a) What is the ROP to satisfy a %90 probability of not stocking out? b) What is the safety stock? c) What is the probability of stocking out if the manager has decided not to keep any safety s What is the Z value, and what is the probability?
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- Problem 20-10 (Algo) You are a newsvendor selling San Pedro Times every morning. Before you get to work, you go to the printer and buy the day's paper for $0.30 a copy. You sell a copy of San Pedro Times for $1.10. Daily demand is distributed normally with mean = 265 and standard deviation = 53. At the end of each morning, any leftover copies are worthless and they go to a recycle bin. a. How many copies of San Pedro Times should you buy each morning? (Use Excel's NORMSINV() function to find the correct critical value for the given a-level. Round your z-value to 2 decimal places and final answer to to 2 decimal places.) Optimal order quantity b. Based on a, what is the probability that you will run out of stock? (Round your answer to the nearest whole number.) ProbabilityQ: A hardware company stocks nuts and bolts and orders them from a local supplier once every 2 weeks (10 working days). Lead time is 2 days. The company has determined that the average demand for 1⁄2 inch bolts is 150 per week (5 working days), and it wants to keep a safety stock of 3 days’ supply on hand. An order is to be placed this week, and the stock on hand is 130 bolts.a. What is the target level?b. How many 1⁄2 inch bolts should be ordered this time?If a firm has an expected demand of 50 for its product but demand increases to 55 units 10% of the time, what would the expected cost of stock outs be if one unit costs R500 and the company held no safety inventory?
- 1. The demand for a product of Carolina Industries varies greatly from month to month. Based on the past three years of data, the following shows the monthly demand at Carolina Industries. Unit Demand # Months 300 6 400 8 500 12 600 10 A.If the company places monthly orders equal to the expected value of the monthly demand, what should Carolina’s monthly order quantity be for this product? B. What are the variance and the standard deviation for the number of units demanded?The amount of denim used daily by the Southwest ApparelCompany in its manufacturing process to make jeans isnormally distributed with an average of 4000 yards ofdenim and a standard deviation of 600 yards. The lead timerequired to receive an order of denim from the textile mill is a constant 7 days. Determine the safety stock and re-order point if the company wants to limit the probability of a stockout and work stoppage to 5%.A warehouse manager at Mary Beth Marrs Corp. needs to simulate the demand placed on a product that does not fit standard models. The concept being measured is "demand during lead time," where both lead time and daily demand are variable. The historical record for this product, along with the cumulative distribution, appear in the table. Demand During Lead Time Cumulaive Probability Probability 120 0.01 0.01 140 0.12 0.13 160 0.35 0.48 180 0.20 0.68 200 0.04 0.72 220 0.08 0.80 240 0.20 1.00 The following random numbers have been generated: 9, 78, 40, 41, and 99. (Note: Assume the random number interval begins at 01 and ends at 00.) Based on the given probabilty distribution, for the given random number the demand during the lead time is: Random Number 9 78 40 41 99 Demand The average demand during the lead time is (enter your response as an integer). The total demand during the lead time based on the five simulations is (enter your response as an integer).
- Problem 20-10 (Algo) You are a newsvendor selling San Pedro Times every morning. Before you get to work, you go to the printer and buy the day’s paper for $0.50 a copy. You sell a copy of San Pedro Times for $1.25. Daily demand is distributed normally with mean = 335 and standard deviation = 67. At the end of each morning, any leftover copies are worthless and they go to a recycle bin. a. How many copies of San Pedro Times should you buy each morning? (Use Excel's NORMSINV() function to find the correct critical value for the given α-level. Round your z-value to 2 decimal places and final answer to to 2 decimal places.) b. Based on a, what is the probability that you will run out of stock? (Round your answer to the nearest whole number.)Given this information:Lead-time demand 600 poundsStandard deviation of lead time demand 52 pounds (Assume normality.)Acceptable stockout risk during lead time 4 percenta. What amount of safety stock is appropriate?b. When should this item be reordered?c. What risk of stockout would result from a decision not to have any safety stock?A retailer carries 10,000 items in its store. During the week, there is some demand for 6000 of the items. Among those, there are 100 products for which all of the demand was not satisfied and 400 products for which only some of demand was satisfied. a. What is their in-stock probability for this week?b. What is their stockout probability for this week?
- The injection molding department of a company uses an average of 30 gallons of special lubricanta day. The supply of the lubricant is replenished when the amount on hand is 170 gallons. It takesfour days for an order to be delivered. Safety stock is 50 gallons, which provides a stockout risk of9 percent. What amount of safety stock would provide a stockout risk of 3 percent? Assumenormality.One item a computer store sells is supplied by a vendor who handles only that item. Demand forthat item recently changed, and the store manager must determine when to replenish it. The managerwants a probability of at least 96 percent of not having a stockout during lead time. The managerexpects demand to average a dozen units a day and have a standard deviation of two units a day.Lead time is variable, averaging four days with a standard deviation of one day. Assume normalityand that seasonality is not a factor.a. When should the manager reorder to achieve the desired probability?b. Why might the model not be appropriate if seasonality were present?Chris usually sells 120 copies of newspaper each day and believe that sale are normally distributed, with a standard deviation of 15 papers. He pays 70 cents for each paper, which sells $1.25. For each unsold paper, he receives 30-cent credit. a) determine how many papers he should order each day b) calculate the stockout risk for that quantity.