The Newsvendor model helps us to decide what is the optimal (profit-maximizing) order quantity for an order decision taken before a given selling season. If there is not enough stock during the selling season, then we would lose a sale (Cu = p - c). After the selling season the remaining inventory from this first order would have to be sold at a much lower price - salvaged (Co = c - v).

1. Newsvendor Model Lesson The lesson of the newsvendor model was "don't order the forecast!" Your profit-maximizing order quantity should take into account the overage (Co) and underage (Cu) costs. The critical ratio = Cu/(Cu + Co) gives you the in-stock probability.

1a. If Cu > Co, then your critical ratio will be greater than 0.5 should you order more or less than the forecasted demand? Explain.

1b. If Cu < Co, then your critical ratio will be less than 0.5. should you order more or less than the forecasted demand? Explain.

2. Books End, a bookstore on James St. in Syracuse, NY, is trying to decide on how many copies of the book, Fun with Operations Management to purchase at the start of the upcoming selling season (fall semester at Syracuse University). The book retails at $28.00. The publisher sells the book to Books End at $20.00. Books End will dispose of all of the unsold copies of the book at 50% off the retail price, at the end of the season. Books End estimates that demand for this book during the season is Normal with a mean of 1000 and a standard deviation of 250.

2a. What is the Underage (Cu) and Overage (Co) cost for Books End in this situation? Cu = p - c Co = c - v Select one: a) Cu = $8, Co = $20 b) Cu = $8, Co = $6 c) Cu = $8, Co = $10 d) Cu = $28, Co = $20

2b. Suppose Books End wants to maximize his expected profits from the sale of this book. How many copies should he order from the publisher? 2/2 Hint: here you need to calculate the critical ratio using the overage and underage costs. Critical Ratio = Cu/(Cu + Co. In this case the Critical Ratio = 0.5714. Then look up the corresponding z value and convert to Q *= + z. (z = 0.18)

2c. Suppose Books End orders 1100 copies. What is their expected out-of-stock probability? Hint: first calculate the z-statistic for 1100 copies: z = (1100 - 1000)/250 = 0.40 Then look up the F(Q) value in the Standard Normal Table which corresponds to z = 0.4 Don't forget: F(Q) = Prob(Demand <= Q) Probability of out-of-stock Prob(Demand > Q) = 1 - F(Q) Session 8: Inventory Management - ROL and Safety Stock

3. Mozer's Garden Solutions has a chain of retail stores in the mid-west. Mozer's orders hedge trimmers from a wholesaler. Every year Mozer's requires 9,000 hedge trimmers. The trimmers cost $250 per trimmer from their wholesaler. The estimated cost of ordering at the wholesaler and paying shipping fees is $200 per order: K = $200 The holding cost per hedge trimmer is estimated to be 10% of the cost of the trimmer h = 0.1 $250 = $25 The EOQ for the hedge trimmers is 379 trimmers.

3a. Describe an appropriate ordering policy if the lead time (LT) for the hedge trimmers is constant at 3 months. Specify the amount that should be ordered at the ROL.

3b. If Mozer's guarantees a 95% in-stock rate, what should their Safety Stock of hedge trimmers be? What is the total ROL = demand during lead time + Safety Stock? The standard deviation of the monthly demand is 300. For a 95% in-stock rate, the z value is 1.96. Hint: Safety Stock = LT Reorder Level: demand during lead time + Safety Stock = LT R + z LT