A producer makes a product at a constant cost of $60 per unit and sells to a retailer at a wholesale price of $70, offering a buyback price (B). The retailer sells the product at $100 per unit, and each unsold unit is sold back to the producer at the buyback price (B), retaining a salvage value of $50. Demand for the product is random, following a normal distribution with a mean of 3000 and a standard deviation of 300. What value of the buyback price (B) will coordinate the supply chain?

A producer makes a product at a constant cost of $60 per unit and sells to a retailer at a wholesale price of $70, offering a buyback price (B). The retailer sells the product at $100 per unit, and each unsold unit is sold back to the producer at the buyback price (B), retaining a salvage value of $50. Demand for the product is random, following a normal distribution with a mean of 3000 and a standard deviation of 300. What value of the buyback price (B) will coordinate the supply chain?

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.
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 the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.
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.
Based on Marcus (1990). The Balboa mutual fund has beaten the Standard and Poors 500 during 11 of the last 13 years. People use this as an argument that you can beat the market. Here is another way to look at it that shows that Balboas beating the market 11 out of 13 times is not unusual. Consider 50 mutual funds, each of which has a 50% chance of beating the market during a given year. Use simulation to estimate the probability that over a 13-year period the best of the 50 mutual funds will beat the market for at least 11 out of 13 years. This probability turns out to exceed 40%, which means that the best mutual fund beating the market 11 out of 13 years is not an unusual occurrence after all.
From several years’ records, a fish market manager has determined that the weight of deep sea bream sold in the market (X), is approximately normally distributed with a mean of 500 grams and a standard deviation of 100 grams. Assuming this distribution will remain unchanged in the future, the expected proportions of deep sea bream sold over the next year weighing .(i) Between 300 grams and 400 grams is A. 0.1359 B. 0.4681 C. 0.5319 D. None of the options above
Consider the case where the left tail of the implied distribution is thinner than that of the log-normal distribution and the right tail of the implied distribution is fatter than that of the log-normal distribution with the same mean and standard deviation. Which of the following statements is correct? A) The implied volatility of a deep out-of-the money put is greater than the one obtained from the Black-Scholes price. B) The implied volatility decreases as the strike price increases. C) The implied volatility of a deep out-of-the money call is smaller than the one obtained from the Black-Scholes price. D) The implied volatility increases as the strike price increases. Please explain and justify your choice. In your answer, discuss the shape of the relation of implied volatility to the strike price and explain how this is obtained.
After meeting with the regional sales managers, Lauretta Anderson, president of Cowpie Computers, Inc., you find that she believes that the probability that sales will grow by 10% in the next year is 0.70. After coming to this conclusion, she receives a report that John Cadariu of Minihard Software, Inc., has just announced a new operating system that will be available for customers in 8 months. From past history she knows that in situations where growth has eventually occurred, new operating systems have been announced 30% of the time. However, in situations where growth has not eventually occurred, new operating systems have been announced 10% of the time. Based on all these facts, what is the probability that sales will grow by 10%?
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?
25. Billy’s Bakery bakes fresh bagels each morning. The daily demand for bagels is a random variable with a distribution estimated from prior experience given by # of bagels sold in one day probability 0 .05 5 .10 10 .10 15 .20 20 .25 25 .15 30 .10 35 .05 The bagels cost Billy’s 8 cents to make, and they are sold for 35 cents each. Bagels unsold at the end of the day are purchased by a nearby charity soup kitchen for 3 cents each a) Based on the discrete distribution above, how many bagels should Billy’s bake at the start of each day? b) Determine the optimal number of bagels to bake each day using a normal distribution approximation. (Hint: You must compute the mean and the variance of the demand from the discrete distribution above.)26. Weiss’s paint store uses a reorder point inventory system to control its stock levels. For a particularly popular white latex paint, historical data show that the distribution of monthly demand is approximately normal, with mean 28 and standard…
I need a detailed explanation on how to solve this problem: A bagel shop buys each bagel for $0.08 and sells each bagel for $0.35. Leftover bagels at the end of the day are purchased by a local soup kitchen for $0.03 per bagel. The shop’s owner has observed for the daily demand, Q, the following probabilities, f(Q): Q 0 5 10 15 20 25 30 35 f(Q) 0.05 0.10 0.10 0.20 0.25 0.15 0.10 0.05 - What is the optimal daily order in multiples of 5 (include the model name and formula)? - If the daily demand is normally distributed (the mean and variance can be obtained from the table above), then what is the optimal daily order?
Consider a firm selling Calnders. Suppose you need to order 2019 calnders to sell next year. Each calendar you order will cost you $7. The price of the calnders is fixed at $10. Demand is uncertain but suppose that uou have historical data and you think that the average demand is around 300. Demand obviously varies from year to year but it actually looks somewhat symmetric and Normal-shaped with a standard deviation of 15. Unsold calenders have no salvage valuw and will be discrded a) suppose you order 200 calenders. simulate the profit using 1000 random draws from the uncertain demand. What is your average profit? Be sure to include a prediction interval and confidence interval with your estimated average profit Use excel