An e-commerce retailer is trading a successful haircare product imported from overseas suppliers. It takes 6 weeks for the item to reach the warehouse from suppliers. Due to various import documentation requirements, placing an order costs £45 per unit. Weekly demand for this item varies, with an average of 350 units and a standard deviation of 25 units. It is purchased from suppliers at a cost of £30 per unit, and the warehousing cost amounts to 15 percent of the item cost. Being an e-commerce retailer, the firm operates throughout the year.
a. What is the optimal order quantity for this item?
b. How many units of the item should be maintained as safety stock for 99 percent protection against stockouts during an order cycle?
c. If supply lead time can be reduced to 4 weeks, what is the reduction in the number of units maintained as safety stock for the same 99 percent stockout protection?
d. If through appropriate sales promotions, the demand variability is reduced so that the standard deviation of weekly demand is 15 units instead of 25, what is the percent reduction in the number of units maintained as safety stock for the same 99 percent stockout protection?