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Operations Management Sustainability And Supply Chain Management Global Edition 12th Edition Jay Heizer, Barry Render, Chuck Munson - Solutions
One mechanic services 5 drilling machines for a steel plate manufacturer. Machines break down on an average of once every 6 working days, and breakdowns tend to follow a Poisson distribution. The mechanic can handle an average of one repair job per day. Repairs follow a negative exponential
A technician monitors a group of 5 computers that run an automated manufacturing facility. It takes an average of 15 minutes (negative exponentially distributed) to adjust a computer that develops a problem. On average, one of the computers requires adjustment every 85 minutes. Determine the
Renuka Jain’s Car Wash takes a constant time o 4.5 minutes in its automated car wash cycle. Autos arrive following a Poisson distribution at the rate of 10 per hour. Renuka wants to know:a) The average waiting time in line.b) The average length of the line 17 Debra Bishop’s cabinet-making shop,
The typical subway station in Washington, DC, has six turnstiles, each of which can be controlled by the station manager to be used for either entrance or exit control—but never for both. The manager must decide at different times of the day how many turnstiles to use for entering passengers and
Altug’s Coffee Shop decides to install an automatic coffee vending machine outside one of its stores to reduce the number of people standing in line inside. Mehmet Altug charges$3.50 per cup. However, it takes too long for people to make change. The service time is a constant 3 minutes, and the
Janson’s Department Store in Stark, Ohio, maintains a successful catalog sales department in which a clerk takes orders by telephone. If the clerk is occupied on one line, incoming phone calls to the catalog department are answered automatically by a recording machine and asked to wait. As soon
The wheat harvesting season in the American Midwest is short, and farmers deliver their truckloads of wheat to a giant central storage bin within a 2-week span. Because of this, wheatfilled trucks waiting to unload and return to the fields have been known to back up for a block at the receiving
Bill Youngdahl has been collecting data at the TU student grill. He has found that, between 5:00 p.m. and 7:00 p.m., students arrive at the grill at a rate of 25 per hour (Poisson distributed) and service time takes an average of 2 minutes (negative exponential distribution). There is only 1
Each of the eight auditoriums plays a different film; the schedule staggers starting times to avoid the large crowds that would occur if all four movies started at the same time. The theater has a single ticket booth and a cashier who can maintain an average service rate of 280 patrons per hour.
Beate Klingenberg manages a Poughkeepsie, New York, movie theater complex called Cinema
Neve Commercial Bank is the only bank in the town of York, Pennsylvania. On a typical Friday, an average of 10 customers per hour arrive at the bank to transact business. There is currently one teller at the bank, and the average time required to transact business is 4 minutes. It is assumed that
Virginia’s Ron McPherson Electronics Corporation retains a service crew to repair machine breakdowns that occur on average l 5 3 per 8-hour workday (approximately Poisson in nature). The crew can service an average of m 5 8 machines per workday, with a repair time distribution that resembles the
Automobiles arrive at the drive-through window at the downtown Baton Rouge, Louisiana, post office at the rate of 4 every 10 minutes. The average service time is 2 minutes. The Poisson distribution is appropriate for the arrival rate and service times are negative exponentially distributed.a) What
Calls arrive at Lynn Ann Fish’s hotel switchboard at a rate of 2 per minute. The average time to handle each is 20 seconds. There is only one switchboard operator at the current time.The Poisson and negative exponential distributions appear to be relevant in this situation.a) What is the
The pharmacist at Arnold Palmer Hospital, Wende Huehn-Brown, receives 12 requests for prescriptions each hour, Poisson distributed. It takes her a mean time of 4 minutes to fill each, following a negative exponential distribution. Use the waitingline table, Table D.5 , and W q 5 L q>l , to answer
Dr. Tarun Gupta, a Michigan vet, is running a rabies vaccination clinic for dogs at the local grade school. Tarun can“shoot” a dog every 3 minutes. It is estimated that the dogs will arrive independently and randomly throughout the day at a rate of one dog every 6 minutes according to a Poisson
Paul Fenster owns and manages a chili-dog and softdrink stand near the Kean U. campus. While Paul can service 30 customers per hour on the average (m), he gets only 20 customers per hour (l). Because Paul could wait on 50% more customers than actually visit his stand, it doesn’t make sense to him
There is only one copying machine in the student lounge of the business school. Students arrive at the rate of l 5 40 per hour (according to a Poisson distribution). Copying takes an average of 40 seconds, or m 5 90 per hour (according to a negative exponential distribution). Compute the
Customers arrive at Rich Dunn’s Styling Shop at a rate of 3 per hour, distributed in a Poisson fashion. Rich’s service times follow a negative exponential distribution, and Rich can complete an average of 5 haircuts per hour.a) Find the average number of customers waiting for haircuts.b) Find
Why is Little’s Law a useful queuing concept?
What dollar value do you place on yourself per hour that you spend waiting in lines? What value do your classmates place on themselves? Why do the values differ?
What happens if two single-server systems have the same mean arrival and service rates, but the service time is constant in one and exponential in the other?
Do doctors’ offices generally have random arrival rates for patients? Are service times random? Under what circumstances might service times be constant?
What are the components of the following queuing systems?Draw and explain the configuration of each.a) Barbershopb) Car washc) Laundromatd) Small grocery store
Provide examples of four situations in which there is a limited, or finite, waiting line.
Discuss the likely outcome of a waiting line system where m . l but only by a tiny amount (e.g., m 5 4.1, l 5 4).
Describe the behavior of a waiting line where l . m. Use both analysis and intuition.
Briefly describe three situations in which the first-in, first-out(FIFO) discipline rule is not applicable in queuing analysis.
Which is larger, W s or W q ? Explain.
Describe what is meant by the waiting-line terms balk and renege . Provide an example of each.
Is it good or bad to operate a supermarket bakery system on a strict first-come, first-served basis? Why?
State the assumptions of the “basic” single-server queuing model (Model A, or M/M/1).
State the seven common measures of queuing system performance.
Name the three factors that govern the structure of “arrivals”in a queuing system.
When designing a waiting line system, what “qualitative”concerns need to be considered?
Name the three parts of a typical queuing system.
If a solution to a transportation problem is degenerate, then:a) it will be impossible to evaluate all empty cells without removing the degeneracy.b) a dummy row or column must be added.c) there will be more than one optimal solution.d) the problem has no feasible solution.e) increase the cost of
The purpose of a dummy source or a dummy destination in a transportation problem is to:a) provide a means of representing a dummy problem.b) obtain a balance between total supply and total demand.c) prevent the solution from becoming degenerate.d) make certain that the total cost does not exceed
The purpose of the stepping-stone method is to:a) develop the initial solution to a transportation problem.b) identify the relevant costs in a transportation problem.c) determine whether a given solution is feasible.d) assist one in moving from an initial feasible solution to the optimal
With the transportation technique, the initial solution can be generated in any fashion one chooses. The only restriction(s)is that:a) the solution be optimal.b) one use the northwest-corner method.c) the edge constraints for supply and demand be satisfied.d) the solution not be degenerate.e) all
Explain what is meant by the term degeneracy within the context of transportation modeling.
How can the transportation method address production costs in addition to transportation costs?
Explain the significance of a negative improvement index in a transportation-minimizing problem.
How many occupied cells must all solutions use?
What is meant by an unbalanced transportation problem, and how would you balance it?
Develop a northeast -corner rule and explain how it would work. Set up an initial solution for the Arizona Plumbing problem analyzed in Example C1.
All of the transportation examples appear to apply to long distances. Is it possible for the transportation model to apply on a much smaller scale, for example, within the departments of a store or the offices of a building? Discuss.
The more sources and destinations there are for a transportation problem, the smaller the percentage of all cells that will be used in the optimal solution. Explain.
Which starting technique generally gives a better initial solution, and why?
How do you know when an optimal solution has been reached?
Identify the three “steps” in the northwest-corner rule.
What are the steps in the intuitive lowest-cost method?
What are the three information needs of the transportation model?
When applying LP to diet problems, the objective function is usually designed to:a) maximize profits from blends of nutrients.b) maximize ingredient blends.c) minimize production losses.d) maximize the number of products to be produced.e) minimize the costs of nutrient blends.
For these two constraints, which point is in the feasible region of this minimization problem?14x + 6y Ú 42 and x + y Ú 3a) x = -1, y = 1b) x = 0, y = 4c) x = 2, y = 1d) x = 5, y = 1e) x = 2, y = 0
A zero shadow price for a resource ordinarily means that:a) the resource is scarce.b) the resource constraint was redundant.c) the resource has not been used up.d) something is wrong with the problem formulation.e) none of the above.
Consider the following linear programming problem:Maximize 4X + 10Y Subject to: 3X + 4Y … 480 4X + 2Y … 360 X, Y Ú 0 The feasible corner points are (48,84), (0,120), (0,0), and (90,0). What is the maximum possible value for the objective function?a) 1,032b) 1,200c) 360d) 1,600e) 840
Using a graphical solution procedure to solve a maximization problem requires that we:a) move the iso-profit line up until it no longer intersects with any constraint equation.b) move the iso-profit line down until it no longer intersects with any constraint equation.c) apply the method of
Which of the following is not a valid LP constraint formulation?a) 3X + 4Y … 12b) 2X * 2Y … 12c) 3Y + 2Z = 18d) 100 Ú X + Ye) 2.5X + 1.5Z = 30.6
Estimate the direct costs to the airline should the crew “time out” and not be able to fly its Boeing 737 back to Seattle from Chicago on the same day. These direct variable costs should include moving and parking the plane overnight along with hotel and meal costs for the crew and passengers.
What were the risks of keeping the same crew on the Seattle—Chicago—Seattle route?
What operational considerations may prohibit Alaska from adding flights and more cities to its network?
Why is scheduling for Alaska more complex than for other airlines?
Solve to find the best solution.
Formulate an LP problem to determine what blend of the four chemicals will allow Quain to minimize the cost of a 50-lb bag of the fertilizer.
Porter Investments needs to develop an investment portfolio for Mrs. Singh from the following list of possible investments:Mrs. Singh has a total of $60,000 to invest. The following conditions must be met: (1) If investment F is chosen, then investment G must also be part of the portfolio, (2) at
You have just been hired as a planner for the municipal school system, and your first assignment is to redesign the subsidized lunch program. In particular, you are to formulate the least expensive lunch menu that will still meet all state and federal nutritional guidelines.The guidelines are as
The donkey driver Donky King is using a donkey to carry goods from the harbor city to a village up in the mountains.The people living in the village are willing to buy gold, silk, salt and sponge. Donky King is able to earn 500 € for each gold bullion, 200 €for each roll of silk, 150 for each
Leach Distributors packages and distributes industrial supplies. A standard shipment can be packaged in a class A container, a class K container, or a class T container. A single class A container yields a profit of $9; a class K container, a profit of $7;and a class T container, a profit of $15.
Wichita’s famous Sethi Restaurant is open 24 hours a day. Servers report for duty at 3 a.m., 7 a.m., 11 a.m., 3 p.m., 7 p.m., or 11 p.m., and each works an 8-hour shift. The following table shows the minimum number of workers needed during the 6 periods into which the day is divided:Owner Avanti
The Rio Credit Union has $250,000 available to invest in a 12-month commitment. The money can be placed in Brazilian treasury notes yielding an 8% return or in riskier high-yield bonds at an average rate of return of 9%. Credit union regulations require diversification to the extent that at least
The Hills County, Michigan, superintendent of education is responsible for assigning students to the three high schools in his county. He recognizes the need to bus a certain number of students, because several sectors, A–E, of the county are beyond walking distance to a school. The
A tailor sews dresses and suits. For a suit the tailor uses 3 m 2 of wool and 1 m 2 of cotton. For a dress the tailor uses 2 m 2 of wool and 2 m 2 of cotton. The tailor has 80 m 2 of cotton and 120 m 2 of wool in storage. How many dresses and suits will be tailor to be able to maximize his profit
Solve the following linear programming problem graphically:
Consider Paul Jordan’s following linear programming formulation:a) Graphically illustrate the feasible region to indicate to Jordan which corner point produces the optimal solution.b) What is the cost of this solution?
The Sweet Smell Fertilizer Company markets bags of manure labeled “not less than 60 lb dry weight.” The packaged manure is a combination of compost and sewage wastes. To provide good-quality fertilizer, each bag should contain at least 30 lb of compost but no more than 40 lb of sewage. Each
Doug Turner Food Processors wishes to introduce a new brand of dog biscuits composed of chicken- and liver-flavored biscuits that meet certain nutritional requirements. The liver-flavored biscuits contain 1 unit of nutrient A and 2 units of nutrient B;the chicken-flavored biscuits contain 1 unit of
Solve the following LP problem graphically:
Solve the following linear program graphically:
A fertilizer manufacturer has to fulfill supply contracts to its two main customers (650 tons to Customer A and 800 tons to Customer B). It can meet this demand by shipping existing inventory from any of its three warehouses. Warehouse 1 (W1)has 400 tons of inventory on hand, Warehouse 2 (W2) has
Kalyan Singhal Corp. makes three products, and it has three machines available as resources as given in the following LP problem:
Baton Rouge’s Mt. Cedar Hospital is a large, private, 600-bed facility complete with laboratories, operating rooms, and X-ray equipment. In seeking to increase revenues, Mt. Cedar’s administration has decided to make a 90-bed addition on a portion of adjacent land currently used for staff
The Denver advertising agency promoting the new Breem dishwashing detergent wants to get the best exposure possible for the product within the $100,000 advertising budget ceiling placed on it. To do so, the agency needs to decide how much of the budget to spend on each of its two most effective
Par, Inc., produces a standard golf bag and a deluxe golf bag on a weekly basis. Each golf bag requires time for cutting and dyeing and time for sewing and finishing, as shown in the following table:
Each coffee table produced by Kevin Watson Designers nets the firm a profit of $9. Each bookcase yields a $12 profit. Watson’s firm is small and its resources limited. During any given production period (of 1 week), 10 gallons of varnish and 12 lengths of high-quality redwood are available. Each
A craftsman named William Barnes builds two kinds of birdhouses, one for wrens and a second for bluebirds.Each wren birdhouse takes 4 hours of labor and 4 units of lumber. Each bluebird house requires 2 hours of labor and 12 units of lumber. The craftsman has available 60 hours of labor and 120
Consider the following LP problem developed at Zafar Malik’s Carbondale, Illinois, optical scanning firm:Maximize profit = +1X1 + +1X2 Subject to: 2X1 + 1X2 … 100 1X1 + 2X2 … 100a) What is the optimal solution to this problem? Solve it graphically.b) If a technical breakthrough occurred that
The firm employs 5 technicians, working 160 hours each per month, on its assembly line. Management insists that full employment(that is, all 160 hours of time) be maintained for each worker during next month’s operations. It requires 20 labor-hours to assemble each Alpha 1 robot and 25
The Lifang Wu Corporation manufactures two models of industrial robots, the Alpha 1 and the Beta
Green Vehicle Inc. manufactures electric cars and small delivery trucks. It has just opened a new factory where the C1 car and the T1 truck can both be manufactured. To make either vehicle, processing in the assembly shop and in the paint shop are required. It takes 1/40 of a day and 1/60 of a day
The Chris Beehner Company manufactures two lines of designer yard gates, called model A and model B. Every gate requires blending a certain amount of steel and zinc; the company has available a total of 25,000 lb of steel and 6,000 lb of zinc. Each model A gate requires a mixture of 125 lb of steel
The Attaran Corporation manufactures two electrical products: portable air conditioners and portable heaters.The assembly process for each is similar in that both require a certain amount of wiring and drilling. Each air conditioner takes 3 hours of wiring and 2 hours of drilling. Each heater must
Consider the following linear programming problem:
Solve the following linear programming problem graphically:
Solve the following linear programming problem graphically:
Formulate an own optimization (maximization) problem with three variables, one objective and three constraints.
Why is it bad to round optimal solutions to nearest integer?
Where a constraint crosses the vertical or horizontal axis, the quantity is fairly obvious. How does one go about finding the quantity coordinates where two constraints cross, not at an axis?
Compare how the corner-point and iso-profit line methods work for solving graphical problems.
Explain how to use the iso-cost line in a graphical minimization problem.
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