23 of Session 14

Problem I-3. Please make an example that is similar to a problem on page 23 of Session 14. You should consider two types of demand distributions: 1) a discrete distribution and 2) a normal distribution. Answer the following questions. Note that you are allowed to make a few assumptions to simplify the calculation. (a) Find the unit overage cost and the unit underage cost. (b) Find the optimal order quantity. (c) Find the expected profit (or cost) with the optimal order quantity. Zara t-shirt: Optimal order quantity Demand (X) Probability F(X) Purchase cost: $4 / unit Selling price: $12/ unit Salvage value: $2 / unit 200 0.15 0.15 250 0.25 0.40 Cu and Co Cu = $12 - $4 = $8 per unit 300 0.25 0.65 Co = $4 - $2 = $2 per unit Critical Ratio: Cu/(Cu+Co) 350 0.25 0.90 = 8/(8+2) = 0.8 400 0.10 1.00 Round-up rule: if the critical ratio falls between two values, take the larger one of the two. Expected profit-maximizing order quantity: Q* = 350