The Home and Garden (HG) chain of superstores imports decorative planters from Italy. Weekly demand for planters averages 1,500 with a standard deviation of 800. Each planter costs $ 10. HG incurs a holding cost of 25% per year to carry inventory. HG has an opportunity to set up a superstore in the Phoenix region. Each order shipped from Italy incurs a fixed transportation and delivery cost of $ 10,000. Consider 52 weeks in the year.
a. Determine the optimal order quantity of planters for HG.
b. If the delivery lead time from Italy is 4 weeks and HG wants to provide its customers a cycle service level of 90%, how much safety stock should it carry?
c. Fastship is a new shipping company that promises to reduce the delivery lead time for planters from 4 weeks to 1 week using a faster ship and expedited customs clearance. Using Fastship will add $ 0.2 to the cost of each planter. Should HG go with Fastship? Why or why not? Quantify the impact of the change.