P&G, the maker of Puffs tissues, traditionally sells these tissues for $9.40 per case, where a case contains eight boxes. A retailer's average weekly demand is 25 cases of a particular Puffs SKU (color, scent, etc.). P&G has decided to change its pricing strategy by offering two different plans. With one plan, the retailer can purchase that SKU for the everyday-low-wholesale price of $9.25 per case. With the other plan, P&G charges the regular price of $9.40 per case throughout most of the year, but purchases made for a single delivery at the start of each quarter are given a 5 percent discount. The retailer receives weekly shipments with a one-week lead time between ordering and delivery. Sup- pose with either plan the retailer manages inventory so that at the end of each week there is on average a one-week supply of inventory. Holding costs are incurred at the rate of 0.4 percent of the value of inventory at the end of each week. Assume 52 weeks per year.
a. Suppose the retailer chose the first plan ($9.25 per case throughout the year). What is the retailer's expected annual purchasing and inventory holding cost?
b. Suppose the retailer chooses the second plan and only buys at the discount price ($9.40 is the regular price and a 5 percent discount for delivery at the start of each quarter). What is the retailer's expected annual purchasing and inventory holding cost?
c. Consider the first plan and propose a new everyday-low wholesale price. Call this the third plan. Design your plan so that both P&G and the retailer prefer it relative to the second plan.