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• Charles Wetherbee

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Le Club Wine Optimization Question 1 The underage cost-- the cost of having one bottle too few in inventory-- is an opportunity cost equal to the potential profit gained by that unit. A bottle of wine retailing for 10 Euro has a procurement cost of half its retail price (5 Euro) plus a flat 1.50 Euro transportation cost.The profit on a 10 Euro bottle is 10 - (5 + 1.25) = 3.75 Euro. The underage cost is therefore 3.75 Euro. The overage cost-- the cost of having one bottle too many in inventory-- is the cost associated with storing the item, the cost of capital sunk in the bottle that could be invested or paid to creditors, and the decreased revenue if the bottle is eventually sold at a discount. For Le Club, this cost varies between red and white wines because of the increased perishability of whites. If overbought, a white wine retailing for 10 Euro per bottle sells at a 40% discount, or 4 Euro below retail. The procurement cost is 50% of retail (5 Euro) and the cost of capital is 15% per annum, or 1.25% per month that capital is tied up in unsold inventory. The monthly opportunity cost of capital is .0125 x 5 = .0625 Euro per month. Add the warehousing cost of .10 Euro per month and the total inventory cost is .1625 Euro per month. The transportation cost remains a constant 1.25 Euro. For the average bottle of overbought white, sold 8 months after procurement, the profit is (5 + 1.25 + 8 x .1625) - (10 - 4) = 1.55, for an overage cost of 1.55 Euro. An overbought red ha the same per-month opportunity cost of capital, per-month warehousing cost, and transportation cost. Red wine is discounted 30%, or 3 Euros below retail. Overbought reds are also stored longer than whites before sale. For the average bottle of overbought red, sold 15 months after procurement, the profit is (5 + 1.25 + 15 x .1625) - (10 - 3) = 1.6875, for an overage cost of 1.6875 Euro. Question 2 Using the critical ratio F(Q) = C / (C + C ) , where F(Q) equals the probability that the actual demand is less than the forecasted demand, C is the unit underage cost, and C is the unit overage cost, we find a critical ratio of 3 / (3 + 1) = .75. Using the empirical distribution table, we find the A/F ratio of 1.08 associated with the 75th percentile. The optimal order Q equals forecasted demand x A/F ratio, or 2,000 x 1.08 = 2,160 units. Applying the same method to the resulting underage and overage costs from question one, we find: For white wine, F(Q) = 3.75 / (1.55 + 3.75) = .70755. Using the empirical distribution table and rounding up to .725, we find an A/F ratio of 1.05 associated with the 72.5th percentile. The optimal order Q equals forecasted demand x A/F ratio, or 2,000 x 1.05 = 2,100 units of white. For red wine, F(Q) = 3.75 / (1.6875 + 3.75) = .68966. Using the empirical distribution table and rounding up to .70, we find an A/F ratio of 1.04 associated with the 70th percentile. The optimal order Q equals forecasted demand x A/F ratio, or 2,000 x 1.04 = 2,080 units of red. u

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Question 3 Please refer to the column titled “Optimal Order Q” in sheet Figure 2 of attached Excel file. Here are the steps we took to determine the optimal order quantity for each wine: 1. In Figure 1 (containing the prior year’s wines, forecasted, and actual demand), calculate the A/F ratio for each wine by dividing Demand by Forecast (Column G / Column F). 2. Find the mean A/F ratio for the dataset (AVG Column H).

3. Find the standard deviation of the A/F ratio for the dataset (STDDEV Column H). 4. Move to Figure 2 (containing the current year’s wines and forecasted demand). Find the clearance price by applying a 30% discount to reds and a 40% discount to whites. For the purposes of this exercise, we classify Rosés as whites. (IF(Column E="Rouge", 0.7*FColumn F, ELSE 0.6*COLUMN F)) 5. Calculate the procurement cost, 50% of retail. ( .5*Column F) 6. Calculate average months before clearance, 15 for reds and 8 for whites (IF(Column E="Rouge", 15, ELSE 8)) 7. Calculate per-month cost, which is the sum of opportunity cost of capital (1.25% of retail price) and warehousing cost (.1 Euro) each month. (Column H*0.0125+0.1) 8. Calculate total holding cost, which is average number of months times per-month costs. (Column I * Column J). 9. Transit cost is 1.25 Euro for all bottles. (Column L) 10. Underage cost is the lost profit the company missed out on by underestimating demand. It equals the retail price minus procurement and transit costs (Column F - Column H - Column L). 11. Overage cost is cost the company incurs by overestimating demand. It equals the sum of procurement, transit, and total holding costs, minus clearance price. (Column H + Column K + Column L - Column G). 12. Calculate the critical ratio, overage cost divided by the sum of overage and underage costs (Column M / (Column M + Column N). 13. Calculate the Expected Actual Demand by multiplying the prior year’s observed mean by the current forecast. (F33 * Column P) 14. Calculate the SD of Expected Actual Demand by multiplying the prior year’s observed standard deviation by the current forecast. (F34 * Column P) 15. Calculate the Optimal Order Q using the inverse normal distribution function, with mu = Expected Actual Demand, sigma = SD of Expected Actual Demand, and P(z < Z) = the critical ratio (NORM.INV(Column O, Column Q, Column R)). We assume the A/F ratios for the prior year approximate a normal distribution because the size of the dataset is at least 30 types of wine (n=30 being the minimum sample size necessary to assume the population mean equals the sample mean.) For the cartons of wine, we cannot calculate the optimal order quantity because the overage and underage cost is a function of the types of wine in the carton. To include the wines sold in cartons into the forecast, we would add each bottle into the individual forecast for its type. For example, if the Carton Panache contained 6 bottles of Faugeres and 3200 cartons were forecast, we would increase the forecast for individual bottles of Faugeres by 6*3200, raising it from 12,000 to 31,200 individual bottles. This mitigates the challenge of calculating the Overage and underage costs for entire cartons.