Question: On December 16, 1944, in the last
On December 16, 1944, in the last year of World War II, two German panzer armies, supported by a third army of infantry, together totaling more than 250,000 men, staged a massive counteroffensive in northern France, overwhelming the American First Army in the Ardennes. The offensive emanated from the German defensive line along the Our River, north of the city of Luxembourg and was directed almost due west toward Namur and Liége in Belgium. The result, after several days of fighting, was a huge “bulge†in the Allied line and, therefore, this last major ground battle of World War II became known as the Battle of the Bulge.
On December 20, General Dwight D. Eisenhower, Supreme Allied Commander, called on General George Patton to attack the German offensive with his Third Army, which was then situated near Verdun, approximately 100 miles due south of the German left flank. Patton’s immediate objective was to relieve the 101st Airborne and elements of Patton’s own 9th and 10th Armored Divisions surrounded at Bastogne. Within 48 hours, on December 22, Patton was able to begin his counteroffensive, with three divisions total- ing approximately 62,000 men.
The winter weather was cold with snow and fog, and the roads were icy, making the movement of troops, tanks, sup- plies, and equipment a logistical nightmare. Nevertheless, on December 26 Bastogne was relieved, and on January 12, 1945, the Battle of the Bulge effectively ended in one of the great Allied victories of the war.
General Patton’s staff did not have knowledge of the maximal flow technique nor access to computers to help plan the Third Army’s troop movements during the Battle of the Bulge. However, the figure on the following page shows the road network between Verdun and Bastogne, with (imagined) troop capacities (in thousands) along each road branch between towns. Using the maximal flow technique (and your imagination), determine the number of troops that should be sent along each road to get the maximum number of troops to Bastogne. Also indicate the total number of troops that would be able to get to Bastogne.
> The emergency room of the community hospital in Farmburg has one receptionist, one doctor, and one nurse. The emergency room opens at time zero, and patients begin to arrive some time later. Patients arrive at the emergency room according to the followin
> Compcomm, Inc., is an international communications and information technology company that has seen the value of its common stock appreciate substantially in recent years. A stock analyst would like to use simulation to predict the stock prices of Compco
> A robbery has just been committed at the Corner Market in the downtown area of the city. The market owner was able to activate the alarm, and the robber fled on foot. Police officers arrived a few minutes later and asked the owner, “How long ago did the
> The Paymore Rental Car Agency rents cars in a small town. It wants to determine how many rental cars it should maintain. Based on market projections and historical data, the manager has determined probability distributions for the number of rentals per d
> Christine Yamaguchi is the manager of the A-to-Z Office Supply Company in Charlotte. The company attempts to gain an advantage over its competitors by providing quality customer service, which includes prompt delivery of orders by truck or van and always
> Loebuck Grocery orders milk from a dairy on a weekly basis. The manager of the store has developed the following probability distribution for demand per week (in cases): The milk costs the grocery $10 per case and sells for $16 per case. The carrying cos
> A city is served by two newspapers—the Tribune and the Daily News. Each Sunday readers purchase one of the newspapers at a stand. The following matrix contains the probabilities of a customer’s buying a particular news
> Each semester, the students in the college of business at State University must have their course schedules approved by the college adviser. The students line up in the hallway outside the adviser’s office. The students arrive at the of
> University is playing Tech in their annual football game on Saturday. A sportswriter has scouted each team all season and accumulated the following data: State runs four basic plays—a sweep, a pass, a draw, and an off tackle; Tech uses
> A hypermarket sells a specific brand of mobile phones and earns a profit of AED100 per mobile. It incurs a holding cost of AED40 per mobile per month if a stocked mobile is not sold. Holding cost is a portion of rent, insurance, and other expenses. If th
> The Hoylake Rescue Squad receives an emergency call every 1, 2, 3, 4, 5, or 6 hours, according to the following probability distribution. The squad is on duty 24 hours per day, 7 days per week: a. Simulate the emergency calls for 3 days (note that this w
> A small grocery market has one checkout counter. The counter clerk takes an average of 3 minutes to serve a customer. Customers arrive at the counter at the rate of 15 per hour. The manager of the store receives feedback from customers that the wait time
> A gas station at a busy highway offers free air service for tires of cars that use the pump. The attendant checks tire pressure and inflates or deflates to the recommeded level. On an average, the attendant takes 2 minutes to check one car. Cars arrive f
> The management of Dynaco Manufacturing Company (see Problem 6) likes to have its operators working 90% of the time. What must the assembly line arrival rate be for the operators to be as busy as management would like?
> The Dynaco Manufacturing Company produces a particular product in an assembly line operation. One of the machines on the line is a drill press that has a single assembly line feeding into it. A partially completed unit arrives at the press to be worked o
> The Fort Worth Texans have won three Super Bowls in the past 5 years, including two in a row the past 2 years. As a result, sportswear such as hats, sweatshirts, sweatpants, and jackets with the Texans logo are particularly popular in Texas. The Texans o
> The Old Colony theme park has a new ride, the Double Cyclone. The ride holds 30 people in double roller coaster cars, and it takes 3.8 minutes to complete the ride circuit. It also takes the ride attendants another 3 minutes (with virtually no variation)
> The Hampton County emergency medical service (EMS) covers an area of 500 square miles with a population of over 100,000. In addition to ambulances and fire engines, the EMS is considering purchased three quick response vehicles—SUVs equipped with medical
> A laundry machine at a laundromat operates for 8 hours a day. The time between customer arrivals on average is 25 minutes. Each machine takes an average of 60 minutes (exponentially distributed) to wash and dry a batch of clothes. The manager wants the a
> In Problem 51, the passenger traffic arriving at the airport security gate varies significantly during the day. At times close to flight takeoffs, the traffic is very heavy, while at other times there is little or no passenger traffic through the securit
> In Problem 24, when the students come back for fall semester, the Sub Shop experiences a large increase in demand for about a month before it begins to level off again, such that the number of phone orders increases to an average of 8 per hour (Poisson d
> Refer to Problem 52. The clinic does not want to add a fourth doctor but plans to increase the efficiency of the existing doctors. By proper training and innovative adoption of technologies, doctors can attend up to 40 patients a day. If the arrival rate
> A renowned healthcare provider, Mediclinic, has a branch in Marina, Dubai. The clinic remains open for 8 hours a day. At present, three doctors are available to attend arriving patients. Each doctor can serve 32 patients per day (exponentially distribute
> TSA security agents at the security gate at the Tri-Cities Regional Airport are able to check passengers and process them through the security gate at a rate of 50 per hour (Poisson distributed). Passengers arrive at the gate throughout the day at a rate
> Judith Lewis is a doctoral student at State University, and she also works full-time as an academic tutor for 10 scholarship student athletes. She took the job, hoping it would leave her free time between tutoring to devote to her own studies. An athlete
> Starbucks Café at the cafeteria of a university has a single attendant who receives orders from the arriving students and passes the orders to its serviceman who prepares and delivers the ordered items to the students. The serviceman at the café can serv
> The Northwoods General Store in Vermont sells a variety of outdoor clothing items and equipment and several food products at its modern but rustic-looking retail store. Its food products include salmon and maple syrup. The store also runs a lucrative cat
> Jim Carter builds custom furniture, primarily cabinets, bookcases, small tables, and chairs. He works on only one piece of furniture for a customer at a time. It takes him an average of 5 weeks (exponentially distributed) to build a piece of furniture. A
> The Delacroix Inn in Alexandria is a small, exclusive hotel with 20 rooms. Guests can call house- keeping from 8:00 A.M. to midnight for any of their service needs. Housekeeping keeps one person on duty during this time to respond to guest calls. Each ro
> Ships arrive at the port of Savannah at the rate of 40 per 30-day month (Poisson distributed), generally with a full cargo of containers. It takes an average of 12 hours (exponentially distributed) to unload and load an average size container ship. Curre
> The Clip Joint is a hairstyling salon at University Mall. Four stylists are always available to serve customers on a first-come, first-served basis. Customers arrive at an average rate of 5 per hour, and the stylists spend an average of 35 minutes on eac
> The Waterfall Buffet in the lower level of the National Art Gallery serves food cafeteria-style daily to visitors and employees. The buffet is self-service. From 7:00 A.M. to 9:00 A.M. customers arrive at the buffet at a rate of 10 per minute; from 9:00
> Dubai airport has three immigration officers that inspect arriving tourists’ travel documents and permit them to enter the country if their visa is genuine. Each officer can check 20 tourists per hour (exponentially distributed). On an average, a tourist
> Partially completed products arrive at a workstation in a manufacturing operation at a mean rate of 40 per hour (Poisson distributed). The processing time at the workstation averages 1.2 minutes per unit (exponentially distributed). The manufacturing com
> Amanda Fall is starting up a new house painting business, Fall Colors. She has been advertising in the local newspaper for several months. Based on inquiries and informal surveys of the local housing market, she anticipates that she will get painting job
> Hudson Valley Books is a small, independent publisher of fiction and nonfiction books. Each week the publisher receives an average of seven unsolicited manuscripts to review (Poisson distributed). The publisher has 12 freelance reviewers in the area who
> The Escargot is a small French restaurant with six waiters and waitresses. The average service time at the restaurant for a table (of any size) is 85 minutes (Poisson distributed). The restaurant does not take reservations, and parties arrive for dinner
> Since the terrorist attacks of 9/11 and because of the ensu- ing measures to increase airline security, airports have faced the problem of long waiting lines and waiting times at secu- rity gates. Waiting lines can be as long as hundreds of yards, and wa
> The ticket booth on the Tech campus is operated by one person, who is selling tickets for the annual Tech versus State football game on Saturday. The ticket seller can serve an average of 12 customers per hour; on average, 10 customers arrive to purchase
> Maggie Attaberry is a nurse on the evening shift from 10:00 p.M. to 6:00 A.M. at Community Hospital. She has 15 patients for whom she is responsible in her area. She averages two calls from each of her patients every evening, on average (Poisson distribu
> In Problem 37, suppose that Moore’s television repair service cannot accommodate more than 30 TV sets at a time. What is the probability that the number of TV sets on hand (under repair and waiting for service) will exceed the shop capacity?
> Moore’s television repair service receives an average of six TV sets per 8-hour day to be repaired. The service manager would like to be able to tell customers that they can expect 1-day service. What average repair time per set will the repair shop have
> When customers arrive at Gilley’s Ice Cream Shop, they take a number and wait to be called to purchase ice cream from one of the counter servers. From experience in past summers, the store’s staff knows that customers arrive at a rate of 40 per hour on s
> The Footrite Shoe Company is going to open a new branch at a mall, and company managers are attempting to determine how many salespeople to hire. Based on an analysis of mall traffic, the company estimates that customers will arrive at the store at a rat
> The Riverview Clinic has two general practitioners who see patients daily. An average of six patients arrive at the clinic per hour. Each doctor spends an average of 15 minutes with a patient. The patients wait in a waiting area until one of the two doct
> Customers arrive to check in at the exclusive and expensive Regency Hotel’s lobby at a rate of 40 per hour (Poisson distributed). The hotel normally has three clerks available at the desk to check in guests. The average time for a clerk to check in a gue
> From 3:00 p.M. to 8:00 p.M. the local K-Star Supermarket has a steady stream of customers. Customers finish shopping and arrive at the checkout area at a rate of 70 per hour (Poisson distributed). It is assumed that when customers arrive at the cash regi
> The local Burger Doodle fast-food restaurant has a drive-through window. Customers in cars arrive at the window at the rate of 10 per hour (Poisson distributed). It requires an average of 4 minutes (exponentially distributed) to take and fill an order. T
> The Valley Swim Club has 300 stockholders, each holding one share of stock in the club. A share of club stock allows the shareholder’s family to use the club’s heated outdoor pool during the summer, upon payment of ann
> The Regency Hotel has enough space at its entrance for six taxicabs to line up, wait for guests, and then load passengers. Cabs arrive at the hotel every 8 minutes; if a taxi drives by the hotel and the line is full, it must drive on. Hotel guests requir
> A single-server queuing system with an infinite calling population and a first-come, first-served queue discipline has the following arrival and service rates (Poisson distributed): = 16 customers per hour = 24 customers per hour Determine P0, P3, L,
> A company has 20 computers in its office in Johannesburg. Though the computers are brand new, they do fail and this affects the company’s work. A computer crashes every 25 days. The company estimates that it loses R10,000 a day from a faulty computer. Si
> The associate dean of the college of business at Tech is determining which of two copiers he should lease for the college’s administrative suite. A regular copier leases for $8 per hour, and it takes an employee an average of 6 minutes (exponentially dis
> Cakes baked by the Freshfood Bakery are transported from the ovens to be packaged by one of three wrappers. Each wrapper can wrap an average of 200 cakes per hour. The cakes are brought to the wrappers at the rate of 500 per hour. If a cake sits longer t
> In Problem14 , the Dynaco Company has found that if more than three units (average) are waiting to be processed at any one workstation, then too much money is being tied up in work-in-process inventory (i.e., units waiting to be processed). The company e
> The Riverton Post Office has four stations for service. Customers line up in single file for service on a FIFO basis. The mean arrival rate is 40 per hour, Poisson distributed, and the mean service time per server is 4 minutes, exponentially distributed.
> The College Avenue Sub Shop is located in a small college town. Virtually all of its phone delivery orders are in the evening, between 5:00 p.M. and 1:00 A.M., so the shop has a delivery person for that time period. It receives an average of about 3 orde
> In Problem 10, in addition to course approvals, suppose that the advisor also answers questions and provides course counseling, such that the service time can no longer be assumed to be exponentially distributed. Instead, the service time distribution is
> The Rowntown Cab Company has four cabs that are on duty during normal business hours. The cab company dispatcher receives requests for service every 8 minutes, on average, according to an exponential distribution. The average time to complete a trip is 2
> The University Bookstore is owned and operated by State University through an independent corporation with its own board of directors. The bookstore has three locations on or near the State University campus. It stocks a range of items, including textboo
> The Bay City Police Department has eight patrol cars that are on constant call 24 hours per day. A patrol car requires repairs every 20 days, on average, according to an exponential distribution. When a patrol car is in need of repair, it is driven into
> NesCafé has installed a coffee vending machine at an airport. The installed vending machine has the capacity to dispense 25 cups of coffee per hour. Currently, the demand for coffee on average is 22 cups per hour. NesCafé has noticed through its sales th
> In the Fast Shop Market example in this chapter, Alternative II was to add a new checkout counter at the market. This alternative was analyzed using the single-server model. Why was the multiple- server model not used?
> A vending machine at City Airport dispenses hot coffee, hot chocolate, or hot tea, in a constant service time of 20 seconds. Customers arrive at the vending machine at a mean rate of 60 per hour (Poisson distributed). Determine the average length of the
> An ATM at a busy airport disburses money or accepts deposits from customers. The ATM takes a constant time of 2 minutes to accept instructions and complete a transaction. If customers arrive at the rate of 20 per hour (Poisson distributed), a. Determine
> Game World, a video game arcade at Tanglewood Mall, has just installed a new virtual reality battle game. It requires exactly 2.7 minutes to play. Customers arrive, on average, every 2.9 minutes (Poisson distributed) to play the game. How long will the l
> McBurger’s fast-food restaurant has a drive-through window with a single server who takes orders from an intercom and also is the cashier. The window operator is assisted by other employees who prepare the orders. Customers arrive at the ordering station
> The Acme Machine Shop has five machines that periodically break down and require service. The average time between breakdowns is 4 days, distributed according to an exponential distribution. The average time to repair a machine is 1 day, distributed acco
> The Dynaco Manufacturing Company has an assembly line that feeds two drill presses. As partially completed products come off the line, they are lined up to be worked on as drill presses become available. The units arrive at the workstation (containing bo
> In Problem 10, the dean of the college of business at State University is considering the addition of a second adviser in the college advising office to serve students waiting to have their schedules approved. This new adviser could serve the same number
> During the past few years, the legislature has severely reduced funding for State University. In reaction, the administration at State has significantly raised tuition each year for the past 5 years. Perceived as a bargain 5 years ago, State is now consi
> In Problem 11, suppose passing truck drivers look to see how many trucks are waiting to be weighed at the weigh station. If they see four or more trucks in line, they will pass by the station and risk being caught and ticketed. What is the probability th
> All trucks traveling on Interstate 40 between Albuquerque and Amarillo are required to stop at a weigh station. Trucks arrive at the weigh station at a rate of 200 per 8-hour day, and the station can weigh, on the average, 220 trucks per day. a. Determin
> During registration at State University every semester, students in the college of business must have their courses approved by the college adviser. It takes the adviser an average of 2 minutes to approve each schedule, and students arrive at the adviser
> For each of the following queuing systems, indicate whether it is a single- or multiple-server model, the queue discipline, and whether its calling population is infinite or finite. a. Hair salon b. Bank c. Laundromat d. Doctor’s office e. Adviser’s offi
> A television network is attempting to decide during the summer which of the following three football games to televise on the Saturday following Thanksgiving Day: Alabama versus Auburn, Georgia versus Georgia Tech, or Army versus Navy. The estimated view
> A local real estate investor in Orlando is considering three alternative investments: a motel, a restaurant, or a theater. Profits from the motel or restaurant will be affected by the availability of gasoline and the number of tourists; profits from the
> The owner of the Columbia Construction Company must decide between building a housing development, constructing a shopping center, and leasing all the company’s equipment to another company. The profit that will result from each alterna
> Labran Jones has played for the Cleveland professional basketball team for the past eight seasons and has established himself as one of the top players in the league. He has recently become a free agent, meaning he can sign a new contract with Cleveland
> Annie Hays recently sold a condominium she had bought and lived in while she was a college student over 15 years ago. She received $150,000 for the condominium and is considering two investment alternatives. Annie can invest the entire amount in a bank m
> A young couple has $5,000 to invest in either savings bonds or a real estate deal. The expected return on each investment, given good and bad economic conditions, is shown in the following payoff table: The expected value of investing in savings bonds is
> Concerned about recent weather-related disasters, fires, and other calamities at universities around the country, university administrators at Tech have initiated several planning projects to determine how effectively local emergency facilities can handl
> The Place-Plus real estate development firm in Problem 26 is dissatisfied with the economist’s estimate of the probabilities of future interest rate movement, so it is considering having a financial consulting firm provide a report on future interest rat
> In Problem 14, the management of the Oakland Bombers is considering hiring superscout Jerry McGuire to evaluate the team’s chances for the coming season. McGuire will evaluate the team, assuming that it will sign one of the four free agents. The team’s m
> In Problem 61, the decision analysis is for automobiles and light trucks. Blue Ridge Power and Light would like to reformulate the problem for its heavy construction equipment. Emergency maintenance is much more expensive for heavy equipment, costing $15
> Blue Ridge Power and Light is an electric utility company with a large fleet of vehicles, including automobiles, light trucks, and construction equipment. The company is evaluating four alternative strategies for maintaining its vehicles at the lowest co
> Ellie Daniels has $200,000 and is considering three mutual funds for investment—a global fund, an index fund, and an Internet stock fund. During the first year of investment, Ellie estimates that there is a .70 probability that the mark
> A company must decide now which of three products to make next year to plan and order proper materials. The cost per unit of producing each product will be determined by whether a new union labor contract passes or fails. The cost per unit for each produ
> In Problem 58, determine the expected value of sample information (EVSI; i.e., the test market value) and the expected value of perfect information (EVPI).
> Kroft Food Products is attempting to decide whether it should introduce a new line of salad dressings called Special Choices. The company can test market the salad dressings in selected geographic areas or bypass the test market and introduce the product
> A car manufacturer buys fasteners such as bolts and nuts for its cars. On an average, the company buys 1 million such pairs per month. The company inspects the arriving lots and transfers the lots to its store yard. The price that Suppliers A and B charg
> Tech has three health care plans for its faculty and staff to choose from, as follows: Plan 1—monthly cost of $32, with a $500 deductible; the participants pay the first $500 of medical costs for the year; the insurer pays 90% of all re
> The U.S. Army Corps of Engineers has historically constructed dams on various rivers in the southeastern United States. Its primary instrument for evaluating and selecting among many projects under consideration is benefit–cost analysis
> Jay Seago is suing the manufacturer of his car for $3.5 million because of a defect that he believes caused him to have an accident. The accident kept him out of work for a year. The company has offered him a settlement of $700,000, of which Jay would re
> Tech is playing State in the last conference game of the season. Tech is trailing State 21 to 14, with 7 seconds left in the game, when Tech scores a touchdown. Still trailing 21 to 20, Tech can either go for 2 points and win or go for 1 point to send th
> If Suntrek, in Problem 36, wants to hire a supply chain analyst to help it determine more accurately what future logistics costs will be, what is the maximum amount they should pay the analyst?
> In Problems 10 and 23, Ann Tyler is considering hiring a financial analyst to help her determine the best investment. What is the maximum amount she should pay an analyst?
> Jeffrey Mogul is a Hollywood film producer, and he is currently evaluating a script by a new screenwriter and director, Betty Jo Thurston. Jeffrey knows that the probability of a film by a new director being a success is about .10 and that the probabilit
> Refer to Problem 43. Volkswagen considers hiring a consultant. If a consultant helps Volkswagen by giving perfect information, what is the expected value of perfect information?
> A farmer in Georgia must decide which crop to plant next year on his land: corn, peanuts, or soybeans. The return from each crop will be determined by whether a new trade bill with Russia passes the Senate. The profit the farmer will realize from each cr
