In a production phase, a corporation requires 85 circuit boards every day.This is the maxim that the individual who orders the boards follows: When the number of boards on hand reaches 625, place an order. Orders are usually shipped six days after they are placed. With a mean of six days and a standard deviation of 1.10 days, the distribution period is average. If circuit boards are reordered as the number on hand decreases to 625, what is the likelihood that the stock will be depleted before the order is received

In a production phase, a corporation requires 85 circuit boards every day.This is the maxim that the individual who orders the boards follows: When the number of boards on hand reaches 625, place an order. Orders are usually shipped six days after they are placed. With a mean of six days and a standard deviation of 1.10 days, the distribution period is average. If circuit boards are reordered as the number on hand decreases to 625, what is the likelihood that the stock will be depleted before the order is received

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter10: Introduction To Simulation Modeling

Section10.5: Introduction To @risk

Problem 20P: Use @RISK to analyze the sweatshirt situation in Problem 14 of the previous section. Do this for the...

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Use @RISK to analyze the sweatshirt situation in Problem 14 of the previous section. Do this for the discrete distributions given in the problem. Then do it for normal distributions. For the normal case, assume that the regular demand is normally distributed with mean 9800 and standard deviation 1300 and that the demand at the reduced price is normally distributed with mean 3800 and standard deviation 1400.
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.
A new edition of a very popular textbook will be published a year from now. The publisher currently has 1000 copies on hand and is deciding whether to do another printing before the new edition comes out. The publisher estimates that demand for the book during the next year is governed by the probability distribution in the file P10_31.xlsx. A production run incurs a fixed cost of 15,000 plus a variable cost of 20 per book printed. Books are sold for 190 per book. Any demand that cannot be met incurs a penalty cost of 30 per book, due to loss of goodwill. Up to 1000 of any leftover books can be sold to Barnes and Noble for 45 per book. The publisher is interested in maximizing expected profit. The following print-run sizes are under consideration: 0 (no production run) to 16,000 in increments of 2000. What decision would you recommend? Use simulation with 1000 replications. For your optimal decision, the publisher can be 90% certain that the actual profit associated with remaining sales of the current edition will be between what two values?
Assume that all of a companys job applicants must take a test, and that the scores on this test are normally distributed. The selection ratio is the cutoff point used by the company in its hiring process. For example, a selection ratio of 25% means that the company will accept applicants for jobs who rank in the top 25% of all applicants. If the company chooses a selection ratio of 25%, the average test score of those selected will be 1.27 standard deviations above average. Use simulation to verify this fact, proceeding as follows. a. Show that if the company wants to accept only the top 25% of all applicants, it should accept applicants whose test scores are at least 0.674 standard deviation above average. (No simulation is required here. Just use the appropriate Excel normal function.) b. Now generate 1000 test scores from a normal distribution with mean 0 and standard deviation 1. The average test score of those selected is the average of the scores that are at least 0.674. To determine this, use Excels DAVERAGE function. To do so, put the heading Score in cell A3, generate the 1000 test scores in the range A4:A1003, and name the range A3:A1003 Data. In cells C3 and C4, enter the labels Score and 0.674. (The range C3:C4 is called the criterion range.) Then calculate the average of all applicants who will be hired by entering the formula =DAVERAGE(Data, "Score", C3:C4) in any cell. This average should be close to the theoretical average, 1.27. This formula works as follows. Excel finds all observations in the Data range that satisfy the criterion described in the range C3:C4 (Score0.674). Then it averages the values in the Score column (the second argument of DAVERAGE) corresponding to these entries. See online help for more about Excels database D functions. c. What information would the company need to determine an optimal selection ratio? How could it determine the optimal selection ratio?
Play Things is developing a new Lady Gaga doll. The company has made the following assumptions: The doll will sell for a random number of years from 1 to 10. Each of these 10 possibilities is equally likely. At the beginning of year 1, the potential market for the doll is two million. The potential market grows by an average of 4% per year. The company is 95% sure that the growth in the potential market during any year will be between 2.5% and 5.5%. It uses a normal distribution to model this. The company believes its share of the potential market during year 1 will be at worst 30%, most likely 50%, and at best 60%. It uses a triangular distribution to model this. The variable cost of producing a doll during year 1 has a triangular distribution with parameters 15, 17, and 20. The current selling price is 45. Each year, the variable cost of producing the doll will increase by an amount that is triangularly distributed with parameters 2.5%, 3%, and 3.5%. You can assume that once this change is generated, it will be the same for each year. You can also assume that the company will change its selling price by the same percentage each year. The fixed cost of developing the doll (which is incurred right away, at time 0) has a triangular distribution with parameters 5 million, 7.5 million, and 12 million. Right now there is one competitor in the market. During each year that begins with four or fewer competitors, there is a 25% chance that a new competitor will enter the market. Year t sales (for t 1) are determined as follows. Suppose that at the end of year t 1, n competitors are present (including Play Things). Then during year t, a fraction 0.9 0.1n of the company's loyal customers (last year's purchasers) will buy a doll from Play Things this year, and a fraction 0.2 0.04n of customers currently in the market ho did not purchase a doll last year will purchase a doll from Play Things this year. Adding these two provides the mean sales for this year. Then the actual sales this year is normally distributed with this mean and standard deviation equal to 7.5% of the mean. a. Use @RISK to estimate the expected NPV of this project. b. Use the percentiles in @ RISKs output to find an interval such that you are 95% certain that the companys actual NPV will be within this interval.
A company uses 85 circuit boards a day in a manufacturing process. The person who ordersthe boards follows this rule: Order when the amount on hand drops to 625 boards. Orders are delivered approximately six days after being placed. The delivery time is normal with a mean ofsix days and a standard deviation of 1.10 days. What is the probability that the supply of circuitboards will be exhausted before the order is received if boards are reordered when the amount onhand drops to 625 boards?
Ken Ells, owner, and operator of Kennels, Inc. is concerned that the person in charge of ordering dog food is often incurring an order expediting expense because he is waiting too long (letting the inventory level drop too low) before ordering. Past data indicates that demand during the lead time (when expediting does not occur) is normally distributed with a mean of 340 pounds and a standard deviation of 45 pounds. Ken wants the probability of running out of dog food to be .03. a. If the current order point is 400 pounds, what is the resulting service level? b. If Ken wants a service level of 97% for dog food, what should be the order point? Please show a correct solution. Thank you.
Joe is selling Christmas trees to pay his college tuition.He purchases trees for $10 each and sells them for $25each. The number of trees he can sell is normally distributedwith a mean of 100 and standard deviation of 30. How manytrees should Joe purchase?
A warehouse distributor of carpet keeps 6,000 yards of deluxe shag carpet in stock during a month. The average demand for carpet from the stores that purchase from the distributor is 4,500 yards per month, with a standard deviation of 900 yards. What is the probability that a customer’s order will not be met during a month? (This situation is referred to as a stockout.)
A retail outlet sells a seasonal product for $10 per unit. The cost of the product is $8 per unit. All units not sold during the regular season are sold for half the retail price in an end-of-season clearance sale. Assume that demand for the product is uniformly distributed between 200 and 800. What is the recommended order quantity? What is the probability that at least some customers will ask to purchase the product after the outlet is sold out? That is, what is the probability of a stock-out using your order quantity in part (a)? To keep customers happy and returning to the store later, the owner feels that stock-outs should be avoided if at all possible. What is your recommended order quantity if the owner is willing to tolerate a 0.15 probability of a stock-out?
The manager of a fish market pays 80 cents each The manager of a fish market pays 80 cents each for cod and sells them for $1.50 each. Fish left over at the end of the day are discarded. The daily demand can be approximated by a normal distribution having a mean of 300 and a standard deviation of 50. To maximize his expected profit, how many cod should the manager buy before the market opens each day? The manager of a fish market pays 80 cents each
A milk man buys milk at K10 per litre and sells it at K12 if sold on the same day. If not, it can be sold at K9 per litre the next day. Demand of milk lies between 45 litres and 60 litres per day and is probabilities are uniformly distributed over this demand. If each day’s demand is independent of the previous day’s demand, how many litres should be ordered every day?