Suppose that annually an average of library patrons want to borrow a book. A patron borrows the book for an average of 1/ years. Suppose we observe that the book is actually borrowed an average of R times per year. Explain how we can estimate , which is an unobservable quantity.
> The file P13_42.xlsx contains monthly data on consumer revolving credit (in millions of dollars) through credit unions. a. Use these data to forecast consumer revolving credit through credit unions for the next 12 months. Do it in two ways. First, fit an
> The auditor of Kiely Manufacturing is concerned about the number and magnitude of year-end adjustments that are made annually when the financial statements of Kiely Manufacturing are prepared. Specifically, the auditor suspects that the management of Kie
> The Baker Company wants to develop a budget to predict how overhead costs vary with activity levels. Management is trying to decide whether direct labor hours (DLH) or units produced is the better measure of activity for the firm. Monthly data for the pr
> The file lists the monthly sales for a company (in millions of dollars) for a 10-year period. a. Fit an exponential trend line to these data. b. By what percentage do you estimate that the company will grow each month? c. Why can’t a high rate of exponen
> Again continuing Problem 2, suppose that you want to force the optimal solution to be integers. Do this in Solver by adding a new constraint. Select the decision variable cells for the left side of the constraint, and in the middle dropdown list, select
> Let Yt be the sales during month t (in thousands of dollars) for a photography studio, and let Pt be the price charged for portraits during month t. The data are in the file P13_39.xlsx. a. Use regression to fit the following model to these data: Yt = a
> The file P13_38.xlsx lists the average salary for each Major League Baseball team from 2004 to 2009, along with the number of team wins in each of these years. a. Rearrange the data so that there are four long columns: Team, Year, Salary, and Wins. There
> Callaway Golf is trying to determine how the price of a set of clubs affects the demand for clubs. The file P13_37.xlsx contains the price of a set of clubs (in dollars) and the monthly sales (number of sets sold). a. Assume the only factor influencing m
> When potential workers apply for a job that requires extensive manual assembly of small intricate parts, they are initially given three different tests to measure their manual dexterity. The ones who are hired are then periodically given a performance ra
> The file P13_35.xlsx contains the amount of money spent advertising a product (in thousands of dollars) and the number of units sold (in millions) for eight months. a. Assume that the only factor influencing monthly sales is advertising. Fit the followin
> A small computer chip manufacturer wants to forecast monthly operating costs as a function of the number of units produced during a month. The company has collected the 16 months of data in the file P13_34.xlsx. a. Determine an equation that can be used
> Management of a home appliance store would like to understand the growth pattern of the monthly sales of Blu-ray disc players over the past two years. Managers have recorded the relevant data in the file P13_33.xlsx. a. Create a scatterplot for these dat
> A power company located in southern Alabama wants to predict the peak power load (i.e., the maximum amount of power that must be generated each day to meet demand) as a function of the daily high temperature (X). A random sample of 25 summer days is cho
> Many companies manufacture products that are at least partially produced using chemicals (e.g., paint, gasoline, and steel). In many cases, the quality of the finished product is a function of the temperature and pressure at which the chemical reactions
> A version of simple exponential smoothing can be used to predict the outcome of sporting events. To illustrate, consider pro football. We first assume that all games are played on a neutral field. Before each day of play, we assume that each team has a r
> A textile company produces shirts and pants. Each shirt requires three square yards of cloth, and each pair of pants requires two square yards of cloth. During the next two months the following demands for shirts and pants must be met (on time): month 1,
> The file contains monthly data on production levels and production costs during a four-year period for a company that produces a single product. Use simple regression on all of the data to see how Total Cost is related to Units Produced. Use the resultin
> The file P13_29.xlsx contains monthly time series data for total U.S. retail sales of building materials (which includes retail sales of building materials, hardware and garden supply stores, and mobile home dealers). a. Is seasonality present in these d
> The file P13_28.xlsx contains monthly retail sales of U.S. liquor stores. a. Is seasonality present in these data? If so, characterize the seasonality pattern. b. Use Winters’ method to forecast this series with smoothing constants = = 0.1 and = 0.
> The file contains yearly data on the proportion of Americans under the age of 18 living below the poverty level. a. Create a time series chart of the data. Based on what you see, which of the exponential smoothing models do you think will provide the bes
> The file P13_26.xlsx contains the monthly number of airline tickets sold by the CareFree Travel Agency. a. Create a time series chart of the data. Based on what you see, which of the exponential smoothing models do you think will provide the best forecas
> The file P13_25.xlsx contains the quarterly numbers of applications for home mortgage loans at a branch office of Northern Central Bank. a. Create a time series chart of the data. Based on what you see, which of the exponential smoothing models do you th
> Simple exponential smoothing with = 0.3 is being used to forecast sales of digital cameras at Lowland Appliance. Forecasts are made on a monthly basis. After August camera sales are observed, the forecast for September is 100 cameras. Suppose 120 camer
> You have been assigned to forecast the number of aircraft engines ordered each month by Commins Engine Company. At the end of February, the forecast is that 100 engines will be ordered during April. During March, 120 engines are ordered. Using a 5 0.3 an
> The file P13_22.xlsx contains total monthly U.S. retail sales data. While holding out the final six months of observations for validation purposes, use the method of moving averages with a carefully chosen span to forecast U.S. retail sales in the next y
> The file P13_21.xlsx contains the weekly sales of rakes at a hardware store for a two-year period. Use the moving averages method, with spans of your choice, to forecast sales for the next 30 weeks. Does this method appear to track sales well? If not, wh
> A company manufactures two products on two machines. The number of hours of machine time and labor depends on the machine and product as shown in the file. The cost of producing a unit of each product depends on which machine produces it. These unit cost
> The file P13_20.xlsx contains the monthly sales of iPod cases at an electronics store for a two-year period. Use the moving averages method, with spans of your choice, to forecast sales for the next six months. Does this method appear to track sales well
> The file contains five years of monthly data on sales (number of units sold) for a particular company. The company suspects that except for random noise, its sales are growing by a constant percentage each month and will continue to do so for at least th
> The file P13_19.xlsx contains the weekly sales of a particular brand of paper towels at a supermarket for a one-year period. a. Using a span of 3, forecast the sales of this product for the next 10 weeks with the moving averages method. How well does thi
> The file P13_18.xlsx contains data on over 200 movies that came out in 2006 and 2007. Create a new variable Total Revenue that is the sum of Total US Gross, International Gross, and US DVD Sales. How well can this new variable be predicted from the data
> The owner of a restaurant in Bloomington, Indiana, has recorded sales data for the past 19 years. He has also recorded data on potentially relevant variables. The data are listed in the file P13_17.xlsx. a. Estimate a simple regression equation involving
> Suppose that a regional express delivery service company wants to estimate the cost of shipping a package (Y) as a function of cargo type, where cargo type includes the following possibilities: fragile, semi fragile, and durable. Costs for 15 randomly ch
> Stock market analysts are continually looking for reliable predictors of stock prices. Consider the problem of modeling the price per share of electric utility stocks (Y). Two variables thought to influence this stock price are return on average equity (
> An antique collector believes that the price received for a particular item increases with its age and with the number of bidders. The file P13_14.xlsx contains data on these three variables for 32 recently auctioned comparable items. Estimate a multiple
> A trucking company wants to predict the yearly maintenance expense (Y ) for a truck using the number of miles driven during the year (X1) and the age of the truck (X2, in years) at the beginning of the year. The company has gathered the data given in the
> Suppose you are an analyst for a company that produces four products, and you are trying to decide how much of each product to produce next month. To model this decision problem, you need the unit variable production cost for each product. After some dig
> A company that builds sailboats wants to determine how many sailboats to build during each of the next four quarters. The demand during each of the next four quarters is as follows: first quarter, 160 sailboats; second quarter, 240 sailboats; third quart
> The manager of a commuter rail transportation system was recently asked by her governing board to determine which factors have a significant impact on the demand for rides in the large city served by the transportation network. The system manager collect
> Sometimes curvature in a scatterplot can be fit adequately (especially to the naked eye) by several trend lines. We discussed the exponential trend line, and the power trend line is discussed in the previous problem. Still another fairly simple trend lin
> The file contains the monthly number of airline tickets sold by a travel agency. a. Does a linear trend appear to fit these data well? If so, estimate and interpret the linear trend model for this time series. Also, interpret the R2 and se values. b. Pr
> A fast-food restaurant has one drive-through window. On average, 40 customers arrive per hour at the window. It takes an average of one minute to serve a customer. Assume that interarrival and service times are exponentially distributed. a. On average, h
> Consider a fast-food restaurant where customers enter at a rate of 75 per hour, and three servers are working. Customers wait in a single line and go, in FCFS fashion, to the first of the three servers who is available. Each server can serve one customer
> Consider a bank where potential customers arrive at rate of 60 customers per hour. However, because of limited space, one out of every four arriving customers finds the bank full and leaves immediately (without entering the bank). Suppose that the averag
> Based on Kolesar et al. (1974), Metropolis PD Precinct 88 must determine the minimum number of police cars required to meet its needs for the next 24 hours. An average call for service requires 30 minutes. The number of calls the police department expect
> Zerox has 16 service centers throughout the United States. Zerox is trying to determine how many technicians it should assign to each service center. How would you approach this problem?
> Little’s formula applies to an entire queueing system or to a subsystem of a larger system. For example, consider a single-server system composed of two subsystems. The first subsystem is the waiting line, and the second is the service area, where servic
> Based on Quinn et al. (1991). Winter Riggers handles approximately $400 million in telephone orders per year. Winter Riggers’ system works as follows. Callers are connected to an agent if one is available. Otherwise, they are put on hold (if a trunk line
> A company manufactures mechanical heart valves from the heart valves of pigs. Different heart operations require valves of different sizes. The company purchases pig valves from three different suppliers. The cost and size mix of the valves purchased fro
> Excessive delays have recently been noted on New York City’s 911 system. Discuss how you would use queueing models to improve the performance of the 911 system.
> Bloomington Hospital knows that insurance companies are going to reduce the average length of stay of many types of patients. How can queueing models be used to determine how changes in insurance policies will influence the hospital?
> The mail order firm of L. L. Pea receives an average of 200 calls per hour, where times between calls are exponentially distributed. It takes an L. L. Pea operator an average of three minutes to handle a call. If a caller gets a busy signal, L. L. Pea as
> On average, 90 patrons arrive per hour at a hotel lobby (interarrival times are exponential) waiting to check in. At present there are five clerks, and patrons wait in a single line for the first available clerk. The average time for a clerk to service a
> The Newcoat Painting Company has for some time been experiencing high demand for its automobile repainting service. Because it has had to turn away business, management is concerned that the limited space available to store cars awaiting painting has cos
> The manager of a large group of employees must decide whether she needs another photocopying machine. The cost of a machine is $40 per eight-hour day regardless of whether the machine is in use. On average, four people need to use the copying machine per
> At the Franklin Post Office, patrons wait in a single line for the first open window. On average, 100 patrons enter the post office per hour, and each window can serve an average of 45 patrons per hour. The post office estimates a cost of $0.10 for each
> On average, 40 jobs arrive per day at a factory. The time between arrivals of jobs is exponentially distributed. The factory can process an average of 42 jobs per day, and the time to process a job is exponentially distributed. a. On average, how long do
> Assume that parts arrive at a machining center at a rate of 60 parts per hour. The machining center is capable of processing 75 parts per hour—that is, the mean time to machine a part is 0.8 minute. If you are watching these parts exiting the machine cen
> A company manufactures two types of trucks. Each truck must go through the painting shop and the assembly shop. If the painting shop were completely devoted to painting type 1 trucks, 650 per day could be painted, whereas if the painting shop were comple
> A printing shop receives an average of one order per day. The average length of time required to complete an order is half a day. At any given time, the print shop can work on at most one job. Interarrival times and service times are exponentially distri
> Ships arrive at a port facility at an average rate of two ships every three days. On average, it takes a single crew one day to unload a ship. Assume that interarrival and service times are exponential. The shipping company owns the port facility as well
> On average, 300 customers arrive per hour at a huge branch of Bank 2. It takes an average of two minutes to serve each customer. It costs $10 per hour to keep a teller window open, and the bank estimates that it will lose $50 in future profits for each h
> On average, 50 customers arrive per hour at a small post office. Interarrival times are exponentially distributed. Each window can serve an average of 25 customers per hour. Service times are exponentially distributed. It costs $25 per hour to open a win
> A company’s warehouse can store up to four units of a good. Each month, an average of 10 orders for the good are received. The times between the receipts of successive orders are exponentially distributed. When an item is used to fill an order, a replace
> US Airlines receives an average of 500 calls per hour from customers who want to make reservations, where the times between calls follow an exponential distribution. It takes an average of three minutes to handle each call. Each customer who buys a ticke
> A telephone-order sales company must determine how many telephone operators are needed to staff the phones during the 9-to-5 shift. It is estimated that an average of 480 calls are received during this time period and that the average call lasts for six
> We examined whether an M/M/1 system with a single fast server is better or worse than an M/M/s system with several slow servers. Keeping the same inputs as in the example, use simulation to see whether you obtain the same type of results as with the anal
> Simulate the system in Problem 10. Make any assumptions about the warm-up and run-time periods you believe are appropriate. Try solving the problem with exponentially distributed copying times. Then try it with gamma-distributed copying times, where the
> Given the model in the Multi-server Simulation.xlsm file, what unit cost parameters should be used if we are interested in “optimizing” the system? Choose representative inputs and unit costs, and then illustrate how to use the simulation outputs to esti
> There are three factories on the Momiss River. Each emits two types of pollutants, labeled P1 and P2, into the river. If the waste from each factory is processed, the pollution in the river can be reduced. It costs $1500 to process a ton of factory 1 was
> The current spreadsheet model essentially finds the expected profit in several steps. It first finds the profit in cell B19 for a fixed value of demand. Then it uses a data table to find the profit for each of several demands, and finally it uses SUMPROD
> Do exponentially distributed random numbers have the memoryless property? Here is one way to find out. Generate many exponentially distributed random numbers with mean 5, using the formula in the previous problem. Find the fraction of them that are great
> How long does it take to reach steady state? Use simulation, with the Multiserver Simulation.xlsm file, to experiment with the effect of warm-up time and run time on the key outputs. For each of the following, assume a five-server system with a Poisson a
> The Smalltown Credit Union experiences its greatest congestion on paydays from 11:30 a.m. until 1:00 p.m. During these rush periods, customers arrive according to a Poisson process at rate 2.1 per minute. The credit union employs 10 tellers for these rus
> The small mail-order firm Sea’s Beginning has one phone line. An average of 60 people per hour call in orders, and it takes an average of one minute to handle a call. Time between calls and time to handle calls are exponentially distributed. If the phone
> Two one-barber shops sit side by side in Dunkirk Square. Each shop can hold a maximum of four people, and any potential customer who finds a shop full will not wait for a haircut. Barber 1 charges $15 per haircut and takes an average of 15 minutes to com
> Consider the following two queueing systems. ■ System 1: An M/M/1 system with arrival rate and service rate 3µ. ■ System 2: An M/M/3 system with arrival rate and each server working at rate µ. Which system will have the smaller W and L?
> On average, 100 customers arrive per hour at Gotham City Bank. It takes a teller an average of two minutes to serve a customer. Interarrival and service times are exponentially distributed. The bank currently has four tellers working. The bank manager wa
> The manager of a bank wants to use an M/M/s queueing model to weigh the costs of extra tellers against the cost of having customers wait in line. The arrival rate is 60 customers per hour, and the average service time is four minutes. The cost of each te
> Referring to Problem 18, suppose the airline wants to determine how many checkpoints to operate to minimize operating costs and delay costs over a 10-year period. Assume that the cost of delaying a passenger for one hour is $10 and that the airport is op
> For the M/M/1 queueing model, why do the following results hold? a. W = (L + 1) / b. WQ = L /
> A manufacturing company makes two products. Each product can be made on either of two machines. The time (in hours) required to make each product on each machine is listed in the file. Each month, 500 hours of time are available on each machine. Each mon
> A worker at the State Unemployment Office is responsible for processing a company’s forms when it opens for business. The worker can process an average of four forms per week. Last year, an average of 1.8 companies per week submitted forms for processing
> You can easily generate random numbers in a spreadsheet that have an exponential distribution with a given mean. For example, to generate 200 such numbers from an exponential distribution with = 1/3, enter the formula =-3*LN(RAND()) in cell A4 and co
> A bank is trying to determine which of two machines to rent for check processing. Machine 1 rents for $10,000 per year and processes 1000 checks per hour. Machine 2 rents for $15,000 per year and processes 1600 checks per hour. Assume that machines work
> Consider an airport where taxis and customers arrive (exponential interarrival times) with respective rates of one and two per minute. No matter how many other taxis are present, a taxi will wait. If an arriving customer does not find a taxi, the custome
> The limited source model can often be used to approximate the behavior of a computer’s CPU (central processing unit). Suppose that 20 terminals (assumed to always be busy) feed the CPU. After the CPU responds to a user, the user takes an average of 80 se
> A laundromat has five washing machines. A typical machine breaks down once every five days. A repairman can repair a machine in an average of 2.5 days. Currently, three repairmen are on duty. The owner of the laundromat has the option of replacing them w
> On average, 40 cars per hour are tempted to use the drive-through window at the Hot Dog King Restaurant. (We assume that interarrival times are exponentially distributed.) If a total of more than four cars are in line (including the car at the window), a
> A service facility consists of one server who can serve an average of two customers per hour (service times are exponential). An average of three customers per hour arrive at the facility (interarrival times are assumed to be exponential). The system cap
> On average, 100 customers arrive per hour at the Gotham City Bank. The average service time for each customer is one minute. Service times and interarrival times are exponentially distributed. The manager wants to ensure that no more than 1% of all custo
> MacBurger’s is attempting to determine how many servers to have available during the breakfast shift. On average, 100 customers arrive per hour at the restaurant. Each server can handle an average of 50 customers per hour. A server costs $10 per hour, an
> A furniture company manufactures tables and chairs. Each table and chair must be made entirely out of oak or entirely out of pine. A total of 25,000 board feet of oak and 20,000 board feet of pine are available. A table requires either 17 board feet of o
> In this problem, assume that all interarrival and service times are exponentially distributed. a. At present, the finance department and the marketing department each has its own typists. Each typist can type 25 letters per day. Finance requires that an
> A small bank is trying to determine the number of tellers to employ. The total cost of employing a teller is $100 per day, and a teller can serve an average of 160 customers per day. On average, 210 customers arrive per day at the bank, and both service
> Explain the basic relationship between the exponential distribution and a Poisson process. Also, explain how the exponential distribution and the Poisson distribution are fundamentally different.
> A supermarket is trying to decide how many cash registers to keep open. Suppose an average of 18 customers arrive each hour, and the average checkout time for a customer is four minutes. Interarrival times and service times are exponentially distributed,
> Each airline passenger and his luggage must be checked for security. Suppose that at Gotham City Airport, 3.6 passengers per minute arrive, on average. Also, assume that interarrival times are exponentially distributed. To check passengers for security,
> Expand the MMs Template.xlsm file so that the steady state probability distribution of the number in the system is shown in tabular form and graphically. That is, enter values 0, 1, and so on (up to some upper limit you can choose) in the range from cell
> In the M/M/s model, where µ is the service rate per server, explain why , µ is not the appropriate condition for steady state, but , sµ is.
