A1 - solutions

University of Pennsylvania The Wharton School Department of Operations and Information Management OIDD 615: Spring 2023 Assignment 1 - SOLUTIONS Professor Cachon Instructions: • You may collaborate only with another student currently taking OIDD615. • You may use materials only from this quarter’s version of OIDD615. • You may ask the instructor and TA questions. Please post to the Canvas discussion board for this assignment. • You may use a computer to assist you in your calculations. Excel files that assist with Newsvendor and Order-up-to model calculations are provided on Canvas and may be used with this assignment. • Each question is worth 1 point, unless indicated otherwise. • No partial credit is given on 1-point questions. • Submit your assignment solutions via Canvas. Q1. On average a driver works for Lyft for 8.5 months. What is the annual turnover of drivers at Lyft (as a percentage)? 141 Average months as a driver = 8.5 months Annual turnover = (12 months/yr) / (8.5 months) = 141%/yr

Bloombox is a local nursery that delivers directly to your home. The following table provide data on five of the trees that have for sale this season, including the selling price (Price), the cost Bloombox pays its supplier for each unit (Cost), the discount price used to clear inventory at the end of the season (Discount) and the parameters of the normal distribution used for their demand forecast (Mean, Standard deviation). Q2. What is coefficient of variation of the Flowering Dogwood? Q3. If they are to choose an order quantity to maximize their expected profit, what would be the underage cost for the Crape Myrtle? Q4. What order quantity for the White Fringe Tree should they choose to achieve a 95% in- stock probability? Plant Price Cost Discount Mean Standard deviation Flowering dogwood 30 20 10 450 175 Crape Myrtle 'Pink Velour' 40 25 20 400 100 White Fringe Tree 60 30 20 320 120 Serviceberry 80 50 40 240 80 River birch 90 45 35 160 50 American Witch Hazel 120 60 45 80 40 Magnolia Ann 140 60 35 60 40 Weeping Cherry 150 90 70 50 30 0.389 µ = 450 σ = 175 Coefficient of variation = 175 / 450 = 0.389 15 Price = 40 Cost = 25 Underage cost, Cu = 40 - 25 = 15 518 P (D <= Q) = 0.95 (in-stock-probability) z = 1.65 (from the normal table) µ = 320 σ = 120 Q = 320 + 1.65*120 = 518

Q8. If they order 500 of the Flowering Dogwood, what is the probability (number between 0 and 1) that 125 or more customers will not be able to make a purchase? Q9-10. Fisker Automotive wants to place orders for semiconductor chips. In the upcoming quarter they forecast their needs to be normally distributed with a mean of 25,000 and standard deviation 10,000. Fisker’s primary supplier offers options with a purchase cost of $50 per option and an exercise price of $90. To explain, Fisker pays $50 for each option they purchase upfront, meaning that they must purchase options before they observe demand. Shortly before the start of the quarter they observe demand and can choose to exercise any portion of their options for $90 per unit, up to the number of options they purchased. If demand exceeds the number of options they purchased, they obtain on the spot market the extra chips needed for a cost of $200 each. As an example, say they purchase 20,000 options. Hence, they pay 20K x $50 = $1000K up front. If demand ends up being 18,000, then they exercise 18,000 of their options at $90 per option (and 2,000 of their options are not exercises). If demand ends up being 23,000, then they exercise all 20,000 of the options they purchased (at the $90 exercise price), and they purchase 3,000 chips on the spot market for a cost of $200 each. Q9. If they seek to evaluate the number of options to purchase that minimizes their expected purchasing costs, what would be the appropriate overage cost? Q10. If they seek to evaluate the number of options to purchase that minimizes their expected purchasing costs, what would be the appropriate underage cost? 0.1587 We need to find the probability that demand is greater than 625 µ = 450 σ = 175 z = ((500+125) – 450)/175 = 1 P(D<625) = 0.8413 (from the normal table) P(D>=625) = 1 – 0.8413 = 0.1587 50 Overage cost, Co = 50 (exercise price) 60 Option price = 50 Exercise price = 90 Spot price = 200 Underage cost, Cu = 200 – 90 – 50 = 60