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practical management science

Practical Management Science, Revised 3rd Edition Wayne L Winston, S. Christian Albright - Solutions

Simple exponential smoothing with 0.3 is being used to forecast sales of radios at Lowland Appliance.Forecasts are made on a monthly basis. After August radio sales are observed, the forecast for September is 100 radios.a. During September, 120 radios are sold. After observing September sales,
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 0.3, determine a forecast (at the end of March) for
The file P16_27.xlsx contains quarterly sales of Johnson & Johnson. A time series plot of this series indicates a clear upward trend. Use moving averages to forecast this series, experimenting with the span.What do you conclude about the effectiveness of using moving averages on an upward-trending
Consider the file P16_26.xlsx, which contains total monthly U.S. retail sales data. Use the method of moving averages with a carefully chosen span to forecast U.S. retail sales for the following 12 months. What makes this time series more challenging to forecast?
The file P16_25.xlsx contains the daily closing prices of Wal-Mart stock during a 1-year period. Use the method of moving averages with a carefully chosen span to forecast this time series for the next 3 trading days. Defend your choice of the span used.
The closing value of the Dow Jones Industrial Index for each trading day for a 1-year period is provided in the file P16_24.xlsx.a. Using a span of 2 days, forecast this index for the next trading day with the method of moving averages.How well does the moving average method with span 2 forecast
The closing value of the AMEX Airline Index for each trading day during a 1-year period is given in the file P16_23.xlsx.a. How well does the moving average method track this series when the span is 4 days? When the span is 12 days?b. Using the more appropriate span, forecast the closing value of
The file P16_22.xlsx contains the daily closing prices of American Express stock for a 1-year period.a. Using a span of 3 days, forecast the price of this stock for the next trading day with the method of moving averages. How well does the moving average method with span 3 forecast the known
Suppose that you are interested in predicting the price of a laptop computer based on its various features. The file P16_21.xlsx contains observations on the sales price and a number of potentially relevant variables for a randomly chosen sample of laptop computers.a. Formulate a multiple
A regional express delivery service company recently conducted a study to investigate the relationship between the cost of shipping a package (Y ), the package weight (X1), and the distance shipped (X2). Twenty packages were randomly selected from among the large number received for shipment, and a
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 P16_19.xlsx.a. Estimate a simple regression model involving annual sales (the dependent variable) and the
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, semifragile, and durable. Costs for 15 randomly chosen packages of approximately the same weight
David Savageau and Geoffrey Loftus, the authors of Places Rated Almanac (published in 2000 by Macmillan), have ranked 325 metropolitan areas in the United States with consideration of the following aspects of life in each area: cost of living, transportation, jobs, education, climate, crime, arts,
Consider the enrollment data for Business Week’s top 50 U.S. graduate business programs in the file P16_16.xlsx. Use these data to estimate a multiple regression model to assess whether a systematic relationship exists between the total number of full-time students and the following explanatory
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 (X1) and annual dividend rate (X2). The stock
An antique collector believes that the price received for a particular item increases with its age and with the number of bidders. The file P16_14.xlsx contains data on these three variables for 32 recently auctioned comparable items. Estimate a multiple regression model using the given data.
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 file P16_13.xlsx. Note that each observation
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 digging, you find the historical data on
The management of Beta Technologies, Inc., is trying to determine the variable that best explains the variation of employee salaries using a sample of 52 full-time employees; see the file P16_11.xlsx. Estimate simple linear regression models to identify which of the following has the strongest
Sometimes curvature in a scatterplot can be fit adequately (especially to the naked eye) by several trendlines. We discussed the exponential trendline, and the power trendline is discussed in the previous problem. Still another fairly simple trendline is the parabola, a polynomial of order 2 (also
We discussed linear and exponential trendlines.Another popular choice is a power trendline, also called a constant elasticity trendline. This trendline has the form y axb, and it has the property that when x increases by 1%, y changes by a constant percentage.In fact, this constant percentage is
Based on the data in the file P16_08.xlsx from the U.S.Department of Agriculture, explore the relationship between the number of farms (X) and the average size of a farm (Y) in the United States between 1950 and 1997. Specifically, generate a simple linear regression model and interpret
The file P16_07.xlsx contains observations of the U.S.minimum wage during each of the years from 1950 through 1994. Did the minimum wage grow at roughly a constant rate over this period? Use simple linear regression analysis to address this question. Explain your results.
Do the sales prices of houses in a given community vary systematically with their sizes (as measured in square feet)? Answer this question by estimating a simple regression model where the sales price of the house is the dependent variable, and the size of the house is the explanatory variable. Use
Management of a home appliance store in Charlotte wants to understand the growth pattern of the monthly sales of DVD units over the past 2 years. The managers have recorded the relevant data in the file P16_05.xlsx. Have the sales of DVD units been growing linearly over the past 24 months? By
The file P16_04.xlsx contains monthly data on production levels and production costs during a 4-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 resulting equation to predict total cost in
The file P16_03.xlsx gives the annual sales for Microsoft (in millions of dollars) for a 10-year period.a. Fit an exponential trendline to these data.b. By what percentage do you estimate that Microsoft will grow each year?c. Why can’t a high rate of exponential growth continue for a long time?d.
The file P16_02.xlsx contains quarterly sales at Intel from 1986 through the first quarter of 2001. Chart these sales through the end of 1996 only, and fit an exponential trendline to these points. Interpret the growth rate you find. (Is it annual or quarterly?) Calculate the MAPE for these years.
The file P16_01.xlsx contains quarterly sales at Johnson& Johnson from 1991 through the first quarter of 2001. Chart these sales and fit both a linear trendline and an exponential trendline through the points. Then calculate the MAPE for each. Does either provide a good fit? Which of the two
One problem with our Excel implementation of the CPM method is that the maximum and minimum formulas for the earliest start time and the latest finish times have to be tailored to the specific AON network.That is, we can’t enter formulas for a typical activity and then copy them down for the
Consider a project with six activities. The CPM method has already been implemented, with the results shown in the file P15_38.xlsx. (All times are in months.) This file also shows the number of workers of type A, the number of workers of type B, and the material costs per month for each of the
Now create a table with weeks along the top and projects along the side. Each entry in the table should indicate how many hours are spent on each project each week. IF functions work here. Finally, create one more table with weeks along the top and managers along the side and use SUMIF functions,
Based on LeBlance et al. (2000). A construction company has eight project managers and has 14 projects scheduled for the next 12 weeks. Each project must be assigned a project manager. The start and finish week for each project as well as the hours per week each project manager would need to spend
Real-world projects often have milestones where costs are incurred or payments are received. Usually the costs are incurred relatively early, and the payments are received relatively late. Because of the time value of money, we obviously want to incur the costs as late as possible and receive the
In the previous problem, all of Tom’s activities have fixed durations. Now assume they have PERT distributions with the parameters listed in the file P15_35.xlsx.a. Use @RISK to simulate this project. What is the mean length of time required to complete the project?What is the probability that it
The main concern is when he will complete the project, given that he works only on weekdays. The work proceeds in stages, labeled A through J, as summarized in the table in the file P15_34.xlsx. Three of these activities, wiring, plumbing, and duct work, will be done by separate independent
Tom Jacobs, an independent contractor, has agreed to build a new room on an existing house. He plans to begin work on Monday morning, June
To build Indiana University’s new law building, the activities in the file P15_33.xlsx must be completed(all times are in months). Assume that all activity times are normally distributed with the means and standard deviations given in the file.a. Estimate the probability that the project will
To complete an addition to the Business Building, the activities in the file P15_32.xlsx must be completed(all times are in months). Assume that all activity times are normally distributed with the means and standard deviations given in the file. The project is completed after Room 111 has been
The city of Bloomington is about to build a new water treatment plant. After the plant is designed (D), we can select the site (S), the building contractor (C), and the operating personnel (P). After the site is selected, we can erect the building (B).We can order the water treatment machine (W)
When an accounting firm audits a corporation, the first phase of the audit involves obtaining knowledge of the business. This phase of the audit requires the activities listed in the file P15_30.xlsx.a. Draw the AON project network and determine the critical path and the minimum number of days
A company is planning to manufacture a product that consists of three parts (A, B, and C). The company anticipates that it will take 5 weeks to design the three parts and determine the way in which these parts must be assembled to make the final product. Then the company estimates that it will take
Horizon Cable is about to expand its cable TV offerings in Smalltown by adding MTV and other stations.The activities listed in the file P15_28.xlsx must be completed before the service expansion can be completed.Draw the AON project network and find the critical path and the minimum number of weeks
Consider the (simplified) list of activities and predecessors that are involved in building a house, as shown in the file P15_27.xlsx.a. Draw an AON project network and find the critical path and the minimum number of days needed to build the house. Also, create the associated Gantt chart.b.
The promoters of a rock concert in Indianapolis must perform the tasks shown in the file P15_26.xlsx before the concert can be held. (All durations are in days.) Draw theAONproject network. Then find the critical path and the minimum number of days needed to prepare for the concert, and create the
A company has a project that consists of 11 activities, described in the file P15_25.xlsx. Draw an AON project network and then find the critical path and the minimum number of days required to complete this project. Also, create the associated Gantt chart.
Before a new product can be introduced at Kehls, the activities shown in the file P15_24.xlsx must be completed, where all times are in weeks.a. Draw the AON project network and determine a critical path and the minimum number of weeks required before the new product can be introduced.b. The
What is the mean of this distribution? What are the corresponding values of1 and 2 for the equivalent beta distribution? According to the online help for the generalized beta distribution, its mean is min [1(1 2)] (max min).Does this evaluate to the same mean that you got for the PERT
Most of the literature in project scheduling with uncertain activity times advocates the use of the beta distribution for activity times. This is a continuous distribution with four parameters: a minimum, a maximum, and two parameters 1 and 2 that control the shape of the distribution. (@RISK
We saw in Chapter 11 how to introduce correlation into an @RISK simulation with RISKCORRMAT functions. We implicitly assumed that the activity durations in Example 15.5 are probabilistically independent.However, it is very possible that some of them would be correlated in a real situation.
We indicated in Example 15.5 that the mean project length from the simulation is greater than the project length of 62 days from substituting the mean activity durations (the ones used in earlier sections). Note that the PERT distributions we used in the example, with the exception of activity D,
In the model in Example 15.5, suppose bonuses and penalties are incurred for earliness or lateness. Specifically, suppose a bonus of $2000 is received if the project is completed within 60 days, an extra bonus of $1000 is received if the project is completed within 58 days, and a penalty of $1000
Starting with a project schedule where some activities are noncritical, is it ever optimal to crash any of these noncritical activities to meet a given deadline? The idea is that as you keep crashing to meet a tighter and tighter deadline, a noncritical activity could conceivably become critical,
In the Monitoring People sheet of the Project Monitoring.xlsx file, we created five tables of daily costs, one for each type of people, and we created a chart for all of these. In each table, the start times were the earliest start times. As an alternative, do the following. Delete the bottom four
Then, for example, the cost of reducing the duration of activity H from 12 days to 9 days is c(3) 300(3)2 $2700. Modify the Project Crashing Linear.xlsx model to accommodate this quadratic function, and then optimize to meet a deadline of 54 days. (You can still assume that activity H can be
This function produces the “increasing cost per day” behavior frequently seen. To try it out in Example 15.3, suppose the crashing cost for activity H, wiring offices, exhibits this quadratic behavior, with c
In the crashing model in Example 15.3, we assumed that the cost per day crashed is constant. This is often unrealistic. For example, it might cost $300 to decrease the duration of an activity from 10 days to 9 days, but it might cost $450 to reduce it from 9 days to 8 days. One possible way to
In the model in Example 15.4, suppose each project consists of two activities and the second activity for each project cannot begin until the first activity is completed. Assuming the two activities for a given project could require different numbers of employees, how would you modify the model
Suppose the projects in Example 15.4 are apartment units and the profit is the monthly rent earned from each apartment unit. Assume that rent is paid each month (through month 10) beginning with the month after the project is completed. How can we maximize the profit earned during the next 10
Given the due dates in the previous problem, how would you maximize the number of projects completed on time? (The difference here is that you are ignoring revenues.)
Modify the multiple project-scheduling model in Example 15.4 so that each project has its own due date. These due dates are listed in the file P15_13.xlsx.Assume no revenue is earned unless a project is completed by its due date. Assuming that the objective is still to maximize total revenue, when
In the LAN crashing model in Example 15.3, suppose that activity D is now an immediate successor to activity C, that is, activity D cannot begin until activity C is finished. Everything else stays the same. (However, note that activity B is no longer an immediate predecessor of activity D, and
In the Monitoring Costs sheet of the Project Monitoring.xlsx file, we created two tables of daily costs, one where all activities start at their earliest start times and one where they start at their latest start times. Then we created a single chart for both of these. As an alternative, do the
Suppose, after doing the analysis in Example 15.2, the project manager sees a problem with the current setup.Activity C, selecting the server, requires five systems people, and activity D, selecting the software, requires seven systems people. The problem is that these two activities are scheduled
The “Modeling Issues” section described three alternative types of precedence relationships besides the usual finish-to-start relationship. The following questions ask you to explore the first of these alternatives for the LAN project.a. Start-to-start relationships are sometimes useful for
Expanding on the previous problem, there is a third possible approach for finding the project length and the critical path. We already stated that the critical path is the longest path from the Start node to the Finish node. Using the same approach that we used in Chapter 5 to find the shortest
We have illustrated the traditional CPM algorithm for finding the project length and the critical path. An alternative method is sometimes used. It sets up a Solver model for finding a feasible solution to a set of constraints, and there is no objective to maximize or minimize. Let dj be the
The data in Figure 15.5 for the Gantt chart uses the earliest start times for all activities. These could actually be anywhere between the earliest and latest start times without affecting the project completion time. Enter formulas in the start time cells (column B of Figure 15.5) using Excel’s
How difficult is it to add new activities to an existing project scheduling model? Answer this question by assuming that there are two other activities, labeled P and Q. Activity P moves selected employees to temporary offices while installation occurs, and activity Q moves them back after
In the LAN project, activities C and D can be done concurrently. Suppose instead that activity C is an immediate predecessor of activity D. (Perhaps they use the same employees, and these employees can perform only one activity at a time.) How does the AON diagram change? How much does the project
Use a two-way data table to see how sensitive the project completion time in the LAN project is to the duration of activities E and H (selecting cables and wiring offices). Let the durations of these activities vary from 3 to 6 days and from 10 to 16 days, respectively, in increments of 1 day each.
Repeat the previous problem, but now keep track of the following outputs in your data table: the project completion time and the slack for each activity. As the duration of activity D changes, do any critical activities become noncritical? Do any noncritical activities become critical?
Use a one-way data table to see how sensitive the project completion time in the LAN project is to the duration of activity D (selecting software). Let the duration vary from 10 to 16 days in increments of 1 day.
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 expects to receive during each hour is shown in the
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?
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 is available).A customer can hang up
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. (Hint: Let U be
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 3 minutes to handle a call. If a caller gets a busy signal, L. L. Pea assumes that he or she will call a competing
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 patron is 3 minutes (exponentially
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 cost them in lost revenue. A small vacant lot
The manager of a large group of employees must decide whether she needs another photocopying machine.The cost of a machine is $40 per 8-hour day regardless of whether the machine is in use. On average, four people need to use the copying machine per hour.Each person uses the copier for an average
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 minute a patron waits in line and believes
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 distributed.a. On average, how many jobs are
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 does it take before a job is completed (measured
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 as the ships using that facility. The
It takes an average of 2 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 hour that a customer waits in line. How many teller windows should Bank 2 open?
On average, 300 customers arrive per hour at a huge branch of Bank
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 window, and the post office values the time a
Run the simulation when station 1 is the bottleneck. Repeat when it is station 2; station 3; station 4; station 5.b. Repeat part a when there are only two buffers in front of each station after station 1.c. Suppose station 3 is the bottleneck station and you have 4 buffers to allocate to the whole
Continuing Problem 50, we might expect that the system will be only as good as the station with the smallest value of siμi (called the bottleneck station). This problem asks you to experiment with the simulation to gain some insights into bottlenecks. For each of the following parts, assume a
Repeat the previous problem, but now assume that si 3 at each station. Change the μi’s so that the products siμi are the same as in the previous problem.
Each processing time has mean 1μi 0.6 minute and there are three stations.b. Same as parta, except that there are 10 stations.c. Same as parta, except that each processing time has mean 0.9 minute.d. Same as partc, except that there are 10 stations.e. Repeat parts a to d but now assume there
This problem asks you to experiment with the simulation to gain some insights into congestion. For each of the following parts, assume a Poisson arrival rate of 1 per minute, and assume that processing times are exponentially distributed. Each part should be answered independently. For each, you
Referring to the multistation serial system in the Series Simulation.xlsm file, let si and 1μi be the number of machines and the mean processing time at station i. Then the mean processing rate at station i is siμi. We might expect the system to operate well only if each siμi is greater than ,
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 replacement item is immediately ordered, and it
Consider a series system of the type in the Series Simulation.xlsm file. There are two stations. Each station has three machines, and the mean processing time for each machine is 3.1 minutes. Parts arrive to station 1 at a Poisson rate of 0.8 per minute. The processing times at one station are
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 3 minutes to handle each call. Each customer who buys a ticket contributes $100 to US Airlines profit. It costs
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 6 minutes. There is no “queueing.” If a

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