a larger quantity each time. The head chef would prefer to order more frequently. She has suggested keeping the order quantity constant at 16,000 pounds and ordering once every two weeks. b) What are annual total inventory costs and inventory costs per unit sold under the purchasing managers plan? Under the head chefs? c) What is the optimal order quantity? What are the resulting annual total inventory costs and inventory costs per unit sold?