An automotive warehouse stocks a variety of parts that are sold at neighborhood stores. One particular part, a popular brand of oil filter, is purchased by the warehouse for $1.50 each. It is estimated that the cost of order processing and receipt is $100 per order. The company uses an inventory carrying charge based on a 25 percent annual interest rate. The monthly demand for the filter follows a normal distribution with mean 300 and standard deviation 80. Order lead time is assumed to be five months. Assume that if a filter is demanded when the warehouse is out of stock, then the demand is back-ordered, and the cost assessed for each back- ordered demand is $12.80.
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- Dilberts Department Store is trying to determine how many Hanson T-shirts to order. Currently the shirts are sold for 21, but at later dates the shirts will be offered at a 10% discount, then a 20% discount, then a 40% discount, then a 50% discount, and finally a 60% discount. Demand at the full price of 21 is believed to be normally distributed with mean 1800 and standard deviation 360. Demand at various discounts is assumed to be a multiple of full-price demand. These multiples, for discounts of 10%, 20%, 40%, 50%, and 60% are, respectively, 0.4, 0.7, 1.1, 2, and 50. For example, if full-price demand is 2500, then at a 10% discount customers would be willing to buy 1000 T-shirts. The unit cost of purchasing T-shirts depends on the number of T-shirts ordered, as shown in the file P10_36.xlsx. Use simulation to determine how many T-shirts the company should order. Model the problem so that the company first orders some quantity of T-shirts, then discounts deeper and deeper, as necessary, to sell all of the shirts.Sometimes curvature in a scatterplot can be fit adequately (especially to the naked eye) by several trend lines. We discussed the exponential trend line, and the power trend line is discussed in the previous problem. Still another fairly simple trend line is the parabola, a polynomial of order 2 (also called a quadratic). For the demand-price data in the file P13_10.xlsx, fit all three of these types of trend lines to the data, and calculate the MAPE for each. Which provides the best fit? (Hint: Note that a polynomial of order 2 is still another of Excels Trend line options.)In Problem 12 of the previous section, suppose that the demand for cars is normally distributed with mean 100 and standard deviation 15. Use @RISK to determine the best order quantityin this case, the one with the largest mean profit. Using the statistics and/or graphs from @RISK, discuss whether this order quantity would be considered best by the car dealer. (The point is that a decision maker can use more than just mean profit in making a decision.)
- A golf specialty wholesaler operates 50 weeks per year. Management is trying to determine an inventory policy for its 1-irons, which have the following characteristics:Demand 1D2 = 2,000 units/yearDemand is normally distributedStandard deviation of weekly demand = 3 unitsOrdering cost = $40/orderAnnual holding cost 1H2 = $5/unitsDesired cycle@service level = 90 percentLead time 1L2 = 4 weeksa. If the company uses a periodic review system, what should P and T be? Round P to the nearest week.b. If the company uses a continuous review system, what should R be?Every four years, Blockbuster Publishers revises its textbooks. It has been three years since the best-selling book, The Joy of OR, has been revised. At present, 2,000 copies of the book are in stock, and Blockbuster must determine how many copies of the book should be printed for the next year. The sales department believes that sales during the next year are governed by the distribution in Table 8. Each copy of Joy sold during the next year brings the publisher $35 in revenues. Any copies left at the end of the next year cannot be sold at full price but can be sold for $5 to Bonds Ennoble and Gitano’s bookstores. The cost of a printing of the book is $50,000 plus $15 per book printed. How many copies of Joy should be printed? Would the answer change if 4,000 copies were currently in stock? Table 8: Copies Demanded Probability 5,000 .30 6,000 .20 7,000 .40 8,000 .10Firewire is a high-end manufacturer of surfboards. A surfboard is sourced at a cost of $80 and sold for $125 to surf shops in its home market (United States). One order is placed at the beginning of the summer season. Currently, Firewire disposes any unsold boards to their outlet store affiliates for $70. It costs $10 to hold a board in inventory for the entire season and ship it to outlet affiliates. Demand for this item is forecasted to be normally distributed with a mean of 4,000 units and a standard deviation of 1750 units. A) Please provide ideal service level and order quantity? Expected profits? Expected overstock to outlets?.... under your preferred policy. B) If Firewire chooses instead of outlets to ship to Australia surf shops, the salvage value would increase to $75 per unit (board) including all associated costs (including the aforementioned holding costs). Would this be a better option?….please show each result as in part A for this alternative scenario to justify your…
- Zack Pop has been a producing plant production manager for the last 10 years. One produce item, zucchini, is sold in cases, with daily sales averaging 400 cases. Daily sales are also assumed to be normally distributed. Furthermore, 85% of the time sales are between 350 and 450 cases. Each case is purchased for $10 wholesale and sells for $15 retail. All cases that are not sold must be discarded. 1) Estimate the standard deviation of the sales distribution. 2) Using the standard deviation found in part a, determine how many cases of zucchini Zach should stock.Magdeleine James is a sole trader, who sells souvenir T-shirts. She wishes to sell her T-shirts at the Tobago Jazz festival. Each t-shirt cost $165 to produce and sells for $225. After the festival, she reduces the sale price of the T-shirts by 70% in order to sell them off. Experience from previous years has shown that the demand for these T-shirts at the festival is 82, with a standard deviation of 21. How many T-shirts should Magdeleine take to sell at the festival?Suppose that the manager of a construction supply house determined from historical recordsthat demand for sand during lead time averages 50 tons. In addition, suppose the managerdetermined that demand during lead time could be described by a normal distribution thathas a mean of 50 tons and a standard deviation of 5 tons. Answer these questions, assumingthat the manager is willing to accept a stockout risk of no more than 3 percent:a. What value of z is appropriate?
- A home improvement store sells boxwood shrubs during the spring planting season. Each boxwood sells for $35 and it costs the store $13 to purchase and transport each boxwood from its supplier. At the end of the season, any remaining boxwoods are sold to a local landscaper at a deep discount for $5/boxwood. In the upcoming season, demand for boxwoods is forecast to be normally distributed with a mean of 1,000 and a standard deviation of 200 (you may assume demand is continuous). If the store can only order once at the beginning of the season, how many boxwoods should be stocked?Watch Entice sells high end watches. The annual demand for the company’s product is 57,000 units.Ordering costs are $500 per order and carrying costs are $90 per unit, including $40 in the opportunitycost of holding inventory. It currently takes 2 weeks to supply an order to the store. The following tableshows the probability distribution of various demand levels during the 2-week purchase-order lead time:Total Demand Probability of Demand800 0.05900 0.21,000 0.51,100 0.21,200 0.05 Watch Entice does not hold any safety stock. If the company runs of stock, it has to rush order thecomputers at an additional cost of $10 per computer. What is the stock out cost?A. $21,600B. $14,400C. $7,200D. $17,400Annual demand for number 2 pencils at the campus store is normallydistributed with mean 1,000 and standard deviation 250. The store purchases thepencils for 6 cents each and sells them for 20 cents each. There is a two-monthlead time from the initiation to the receipt of an order. The store accountantestimates that the cost in employee time for performing the necessary paperworkto initiate and receive an order is $20, and recommends a 22 percent annual interest rate for determining holding cost. The cost of a stock-out is the cost of lostprofit plus an additional 20 cents per pencil, which represents the cost of loss ofgoodwill.d. What is the safety stock for this item at the optimal solution?