Question 3 (20 Points)

Weekly demand for Epson printers at Liverpool, a Mexican department store, is normally distributed with a mean of 2,000 and a standard deviation of 900. Each printer costs $100, and averages about 5 kg in weight. Liverpool has traditionally purchased lots of 2,000 printers. The Epsons distribution center ships each Liverpools order within two days of receiving it (The lead time must consider the process time). The store uses annual holding cost of 25%. There are 7 days in a week and 52 weeks in a year.

Now Liverpool receives a proposal from a logistics company, who provides trucking service that charges $40 per 100 kg if the quantity shipped is at least 10,000 kg. The average shipping time is 5 days.

1. Liverpool carries a safety inventory equal to 70 percent of the average demand for printers during the delivery lead time. Calculate the annual total transportation and inventory cost (Note: the in-transits inventory also should be considered.).
2. If the shipping time is uncertain and the standard deviation of the lead time is 3 days. Liverpool carries the safety inventory targeting a cycle service level of 0.91. Calculate the annual total transportation and inventory cost (Note: the in-transits inventory also should be considered.).
3. Following b), evaluate average inventory at Liverpool and average time spent by the printer at Liverpool.