A firm orders apparels from a distant country and can order only once for the entire season. This ordering follows the assumption of the newsvendor model. The firm forecasts that their average demand is likely to be 8500 units. The firm believes that the possible variation in demand is normally distributed and the standard deviation is 650 units. If the apparel cost is $3, the selling price is $25 and the scrap value is zero, what is the ideal order quantity for this apparel?
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- 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 grocer purchases plums for $2.95 per pound and sells them for $4.62 per pound. At the end of the sales cycle, leftover plums are sold for a closeout price of $1.76 per pound. The grocer purchases 10,380 pounds of plums. Expected demand is normally distributed with a mean of 8,304 pounds and a standard deviation of 1,038. What is the grocer's expected profit?The home appliance department in a large department store is using a (Q, R) system to control the replenishment of a model of FM radio. The store sells an average of 12 radios each week. Weekly demand follows a normal distribution with variance 30. (Assume that there are 52 weeks in a year.) The store pays $20 for each radio, which it sells for $85. Fixed order cost is $30 per order. The accounting department recommends a 20% interest rate for the cost of capital. Storage costs are 3% and breakage 2% of the purchasing cost of each item. If a customer demands the radio when it is out of stock, the customer will generally go elsewhere. Loss-of-goodwill costs are estimated to be about $25 per radio. Order lead time is 13 weeks. (The penalty cost includes loss of profit and loss of goodwill.) Find the optimal values of (Q, R) based on the penalty cost. What are the values for Q and R if the stock-out cost is replaced with a 95% Type 1 service level?
- Annual demand for number 2 pencils at the campus store is normally distributed with mean 1,000 and standard deviation 250. The store purchases the pencils for 6 cents each and sells them for 20 cents each. There is a two-month lead time from the initiation to the receipt of an order. The store accountant estimates that the cost in employee time for performing the necessary paperwork to 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 lost profit plus an additional 20 cents per pencil, which represents the cost of loss of goodwill. Consider the problem of satisfying the demand for number 2 pencils faced by the campus store mentioned above.a. Re-solve the problem, substituting a Type 1 service level criterion of 95 percent for the stock-out cost.b. Re-solve the problem, substituting a Type 2 service level criterion of 95 percent for the stock-out cost. Assume that Q is given by the…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?Annual demand for number 2 pencils at the campus store is normallydistributed with mean 1,000 and standard deviation 250. The store purchases the pencils for 6 cents each and sells them for 20 cents each. There is a two-month lead time from the initiation to the receipt of an order. The store accountant estimates that the cost in employee time for performing the necessary paperwork to 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 lost profit plus an additional 20 cents per pencil, which represents the cost of loss of goodwill.a. Find the optimal value of the reorder point R assuming that the lot size used is the EOQ.b. Find the simultaneous optimal values of Q and R.c. Compare the average annual holding, setup, and stock-out costs of the policies determined in parts (a) and (b).d. What is the safety stock for this item at the optimal solution?
- Good Shoes Company manufactures ski boots for children each pair of which costs $40 to manufacture. Good Shoes sells the boots to a well-known sports goods retailer and the retailer sells each pair for $100. Any boots not sold (by the retailer) during the season are sold to a discount retailer for $20 a pair. Demand during the season is assumed to have a Normal distribution with a mean of 850 and a standard deviation of 350. What should the manufacturer charge the retailer per pair to maximize its expected profits? Assume that Good Shoes will consider a price from the following set: (60,65,70,75,80,85 90,95), i.e., The manufacturer's price will be either $60, or $65 or $70, or ......,,$95).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?13 Pam’s demand for hats is normally distributed with mean 500 and standard deviation 100. She sells her hats for $50 each and buys hats for $10 each, and anything she can't sell by the end of the year, the wholesaler will buy for $5 each. How many hats should she order for next year to maximize profit?
- 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 .103. Determine the optimum solution for Electro which uses 10000 gallons of resin per month in the manufacturing process. It costs about $100 to place an order. The storage cost is $3, the estimated backorder cost per gallon per month is $10. Assume that the demand follows a normal probability distribution, with an average of 100 gallons and a standard deviation of 4 gallons.The home appliance department of a large department store is using inventory models to controlthe replenishment of a particular model of Microwave ovens. The daily demand follows anormal distribution with a mean of 150 units and standard deviation of 16 units. The store pays$100 for each oven. Fixed costs of replenishment are $28. The accounting departmentrecommends a 20% annual holding cost rate. Assume that the average lead time is 5 days with astandard deviation of 1 day. Assume 365 days a year.Part A: What is the EOQ?Part B: What is the reorder point if the maximum chance of 5% of stock out (i.e. 95% servicelevel) is desired?Part C: What is the reorder point if a fill rate of 99% is required?Part D: Suppose management wants to simplify the process by setting the reorder point to“1000” units. Based on this policy, what is the implied chance of stock out?