Harvey’s Specialty Shop is a popular spot that specializes in international gourmet foods. One of the items that Harvey sells is a popular mustard that he purchases from an English company. The mustard costs $10 a jar and requires a 2-month lead time for replenishment of stock. The replenishment time is almost constant. Harvey uses a 20% annual interest rate to compute holding costs. Bookkeeping expenses for placing an order amount to about $50. During the 2-month supply time, Harvey estimates that he sells an average of 100 jars but there is substantial variation. He estimates the standard deviation of demand for each 2-month period is 25. Assume that demand is described by a normal distribution. (3 + 3 + 4 + 8 + 12 + 20 = 50 points)

What is the optimal order quantity?

What will be the average time between transactions?

How much safety stock should be maintained for 98% cycle service level?

What should be the reorder point for 98% fill rate?

Now suppose that the English company is ready to send the mustard by a faster ship, which will reduce the replenishment lead time to 1-month and the standard deviation of demand during that period to 17.7, but increase the cost to $15 per jar. What will be the new reorder point for 98% fill rate and 98% cycle service level?

What will be the optimal total inventory cost (Ordering + Holding + Purchase) before and after the decrease of lead time (and resultant price increase)? What managerial insights can you get from this?