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Health Tech (HT), a Hong Kong-based company, sells a small medical device in Europe. The devices are assembled in China and shipped to a central warehouse in Europe. The weekly demand follows the normal distribution with mean of 4600 and standard deviation of 1200. HT has two options to replenish its stocks in Europe. Option 1 ships the product by air with one week shipping lead time and $30 per unit shipping cost. With this option, HT will replenish its stock in Europe once every 3 weeks. Option 2 ships the product by ocean which takes 4 weeks of transportation time. Due to economies of scale in transportation, HT decides to send the replenishment once every 8 weeks and it pays a fixed charge of $98,000 for every shipment regardless of the quantity shipped. Assume that each device costs $400 and the per unit annual inventory carrying cost is 30% of the device's value. HT would like to maintain a 98% cycle service level. Also, assume 52 weeks in a year.
(a) What would be the safety inventory level in Europe's central warehouse for each of the two options?
(b) Based on annual average transportation and average inventory costs, which option would you recommend to HT?
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