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Apr 3, 2024

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University of Pennsylvania The Wharton School Department of Operations and Information Management OIDD 615: Spring 2023 Assignment 2 - 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. A company pays $25 per square foot of retail space. Their annual COGS is $120M, average inventory is $18M and they occupy 0.6M square feet of space. What is their annual holding cost percentage (%) due to retail space? 83.3 Average inventory = $18M Cost of retail space = 0.6*25 $M = $15M Holding cost percentage (18%) = 15/18 = 83.3%
Q2-5. Cabelas is a large retailer of outdoor recreational merchandise. Their store in Hamburg PA reviews inventory daily and has a lead time of 4 days. Q2. On average they sell one unit every 15 days of the Swarovski ATS-80 20-60x80mm scope ($2,995). What mean would best describe the Poisson distribution to represent daily demand (scopes)? Q3. Daily demand for the Celestron 10x32 binoculars ($159) is on average 0.5 units. If they want to ensure a 0.991 in-stock probability, what base stock level should they choose (binoculars)? Q4. Demand for the Yeti Tundra 45 Cooler ($299) is strong, with 1.75 units per days. If they operate with a base stock level of 14, on-average how many units do they have on-hand (coolers)? 0.0667 Daily demand = 1/15 = 0.0667 units/day 7 Lead time, l = 4 days Mean demand = 0.5 units/day Mean demand over l+1 period = 0.5*(4+1) = 2.5 In-stock probability = 0.991 Base stock level, S = 7 (from the Poisson distribution table for µ = 2.5) 5.32 Lead time, l = 4 days Mean demand = 1.75 units/day Mean demand over l+1 period = 1.75*(4+1) = 8.75 Expected end of period inventory = 5.32 (from Poisson distribution inventory table for µ = 8.75)
Q5. The Old Town Sportsman PDL 106 Pedal Sit-On-Top Kayak ($1999.99) demand is 0.04 units per day. If they target a 98% in-stock probability, what is their average on-order inventory (kayaks)? Q6-8. A considerable amount of P&G’s Tide laundry detergent moves through a Walmart distribution center (DC): 150 pallets per day with a standard deviation of 65. The DC orders from P&G daily and orders arrive one day later. Q6. If they want to minimize inventory while keeping their stockout probability no greater than 0.5%, then what should be their order upto level (pallets)? Q7. If they operate with a 450 base stock level, then what would be their average order quantity (pallets)? 0.16 On-order Inventory = L * D = 4 * 0.04 = 0.16. Note, the on-order inventory does not depend on the in-stock probability. 537 Lead time = 1 day Single period: µ = 150 and σ = 65 Demand over l+1 days: µ = 150*(1+1) = 300 and σ = 65*sqrt(1+1) = 91.9 Stock-out probability = 0.5% In-stock probability = 1-0.5% = 99.5% z =2.58 Q = 300 + 2.58*91.9 = 537 150 Order quantity = previous period’s demand = 150. When the order upto model is implemented the average order quantity is always equal to mean demand over one period because the previous period’s demand is what is ordered.
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