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an introduction to management science

Questions and Answers of An Introduction to Management Science

Blue Mountain Coffee Company produces various blends of Free Trade, organic specialty coffees that it sells to wholesale customers. The company imports 25 million pounds of coffee beans annually from
In Problem 44, KanTech Corporation is just as concerned that its U.S. distributors receive shipments in the minimum amount of time as they are about minimizing their shipping costs.Suppose that each
KanTech Corporation is a global distributor of electrical parts and components. Its customers are electronics companies in the United States, including computer manufacturers and audio/visual product
The Midlands Field Produce Company contracts with potato farmers in Colorado, Minnesota, North Dakota, and Wisconsin for monthly potato shipments. Midlands picks up the potatoes at the farms and
Horizon Computers manufactures laptops in Germany, Belgium, and Italy. Because of high tariffs between international trade groups, it is sometimes cheaper to ship partially completed laptops to
A national catalog and Internet retailer has three warehouses and three major distribution centers located around the country. Normally, items are shipped directly from the warehouses to the
Walsh’s Fruit Company contracts with growers in Ohio, Pennsylvania, and New York to purchase grapes. The grapes are processed into juice at the farms and stored in refrigerated vats.Then the juice
A sports apparel company has received an order for a college basketball team’s national championship T-shirt. The company can purchase the T-shirts from textile factories in Mexico, Puerto Rico,
World Foods, Inc., imports food products such as meats, cheese, and pastries to the United States from warehouses at ports in Hamburg, Marseilles, and Liverpool. Ships from these ports deliver the
Al, Barbara, Carol, and Dave have joined together to purchase two season tickets to the Giants’home football games. Because there are eight home games, each person will get tickets to two games.
The National Western Railroad’s rail network covers most of the U.S. West and Midwest. On a daily basis it sends empty freight cars from various locations in its rail network to its customers for
Binford Tools manufactures garden tools. It uses inventory, overtime, and subcontracting to absorb demand fluctuations. Expected demand, regular and overtime production capacity, and subcontracting
Orient Express is a global distribution company that transports its clients’ products to customers in Hong Kong, Singapore, and Taipei. All the products Orient Express ships are stored at three
In Problem 32, National Foods would like to know what the effect would be on the optimal solution and the company’s decision regarding its shipping if it negotiates with its suppliers in
National Foods Company has five plants where it processes and packages fruits and vegetables.It has suppliers in six cities in California, Texas, Alabama, and Florida. The company owns and operates
In Problem 30, suppose that the demand for personal computers increased each month, as follows:Month Demand Month Demand January 410 April 620 February 320 May 430 March 500 June 380 In addition to
PM Computer Services produces personal computers from component parts it buys on the open market. The company can produce a maximum of 300 personal computers per month. PM wants to determine its
Suntrek in Problem 28 supplies its finished denim jeans to its customers’ distribution centers in the United States in New York and New Orleans, and in Europe in Bristol and Marseilles. Denim jeans
Suntrek in Problem 27 manufactures denim fabric at its factories in Shanghai, Karachi, and Saigon and ships it to its denim jeans manufacturing facilities in China, India, Japan, Turkey, and Italy. A
Suntrek in Problem 26 ships the cotton it has purchased from the U.S. ports to overseas ports in Shanghai, Karachi, and Saigon, where its denim fabric factories are also located. The shipping and
Suntrek, based in China, is a global supplier of denim jeans for apparel companies around the world. They purchase raw cotton from producers in Arkansas, Mississippi, and Texas, where it is picked,
During U.S. military action in the Middle East, large amounts of military matériel and supplies had to be shipped daily from supply depots in the United States. The critical factor in the movement
The Roadnet Transport Company expanded its shipping capacity by purchasing 90 trailer trucks from a competitor that went bankrupt. The company subsequently located 30 of the purchased trucks at each
In Problem 21, if Easy Time could arrange to purchase more baby food from one of the outlying locations, which should it be, how many additional cases could be purchased, and how much would this
Suppose that in Problem 21 Easy Time can purchase all the baby food it needs from a New York City distributor at a price that will result in a profit of $9 per case at stores 1, 3, and 4; $8 per case
The Easy Time Grocery chain operates in major metropolitan areas on the East Coast. The stores have a “no-frills” approach, with low overhead and high volume. They generally buy their stock in
In Problem 19, the school board determined that it does not want any of the schools to be overly crowded compared with the other schools. It would like to assign students from each district to each
Bayville has built a new elementary school, increasing the town’s total to four schools—Addison, Beeks, Canfield, and Daley. Each has a capacity of 400 students. The school board wants to assign
The Sav-Us Rental Car Agency has six lots in Nashville, and it wants to have a certain number of cars available at each lot at the beginning of each day for local rental. The agency would like a
A large manufacturing company is closing three of its existing plants and intends to transfer some of its more skilled employees to three plants that will remain open. The number of employees
A severe winter ice storm has swept across North Carolina and Virginia, followed by over a foot of snow and frigid, single-digit temperatures. These weather conditions have resulted in numerous
Computers Unlimited in Problem 13 has determined that when it is unable to meet the demand for microcomputers at the universities it supplies, the universities tend to purchase microcomputers
In Problem 13, Computers Unlimited wants to better meet demand at the four universities it supplies.It is considering two alternatives: (1) expand its warehouse at Richmond to a capacity of 600, at a
Computers Unlimited sells microcomputers to universities and colleges on the East Coast and ships them from three distribution warehouses. The firm is able to supply the following numbers of
In Problem 11, the Shotz Beer Company management negotiated a new shipping contract with a trucking firm between its Tampa brewery and its distributor in Kentucky. This contract reduces the shipping
The Shotz Beer Company has breweries in two cities; the breweries can supply the following numbers of barrels of draft beer to the company’s distributors each month:Brewery Monthly Supply (bbl)A.
The Interstate Truck Rental firm has accumulated extra trucks at three of its truck leasing outlets, as shown in the following table:Leasing Outlet Extra Trucks 1. Atlanta 70 2. St. Louis 115 3.
A manufacturing firm produces diesel engines in four cities—Phoenix, Seattle, St. Louis, and Detroit. The company is able to produce the following numbers of engines per month:Plant Production 1.
Oranges are grown, picked, and then stored in warehouses in Tampa, Miami, and Fresno. These warehouses supply oranges to markets in New York, Philadelphia, Chicago, and Boston. The following table
Coal is mined and processed at the following four mines in Kentucky, West Virginia, and Virginia:Location Capacity (tons)A. Cabin Creek 90 B. Surry 50 C. Old Fort 80 D. McCoy 60 280 These mines
In Problem 5, what would be the effect on the optimal solution of a reduction in production capacity at the Gary mill from 320 tons to 290 tons per week? LO.1
Steel mills in three cities produce the following amounts of steel:Location Weekly Production (tons)A. Bethlehem 150 B. Birmingham 210 C. Gary 320 680 These mills supply steel to four cities, where
Consider the following transportation problem:To (cost)From 1 2 3 Supply A $ 6 $ 9 $ 7 130 B 12 3 5 70 C 4 8 11 100 Demand 80 110 60 Solve it by using the computer. LO.1
Solve the following linear programming problem:minimize Z = 3x11 + 12x12 + 8x13 + 10x21 + 5x22 + 6x23 + 6x31 + 7x32 + 10x33 subject to x11 + x12 + x13 = 90 x21 + x22 + x23 = 30 x31 + x32 + x33 = 100
Consider the following transportation problem:To (cost)From 1 2 3 Supply A $ 6 $ 9 $100 130 B 12 3 5 70 C 4 8 11 100 Demand 80 110 60 Formulate this problem as a linear programming model and solve it
A transportation problem involves the following costs, supply, and demand:To (cost)From 1 2 3 4 Supply 1 $500 $750 $300 $450 12 2 650 800 400 600 17 3 400 700 500 550 11 Demand 10 10 10 10 Solve this
=e. What conclusion do you draw about how sensitive the results from a computer simulation of a queueing system can be to the assumption made about the probability distribution of service times?
=Use computer simulation to refine the results obtained by queueing models as given by the Excel templates in the figures indicated below. Use a translated exponential distribution for the repair
=A key advantage of computer simulation over mathematical models is that it is not necessary to make simplifying approximations like this one. For example, one of the options available in the
=12.20. For the Dupit Corp. case study introduced in Section 11.4, the management science team was able to apply a variety of queueing models by making the following simplifying approximation.
=a. Repeat the simulation run that Fritz previously used to obtain Figure 12.9 (with a mean of 30 minutes for the interarrival-time distribution) except substitute this new distribution of haircut
=12.19. Consider the case study introduced in Section 12.2.After observing the operation of the barber shop, Herr Cutter’s nephew Fritz is concerned that his uncle’s estimate that the time
=Q*e. Management is considering the option of providing new inspection equipment to the inspectors. This equipment would not change the mean time to perform an inspection but it would decrease the
=Q*d. Use the Queueing Simulator to repeat parts b and c with 10,000 arrivals in each case.
=E*c. Repeat part b for the printers.
=E*b. Perform this simulation for the monitors over a period of 100 arrivals.
=E*a. Formulate a spreadsheet model to perform a computer simulation to estimate the average waiting times (both before beginning inspection and after completing inspection) for either the monitors
=12.18. Vistaprint produces monitors and printers for computers. In the past, only some of them were inspected on a sampling basis. However, the new plan is that they all will be inspected before
=E* g. Because both the interarrival-time and service-time distributions are exponential, the M/M/1 and M/M/s queueing models introduced in Sections 11.5 and 11.6 can be used to evaluate all the
=Q*f. Another option is to train the two current mechanics to work on either kind of car. This would increase the mean repair time by 10 percent, from 0.2 days to 0.22 days. Use the Queueing
=Q*e. Hugh is considering hiring a second mechanic who specializes in German cars so that two such cars can be repaired simultaneously. (Only one mechanic works on any one car.) Use the Queueing
=Q*d. Use the Queueing Simulator to do parts b and c with 10,000 car arrivals in each case.
=E*c. Repeat part b for Japanese cars.
=E*b. Perform this simulation for German cars over a period of 100 car arrivals.
=E*a. Formulate a spreadsheet model to perform a computer simulation to estimate what the average waiting time until repair is completed will be next year for either kind of car.
=12.17.* Hugh’s Repair Shop specializes in repairing German and Japanese cars. The shop has two mechanics. One mechanic works on only German cars and the other mechanic works on only Japanese cars.
=d. Suppose you were the manager of this bank. Use your computer simulation results as the basis for a managerial decision on how many tellers to provide.Justify your answer.
=Q*c. Now perform some sensitivity analysis by checking the effect if the level of business turns out to be even higher than projected. In particular, assume that the average time between customer
=Q*b. Repeat part a if three tellers are provided.
=Q*a. Use the Queueing Simulator with 5,000 customer arrivals to estimate the usual measures of performance for this queueing system if two tellers are provided.
=12.16. A major banking institution, Best Bank, plans to open a new branch office in Littletown. Preliminary estimates suggest that two tellers (and teller windows) should be provided, but this
=12.14. While performing a computer simulation of a singleserver queueing system, the number of customers in the system is zero for the first 10 minutes, one for the next 17 minutes, two for the
=a. Determine the new waiting time before beginning a haircut for each of the 5 customers who arrive in the first 100 minutes. Use these results to estimate Wq, the expected waiting time before the
=12.13. Refer to the first 100 minutes of the computer simulation of the current operation of Herr Cutter’s barber shop presented in Figure 12.7 and summarized in Figure 12.8. Now consider the
=E*d. Use the Excel template for the M/G/1 queueing model in this chapter’s Excel file to obtain the expected waiting time analytically for each of the three crew sizes. Which crew size should be
=Q*c. Use the Queueing Simulator to perform this computer simulation over 10,000 breakdowns for each of the three crew sizes.
=E*b. Formulate a spreadsheet model to perform a computer simulation to estimate the average waiting time before repair begins. Perform this simulation over a period of 100 breakdowns for each of
=a. Develop a simulation model for this problem by describing its six basic building blocks listed in Section 12.2 as they would be applied to this situation.
=12.12. The Rustbelt Manufacturing Company employs a maintenance crew to repair its machines as needed. Management now wants a computer simulation study done to analyze what the size of the crew
=12.11. The William Graham Entertainment Company will be opening a new box office where customers can come to make ticket purchases in advance for the many entertainment events being held in the
=E*e. Formulate a spreadsheet model to apply the method of complementary random numbers described in partc. Use 600 random numbers and their complements to generate 600 random observations of the
=d. The true mean of the overall probability distribution of repair times is 1.1. Compare the estimates of this mean obtained in partsa, b, andc. For the method that provides the closest estimate,
=c. Combine the random observations from parts a and b and calculate the average of these six observations to estimate the mean of the overall distribution of repair times. (This is referred to as
=a. Use the random numbers 0.7256, 0.0817, and 0.4392 to simulate whether each of three bicycles requires minor repair or major repair. Then use the random numbers 0.2243, 0.9503, and 0.6104 to
=12.10.* Reconsider Eddie’s Bicycle Shop described in the preceding problem. Forty percent of the bicycles require only a minor repair. The repair time for these bicycles has a uniform
=E*c. Use Excel to generate 500 random observations and calculate the average. Compare this average to the mean of the service-time distribution.
=b. Calculate the average of the five service times and compare it to the mean of the service-time distribution.
=12.9. Eddie’s Bicycle Shop has a thriving business repairing bicycles. Trisha runs the reception area where customers check in their bicycles to be repaired and then later pick up their bicycles
=12.7. Generate three random observations from the uniform distribution between 10 and 40 by using the following random numbers: 0.0965, 0.5692, 0.6658.
=E*e. Formulate a spreadsheet model for performing a computer simulation of the daily sales. Perform 300 replications and obtain the average of the sales over the 300 simulated days.
=d. Use the random numbers 0.4476, 0.9713, and 0.0629 to simulate daily sales over three days. Compare the average with the mean obtained in part b.
=c. Describe how random numbers can be used to simulate daily sales.
=b. Calculate the mean of the distribution obtained in part a.
=a. Use these data to estimate the probability distribution of daily sales.
=12.6. Jessica Williams, manager of kitchen appliances for the Midtown Department Store, feels that her inventory levels of stoves have been running higher than necessary. Before revising the
=E*b. Perform 25 replications of this simulation.c. Trace through these 25 replications to determine the number of times the simulated player would have won the game of craps when each play starts
=E*a. Formulate a spreadsheet model for performing a computer simulation of the throw of two dice. Perform one replication.
=12.5.* The game of craps requires the player to throw two dice one or more times until a decision has been reached as to whether he (or she) wins or loses. He wins if the first throw results in a
=E*b. Now use a computer with the random numbers generated by Excel to perform the simulation requested in part a on a spreadsheet.
=12.1 to simulate the evolution of the weather for 10 days, beginning the day after a clear day.

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