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Kick Flip Inc. makes skateboard decks for specialty skateboard stores. The production process of the skateboard decks is done in batches and consists of the 3 steps shown in the figure below. The size of each batch is 20 decks and demand is one batch per hour. In the first stage the raw material is sanded. This step takes 3 minutes per deck. After this step, the decks are painted using a Lithography machine. This step takes 2 minutes of production time per deck. The decks are then loaded onto a pallet and dried quickly using an ultraviolet lamp. The lamp can dry up to 20 decks at one time. Drying takes 30 minutes. Each state (i.e., sanding, painting, and drying) has one operator. What is the capacity of the “Painting” stage in batches?

Consider the hospital example above. What will be the resulting change in the reorder point with the decrease in service level?

Consider the outdoor grill example above.  Please briefly explain your answer.

Consider the small retailer example above. How many kWs should they pre-purchase to minimize the total under- and over-estimation costs? (use Z value of -0.67) 

Le Meridien in San Francisco has 160 rooms. The hotel has an ample low fare demand at the room rate of $200 per night, but the demand from the high fare class which pays $450 per night on average, is uncertain. The high fare demand is normally distributed with mean 60 and standard deviation 42. (The Normal distribution table is attached below.)  How many rooms should Le Meridien protect for high fare customers to maximize expected revenue?

One warehouse supplies 50 dealers with parts used by the dealers to repair their customers’ heavy equipment. Dealers currently place orders about once a week, because the ordering process is somewhat cumbersome – it is a paper process that must be filled out manually and faxed to the warehouse. The firm will implement a new system that will allow dealers to submit orders electronically. Because this process should be less cumbersome, it is expected that the dealers will submit orders more frequently, maybe some of them even daily. The new system is not expected to change customer demands for parts (i.e., the dealers’ demand processes will be unaffected). What change is this likely to have on the characteristics of the warehouse’s total daily demand (i.e., the total of the dealers’ orders on any given day)?

If the standard deviation of demand increases, what would happen to the optimal order quantity?

A manufacturer of exquisite clocks faces uncertain demands for two of its high-end models. Model “A” faces an uncertain daily demand that is Normally distributed with mean 80 and standard deviation 30. Model “B” also faces an uncertain daily demand that is Normally distributed with mean 120 and standard deviation 60. The most expensive components in these clocks are their respective main gears MA and MB which are outsourced. The lead times for shipment of these gears to the manufacturer are 8 days and 10 days, respectively. How much safety stock of MA would be needed to meet the service level of 90% for model A? (The Normal distribution table is attached below.) 

Consider the Sunny Airline example above. What is the cost of under-estimation?

Weekly demand for bottles of blood type O- at a hospital is distributed with mean 5 and standard deviation 2. The lead time to obtain bottles of this rare blood type is 3 weeks. The hospital, which employs a continuous review system, is weighing whether to decrease the service level for blood type O-, from 99.7% to 97.5%. What will be the direction of change in the optimal order quantity with the decrease in service level?