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practical management science
Practical Management Science 4th Edition Wayne L. Winston, S. Christian Albright - Solutions
What (R,Q) policy should it use? Then find the model 3 cost parameter (the cost per cycle with a shortage) that is equivalent to this service level.
Turn the previous problem around. Now assume that the store’s service level requirement obligates it to meet customer demand on 99% of all order cycles. In other words, use model
The first (R,Q) model in this section assumes that the total shortage cost is proportional to the amount of demand that cannot be met from on-hand inventory.Similarly, the second model assumes that the service level constraint is in terms of the fill rate, the fraction of all customer demand that
We claimed that the critical fractile formula, Equation(12.8), is appropriate because the optimal Q should satisfy cunder (1 F(Q)) cover F(Q), that is, the cost of understocking times the probability of understocking should equal the cost of overstocking times the probability of overstocking.
In Example 12.7, we discussed the equivalence between the model with shortage costs and the model with a service level constraint. We also showed how to illustrate this equivalence with SolverTable. Extend the SolverTable in the Ordering Cameras 1.xlsx file, with the unit shortage cost as the
In both (R,Q) models, the one with a shortage cost and the one with a service level constraint, we set up Solver so that the multiple k is constrained to be nonnegative. The effect is that the reorder point R will be no less than the mean demand during lead time, and the expected safety stock will
In the first (R,Q) model in Example 12.7, the one with a shortage cost, we let both Q and the multiple k be changing cells. However, we stated that the optimal Q depends mainly on the fixed ordering cost, the holding cost, and the expected annual demand. This implies that a good approximation to
Change the model in the file Ordering Cameras 2.xlsx slightly to allow a random lead time with a given mean and standard deviation. If the mean lead time is two weeks, and the standard deviation of lead time is half a week, find the optimal solution if the company desires a fill rate of 98.5%.
You saw in Example 12.6 that the optimal order quantities with the triangular and normal demand distributions are very similar (171 versus 174). Perhaps this is because these two distributions, with the parameters used in the example, have similar shapes. Explore whether this similarity in optimal
Consider each change to the monetary inputs (the purchase cost, the selling price, and the salvage price) one at a time in Example 12.6. For each such change, either up or down, describe how the cost of understocking and the cost of overstocking change, how the critical fractile changes, and how
As stated in Example 12.6, the critical fractile analysis is useful for finding the optimal order quantity, but it doesn’t (at least by itself) show the probability distribution of net profit. Use @RISK, as in Chapter 10, to explore this distribution. Actually, do it twice, once with the
What region is the optimal ordering quantity in if there is no price break at all (k 0). How do you reconcile this with your SolverTable findings?
In the quantity discount model in Example 12.2, the minimum total annual cost is region 3 is clearly the best. Evidently, the larger unit purchase costs in the other two regions make these two regions unattractive.When would a switch take place? To answer this question, change the model slightly.
In the basic EOQ model, revenue is often omitted from the model. The reasoning is that all demand will be sold at the given selling price, so revenue is a fixed quantity that is independent of the order quantity. Change that assumption as follows. Make selling price a decision variable, which must
In the basic EOQ model in Example 12.1, suppose that the fixed cost of ordering and the unit purchasing cost are both multiplied by the same factorf. Use SolverTable to see what happens to the optimal order quantity and the corresponding annual fixed order cost and annual holding cost as f varies
Modify the synchronized ordering model in Example 12.5 slightly so that you can use a two-way SolverTable on the fixed costs. Specifically, enter a formula in cell B9 so that the fixed cost of ordering kings alone is equal to the fixed cost of ordering queens alone. Then let the two inputs for
Example 12.4 illustrates why a company might invest to reduce its setup cost. It all depends on how much this investment costs, as specified (in the model) by the cost of a 10% reduction in the setup cost. Use SolverTable to see how the results change as this cost of a 10% reduction varies. You can
In Example 12.3, SolverTable was used to show what happens when the unit shortage cost varies. As the table indicates, the company orders more and allows more backlogging as the unit shortage cost decreases.Redo the SolverTable analysis, this time trying even smaller unit shortage costs. Explain
The quantity discount model in Example 12.2 uses one of two possible types of discount structures. It assumes that if the company orders 600 units, say, each unit costs $28. This provides a big incentive to jump up to a higher order quantity. For example, the total purchasing cost of 499 units is
In the quantity discount model in Example 12.2, suppose you want to see how the optimal order quantity and the total annual cost vary as the fixed cost of ordering varies. Use SolverTable to perform this analysis, allowing the fixed cost of ordering to vary from $25 to$200 in increments of $25.
In the quantity discount model in Example 12.2, the minimum total annual cost is obtained by ordering enough to achieve the smallest unit purchasing cost.Evidently, the larger unit purchasing costs for smaller order quantities make them unattractive. Could an order quantity below 400 ever be best?
If the lead time in Example 12.1 changes from one week to two weeks, how is the optimal policy affected? Does the optimal order quantity change?
In the basic EOQ model in Example 12.1, suppose that the fixed cost of ordering is $500. Use Solver to find the new optimal order quantity. How does it compare to the optimal order quantity in the example? Could you have predicted this from Equation (12.4)?
Health care is continually in the news. Can (or should)simulation be used to help solve, or at least study, some of the difficult problems associated with health care? Provide at least two examples where simulation might be useful.
Software development is an inherently risky and uncertain process. For example, there are many examples of software that couldn’t be “finished” by the scheduled release date—bugs still remained and features weren’t ready. (Many people believe this was the case with Office 2007.) How might
Suppose you are a financial analyst and your company runs many simulation models to estimate the profitability of its projects. If you had to choose just two measures of the distribution of any important output such as net profit to report, which two would you choose? Why? What information would be
You are an avid basketball fan, and you would like to build a simulation model of an entire game so that you could compare two different strategies, such as manto-man versus zone defense. Is this possible? What might make this simulation model difficult to build?
Suppose you are an HR (human resources) manager at a big university, and you sense that the university is becoming too top-heavy with full professors. That is, there do not seem to be as many younger professors at the assistant and associate levels as there ought to be.How could you study this
We have separated the examples in this chapter into operations, finance, marketing, and sports categories.List at least one other problem in each of these categories that could be attacked with simulation. For each, identify the random inputs, possible probability distributions for them, and any
Suppose you are using an underwater probe to search for a sunken ship. At any time in the search, your probe is located at some point (x,y) in a grid, where the distance between lines in the grid is some convenient unit such as 100 meters. The sunken ship is at some unknown location on the grid,
If two competitors enter the market in year 1, Nucleon sales per pig drop to 0.9 in year 2.■ All cash flows other than the fixed cost on January 1 of year 0 are incurred midyear.Use simulation to model Nucleon’s situation. Based on the simulation output, would you go ahead with this project?
The following information is relevant:■ A fixed cost is incurred on January 1 of year 0 and will be between $1 billion and $5 billion. There is a 20% chance the fixed cost will be less than or equal to $2 billion, a 60% chance that it will be less than or equal to $3 billion, and a 90% chance
Nucleon is trying to determine whether to produce a new drug that makes pigs healthier. The product will be sold in years 1 to
It is January 1 of year 0, and Merck is trying to determine whether to continue development of a new drug.The following information is relevant. You can assume that all cash flows occur at the ends of the respective years.■ Clinical trials (the trials where the drug is tested on humans) are
In years 1 and 2, the product will be sold only in the United States, but starting in year 3, Lilly might sell the product overseas. The year 1 market size in the United States is assumed to be between 500,000 and 3,000,000 units. A market size of 1,000,000 units is assumed to be twice as likely as
It is January 1 of year 0, and Lilly is considering developing a new drug called Dialis. We are given the following information■ On March 15 of year 0, Lilly incurs a fixed cost that is assumed to follow a triangular distribution with best case $10 million, most likely case $35 million, and worst
The tax rate is 40%.■ The car will first come to market during year 2 and is equally likely to sell for 6, 7, or 8 years.■ The market size during year 2 will be between 20,000 and 90,000 cars. There is a 25% chance that the market size will be less than or equal to 50,000 cars, a 50% chance
It is now May 1 of year 0, and GM is deciding whether to produce a new car. The following information is relevant.■ The fixed cost of developing the car is incurred on January 1 of year 1 and is assumed to follow a triangular distribution with smallest possible cost$300 million, most likely cost
You win.Note that only 4 tosses need to be generated for the house, but more tosses might need to be generated for you, depending on your strategy. Develop a simulation and run it for at least 1000 iterations for each of the strategies listed previously. For each strategy, what are the two values
The house tosses a 3 and then a
In this version of “dice blackjack,” you toss a single die repeatedly and add up the sum of your dice tosses.Your goal is to come as close as possible to a total of 7 without going over. You may stop at any time. If your total is 8 or more, you lose. If your total is 7 or less, the “house”
Based on Bukiet et al. (1997). Many Major League teams (including Oakland, Boston, LA Dodgers, and Toronto) use mathematical models to evaluate baseball players. A common measure of a player’s offensive effectiveness is the number of runs generated per inning (RPI) if a team were made up of nine
The Ryder Cup is a three-day golf tournament played every other year with 12 of the best U.S. golfers against 12 of the best European golfers.They play 16 team matches (each match has two U.S. golfers against two European golfers) on Friday and Saturday, and they play 12 singles matches (each match
A popular restaurant in Indianapolis does a brisk business, filling virtually all of its seats from 6 P.M.until 9 P.M. Tuesday through Sunday. Its current annual revenue is $2.34 million. However, it does not currently accept credit cards, and it is thinking of doing so. If it does, the bank will
You are unemployed, 21 years old, and searching for a job. Until you accept a job offer, the following situation occurs. At the beginning of each year, you receive a job offer. The annual salary associated with the job offer is equally likely to be any number between $20,000 and $100,000. You must
The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are
Chemcon has taken over the production of Nasacure from a rival drug company. Chemcon must build a plant to produce Nasacure by the beginning of 2010. Once the plant is built, the plant’s capacity cannot be changed.Each unit sold brings in $10 in revenue. The fixed cost(in dollars) of producing a
Based on Hoppensteadt and Peskin (1992). The following model (the Reed–Frost model) is often used to model the spread of an infectious disease. Suppose that at the beginning of period 1, the population consists of five diseased people (called infectives) and 95 healthy people (called
Rework the previous problem for a case in which the one-year warranty requires you to pay for the new device even if failure occurs during the warranty period. Specifically, if the device fails at time t, measured relative to the time it went into use, you must pay $300t for a new device. For
Suppose you buy an electronic device that you operate continuously. The device costs you $300 and carries a one-year warranty. The warranty states that if the device fails during its first year of use, you get a new device for no cost, and this new device carries exactly the same warranty. However,
A truck manufacturer produces the Off Road truck.The company wants to gain information about the discounted profits earned during the next three years.During a given year, the total number of trucks sold in the United States is 500,000 50,000G – 40,000I, where G is the number of percentage points
It costs a pharmaceutical company $40,000 to produce a 1000-pound batch of a drug. The average yield from a batch is unknown but the best case is 90% yield (that is, 900 pounds of good drug will be produced), the most likely case is 85% yield, and the worst case is 70% yield. The annual demand for
An automobile manufacturer is considering whether to introduce a new model called the Racer. The profitability of the Racer depends on the following factors:■ The fixed cost of developing the Racer is triangularly distributed with parameters $3, $4, and$5, all in billions.■ Year 1 sales are
Each of these 10 possibilities is equally likely.■ At the beginning of year 1, the potential market for the doll is one million. The potential market grows by an average of 5% per year. The company is 95%sure that the growth in the potential market during any year will be between 3% and 7%. It
Play Things is developing a new Hannah Montana doll. The company has made the following assumptions:■ The doll will sell for a random number of years from 1 to
Estimate the mean and standard deviation of the project with the abandonment option. How much would you pay for the abandonment option? (Hint: You can abandon a project at most once. So in year 5, for example, you abandon only if the sum of future expected NPVs is less than the year 5 abandonment
You are considering a 10-year investment project. At present, the expected cash flow each year is $10,000.Suppose, however, that each year’s cash flow is normally distributed with mean equal to last year’s actual cash flow and standard deviation $1000. For example, suppose that the actual cash
Mary Higgins is a freelance writer with enough spare time on her hands to play the stock market fairly seriously. Each morning she observes the change in stock price of a particular stock and decides whether to buy or sell, and if so, how many shares to buy or sell. Assume that on day 1, she has
For example, if you end with$100,000, your annual return is 201/30 – 1 0.105, or 10.5%. Run 1000 replications of an appropriate simulation. Based on the results, you can be 95%certain that your annual return will be between which two values?
You want to estimate your annual return over a 30-year period. If you end with F dollars, your annual return is(F/5000)1/30 –
Suppose you begin year 1 with $5000. At the beginning of each year, you put half of your money under a mattress and invest the other half in Whitewater stock. During each year, there is a 50%chance that the Whitewater stock will double, and there is a 50% chance that you will lose half of your
Consider an oil company that bids for the rights to drill in offshore areas. The value of the right to drill in a given offshore area is highly uncertain, as are the bids of the competitors. This problem demonstrates the “winner’s curse.” The winner’s curse states that the optimal bidding
A common decision is whether a company should buy equipment and produce a product in house or outsource production to another company. If sales volume is high enough, then by producing in house, the savings on unit costs will cover the fixed cost of the equipment. Suppose a company must make such a
The DC Cisco office is trying to predict the revenue it will generate next week. Ten deals may close next week. The probability of each deal closing and data on the possible size of each deal (in millions of dollars)are listed in the file P11_55.xlsx. Use simulation to estimate total revenue. Based
A company is trying to determine the proper capacity level for its new electric car. A unit of capacity provides the potential to produce one car per year. It costs$10,000 to build a unit of capacity and the cost is charged equally over the next five years. It also costs$400 per year to maintain a
The annual demand for Prizdol, a prescription drug manufactured and marketed by the NuFeel Company, is normally distributed with mean 50,000 and standard deviation 12,000. Assume that demand during each of the next 10 years is an independent random number from this distribution. NuFeel needs to
Appliances Unlimited (AU) sells refrigerators. Any refrigerator that fails before it is three years old is replaced for free. Of all refrigerators, 3% fail during their first year of operation; 5% of all one-year-old refrigerators fail during their second year of operation;and 7% of all
Consider a drill press containing three drill bits. The current policy (called individual replacement) is to replace a drill bit when it fails. The firm is considering changing to a block replacement policy in which all three drill bits are replaced whenever a single drill bit fails. Each time the
Consider a device that requires two batteries to function. If either of these batteries dies, the device will not work. Currently there are two new batteries in the device, and there are three extra new batteries.Each battery, once it is placed in the device, lasts a random amount of time that is
You have been asked to simulate the cash inflows to a toy company for the next year. Monthly sales are independent random variables. Mean sales for the months January through March and October through December are $80,000, and mean sales for the months April through September are $120,000. The
Based on Marcus (1990). The Balboa mutual fund has beaten the Standard and Poor’s 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 Balboa’s beating the market 11 out of 13 times is not unusual.
A ticket from Indianapolis to Orlando on Deleast Airlines sells for $150. The plane can hold 100 people.It costs Deleast $8000 to fly an empty plane. Each person on the plane incurs variable costs of $30 (for food and fuel). If the flight is overbooked, anyone who cannot get a seat receives $300 in
Suppose you have invested 25% of your portfolio in four different stocks. The mean and standard deviation of the annual return on each stock are shown in the file P11_46.xlsx. The correlations between the annual returns on the four stocks are also shown in this file.a. What is the probability that
You now have $10,000, all of which is invested in a sports team. Each year there is a 60% chance that the value of the team will increase by 60% and a 40%chance that the value of the team will decrease by 60%. Estimate the mean and median value of your investment after 50 years. Explain the large
You now have $3000. You will toss a fair coin four times. Before each toss you can bet any amount of your money (including none) on the outcome of the toss. If heads comes up, you win the amount you bet.If tails comes up, you lose the amount you bet. Your goal is to reach $6000. It turns out that
You are playing Andy Roddick in tennis, and you have a 42% chance of winning each point. (You are good!)a. Use simulation to estimate the probability you will win a particular game. Note that the first player to score at least four points and have at least two more points than his or her opponent
Based on Morrison and Wheat (1984). When his team is behind late in the game, a hockey coach usually waits until there is one minute left before pulling the goalie out of the game. Using simulation, it is possible to show that coaches should pull their goalies much sooner. Suppose that if both
Consider the following card game. The player and dealer each receive a card from a 52-card deck. At the end of the game the player with the highest card wins;a tie goes to the dealer. (You can assume that Aces count 1, Jacks 11, Queens 12, and Kings 13.) After the player receives his card, he keeps
You go first and spin the wheel.Based on your first spin, you can decide whether you want to spin again. (You can spin no more than twice.)After you are done, it is the house’s turn. If your total is more than 50, the house doesn’t need a turn; it wins automatically. Otherwise, the house spins
The goal is to get a total as close as possible to 50 points without exceeding
You are going to play the Wheel of Misfortune Game against the house. The wheel has 10 equally likely numbers: 5, 10, 15, 20, 25, 30, 35, 40, 45 ,and
Assume a very good NBA team has a 70% chance of winning in each game it plays. During an 82-game season what is the average length of the team’s longest winning streak? What is the probability that the team has a winning streak of at least 16 games? Use simulation to answer these questions, where
You have $5 and your opponent has $10. You flip a fair coin and if heads comes up, your opponent pays you $1. If tails comes up, you pay your opponent $1.The game is finished when one player has all the money or after 100 tosses, whichever comes first. Use simulation to estimate the probability
The game of Chuck-a-Luck is played as follows: You pick a number between 1 and 6 and toss three dice. If your number does not appear, you lose $1. If your number appears x times, you win $x. On the average, use simulation to find the average amount of money you will win or lose on each play of the
A martingale betting strategy works as follows. You begin with a certain amount of money and repeatedly play a game in which you have a 40% chance of winning any bet. In the first game, you bet $1. From then on, every time you win a bet, you bet $1 the next time. Each time you lose, you double your
The Mutron Company is thinking of marketing a new drug used to make pigs healthier. At the beginning of the current year, there are 1,000,000 pigs that could use the product. Each pig will use Mutron’s drug or a competitor’s drug once a year. The number of pigs is forecast to grow by an average
Suppose that GLC earns a $2000 profit each time a person buys a car. We want to determine how the expected profit earned from a customer depends on the quality of GLC’s cars. We assume a typical customer will purchase 10 cars during her lifetime. She will purchase a car now (year 1) and then
We are all aware of the fierce competition by mobile phone service companies to get our business. For example, AT&T is always trying to attract Verizon’s customers, and vice versa. Some even give away prizes to entice us to sign up for a guaranteed length of time.This example is based on one such
The customer loyalty model in Example 11.11 assumes that once a customer leaves (becomes disloyal), that customer never becomes loyal again. Assume instead that there are two probabilities that drive the model, the retention rate and the rejoin rate, with values 0.75 and 0.15, respectively. The
Based on Babich (1992). Suppose that each week each of 300 families buys a gallon of orange juice from company A, B, or C. Let pA denote the probability that a gallon produced by company A is of unsatisfactory quality, and define pB and pC similarly for companies B and C. If the last gallon of
Seas Beginning sells clothing by mail order. An important question is when to strike a customer from the company’s mailing list. At present, the company strikes a customer from its mailing list if a customer fails to order from six consecutive catalogs. The company wants to know whether striking
Do this by assuming that the total market size is fixed at 100,000 customers.(Hint: Use the RISKBINOMIAL function. However, if your model requires more RISKBINOMIAL functions than the number allowed in the academic version of @RISK, remember that you can instead use the CRITBINOM function to
Suppose that Coke and Pepsi are fighting for the cola market. Each week each person in the market buys one case of Coke or Pepsi. If the person’s last purchase was Coke, there is a 0.90 probability that this person’s next purchase will be Coke; otherwise, it will be Pepsi. (You can assume that
The investor uses the following strategy.At the end of March, he exercises the option only if the stock price is above $51.50. At the end of April, he exercises the option (assuming he hasn’t exercised it yet) only if the price is above $50.75. At the end of May, he exercises the option (assuming
The contract allows him to buy 100 shares of ABC stock at the end of March, April, or May at a guaranteed price of $50 per share. He can exercise this option at most once. For example, if he purchases the stock at the end of March, he cannot purchase more in April or May at the guaranteed price. If
A knockout call option loses all value at the instant the price of the stock drops below a given “knockout level.” Determine a fair price for a knockout call option when the current stock price is $20, the exercise price is $21, the knockout price is $19.50, the mean annual growth rate of the
A stock currently sells for $69. The annual growth rate of the stock is 15%, and the stock’s annual volatility is 35%. The risk-free rate is currently 5%. You have bought a six-month European put option on this stock with an exercise price of $70.a. Use @RISK to value this option.b. Use @RISK to
For the data in the previous problem, the following is an example of a butterfly spread: sell two calls with an exercise price of $50, buy one call with an exercise price of $40, and buy one call with an exercise price of$60. Simulate the cash flows from this portfolio.
If you own a stock, buying a put option on the stock will greatly reduce your risk. This is the idea behind portfolio insurance. To illustrate, consider a stock that currently sells for $56 and has an annual volatility of 30%. Assume the risk-free rate is 8%, and you estimate that the stock’s
Suppose you currently have a portfolio of three stocks, A, B, and C. You own 500 shares of A, 300 of B, and 1000 of C. The current share prices are $42.76,$81.33, and $58.22, respectively. You plan to hold this portfolio for at least a year. During the coming year, economists have predicted that
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