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quantitative analysis for management
Quantitative Analysis For Management 12th Edition Barry Render, Ralph M. Stair, Michael E. Hanna - Solutions
= 11-21 The air pollution project discussed in the chapter has progressed over the past several weeks, and it is now the end of week 8. Lester Harky would like to know the value of the work completed, the amount of any cost overruns or underruns for the project, and the extent to which the project
=11-22 Fred Ridgeway has been given the responsibility of managing a training and development program. He knows the earliest start time, the latest start time, and the total costs for each activity. This information is given in the following table.(a) Using earliest start times, determine Fred’s
=11-23 General Foundry’s project crashing data are shown in Table 11.9. Crash this project to 13 weeks using CPM. What are the final times for each activity after crashing?
=11-24 Bowman Builders manufactures steel storage sheds for commercial use. Joe Bowman, president of Bowman Builders, is contemplating producing sheds for home use. The activities necessary to build an experimental model and related data are given in the accompanying table.
=(a) What is the project completion date?
=(b) Formulate an LP problem to crash this project to 10 weeks.Activity Normal Time Crash Time Normal Cost($)Crash Cost($)Immediate Predecessors A 3 2 1,000 1,600 —B 2 1 2,000 2,700 —C 1 1 300 300 —D 7 3 1,300 1,600 A E 6 3 850 1,000 B F 2 1 4,000 5,000 C G 4 2 1,500 2,000 D, E
=11-27 Dream Team Productions was in the final design phases of its new film, Killer Worms, to be released next summer. Market Wise, the firm hired to coordinate the release of Killer Worms toys, identified 16 critical tasks to be completed before the release of the film.
=(a) How many weeks in advance of the film release should Market Wise start its marketing campaign? What are the critical path activities? The tasks are as follows:Table for Problem 11-27 Activity Immediate Predecessors Optimistic Time Most Likely Time Pessimistic Time Task 1 — 1 2 4 Task 2 —
=11-28 The estimated times (in weeks) and immediate predecessors for the activities in a project are given in the following table. Assume that the activity times are independent.Activity Immediate Predecessors a m b A — 9 10 11 B — 4 10 16 C A 9 10 11 D B 5 8 11(a) Calculate the expected time
=distributed, what is the probability that this path will be finished in 22 weeks or less?
=(f) Explain why the probability that the critical path will be finished in 22 weeks or less is not necessarily the probability that the project will be finished in 22 weeks or less.
=11-29 The following costs have been estimated for the activities in a project:Activity Immediate Predecessors Time Cost ($)A — 8 8,000 B — 4 12,000 C A 3 6,000 D B 5 15,000 E C, D 6 9,000 F C, D 5 10,000 G F 3 6,000(a) Develop a cost schedule based on earliest start times.(b) Develop a cost
=11-30 The Scott Corey accounting firm is installing a new computer system. Several things must be done to make sure the system works properly before all the accounts are put into the new system. The following table provides information about this project. How long will it take to install the
=11-31 The managing partner of the Scott Corey accounting firm (see Problem 11-30) has decided that the system must be up and running in 16 weeks. Consequently, information about crashing the project was put together and is shown in the following table:Activity Immediate Predecessors Normal
=(b) List all the paths in this network. After the crashing in part (a) has been done, what is the time required for each path? If the project completion time must be reduced another week so that the total time is 15 weeks, which activity or activities should be crashed? Solve this by inspection.
=11-32 The L. O. Gystics Corporation is in need of a new regional distribution center. The planning is in the early stages of this project, but the activities have been identified along with their predecessors and their activity times in weeks. The table below provides this information. Develop a
=11-33 The Laurenster Corporation needs to perform the following tasks in weeks.Activity IMMEDIATE Predecessors Optimistic Time Most Likely Time Pessimistic Time A 2 3 4 B 4 6 8 C 2 5 8 D A 3 4 5 E B 6 7 8 F C 4 7 10 G A 1 5 9 H B 2 5 8 I C 3 5 7 J D, G 2 2 2 K E, H 4 4 4 L F, I 3 3 3
=Determine the associated PERT network diagram and determine the probability that the project will be complete in 16 weeks or less.
=11-34 The Laurenster Corporation has determined the client will pay them a $10,000 bonus if they complete the project in Problem 11-33 in 14 weeks or less.The associated normal times and costs as well as the crash times and costs are shown below.Activity Normal Time Crash Time Normal Cost
=11-35 There is a network of 25 activities and 13 nodes. The activity durations are normally distributed. The average duration MU and standard deviation, SIGMA are given in the Table, in weeks. The activities are already in topological order. Use the Project Management module in the QM package to
=1. Develop a network drawing for Hill Construction and determine the critical path. How long is the project expected to take?
=2. What is the probability of finishing in 270 days?
=3. If it were necessary to crash to 250 or 240 days, how would Hill do so, and at what costs? As noted in the case, assume that optimistic time estimates can be used as crash times.
=1. Some of the tasks in this project can be done in parallel.Prepare a diagram showing the required network of tasks and define the critical path. What is the length of the project without crashing?
=2. At this point, can the project be done given the personnel constraint of 10 persons?
=3. If the critical path is longer than 60 days, what is the least amount that Dr. Watage can spend and still achieve this schedule objective? How can he prove to Pathminder Foundation that this is the minimum-cost alternative?
=1. Most systems use the queue discipline known as the FIFO rule.a. Trueb. False
=2. Before using exponential distributions to build queuing models, the quantitative analyst should determine if the service time data fit the distribution.a. Trueb. False
=3. In a multichannel, single-phase queuing system, the arrival will pass through at least two different service facilities.a. Trueb. False
=12. In the standard queuing model, we assume that the queue discipline is .
=13. The service time in the M/M/1 queuing model is assumed to be .
=12-1 What is the waiting line problem? What are the components in a waiting line system?
=12-2 What are the assumptions underlying common queuing models?
=12-3 Describe the important operating characteristics of a queuing system.
=12-4 Why must the service rate be greater than the arrival rate in a single-channel queuing system?
=12-5 Briefly describe three situations in which the FIFO discipline rule is not applicable in queuing analysis.
=12-6 Provide examples of four situations in which there is a limited, or finite, population.
=12-7 What are the components of the following systems?Draw and explain the configuration of each.(a) Barbershop(b) Car wash(c) Laundromat(d) Small grocery store
=12-11 The Rockwell Electronics Corporation retains a service crew to repair machine breakdowns that occur on an average of λ = 3 per day (approximately Poisson in nature).The crew can service an average of µ = 8 machines per day, with a repair time distribution that resembles the exponential
=(a) What is the utilization rate of this service system?
=(b) What is the average downtime for a machine that is broken?
=(c) How many machines are waiting to be serviced at any given time?
=(d) What is the probability that more than one machine is in the system? Probability that more than two are broken and waiting to be repaired or being serviced? More than three? More than four?
=12-13 Mike Dreskin manages a large Los Angeles movie theater complex called Cinema I, II, III, and IV.Each of the four auditoriums plays a different film;the schedule is set so that starting times are staggered to avoid the large crowds that would occur if all four movies started at the same
=(a) Find the average number of moviegoers waiting in line to purchase a ticket.
=(b) What percentage of the time is the cashier busy?
=(c) What is the average time that a customer spends in the system?
=(d) What is the average time spent waiting in line to get to the ticket window?(e) What is the probability that there are more than two people in the system? More than three people? More than four?
=12-14 A university cafeteria line in the student center is a self-serve facility in which students select the food items they want and then form a single line to pay the cashier. Students arrive at the cashier at a rate of about four per minute according to a Poisson distribution. The single
=(a) What is the probability that there are more than two students in the system? More than three students? More than four?
=(b) What is the probability that the system is empty?
=(c) How long will the average student have to wait before reaching the cashier?
=(d) What is the expected number of students in the queue?(e) What is the average number in the system?(f) If a second cashier is added (who works at the same pace), how will the operating characteristics computed in parts (b), (c), (d), and (e)change? Assume that customers wait in a single line
=12-16 Ashley’s Department Store in Kansas City 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.
=(b) What is the average number of callers waiting to place an order?
=(c) Ashley’s is considering adding a second clerk to take calls. The store would pay that person the same $10 per hour. Should it hire another clerk?Explain.
=12-17 Automobiles arrive at the drive-through window at a 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 exponentially distributed.(a) What is the average time a car is in
=(b) What is the average number of cars in the system?
=(c) What is the average time cars spend waiting to receive service?(d) What is the average number of cars in line behind the customer receiving service?(e) What is the probability that there are no cars at the window?
=(f) What percentage of the time is the postal clerk busy?
=(g) What is the probability that there are exactly two cars in the system?
=12-18 For the post office in Problem 12-17, a second drivethrough window is being considered. A single line would be formed and as a car reached the front of the line it would go to the next available clerk. The clerk at the new window works at the same rate as the current one.(a) What is the
=(b) What is the average number of cars in the system?(c) What is the average time cars spend waiting to receive service?
=(d) What is the average number of cars in line behind the customer receiving service?(e) What is the probability that there are no cars in the system?
=(f) What percentage of the time are the clerks busy?(g) What is the probability that there are exactly two cars in the system?
=12-26 For the Billy’s Bank situation in Problems 12-24 and
=12-25, the salary and benefits for a teller would be$12 per hour. The bank is open 8 hours each day.It has been estimated that the waiting time cost per hour is $25 per hour in the line.(a) How many customers would enter the bank on a typical day?
=(b) How much total time would the customers spend waiting in line during the entire day if one teller were used? What is the total daily waiting time cost?
=(c) How much total time would the customers spend waiting in line during the entire day if two tellers were used? What is the total waiting time cost?(d) If Billy wishes to minimize the total waiting time and personnel cost, how many tellers should be used?
=12-27 Customers arrive at an automated coffee vending machine at a rate of 4 per minute, following a Poisson distribution. The coffee machine dispenses a cup of coffee in exactly 10 seconds.(a) What is the average number of people waiting in line?
=(b) What is the average number in the system?
=(c) How long does the average person wait in line before receiving service?
=12-28 The average number of customers in the system in the single-channel, single-phase model described in Section 12.4 is L = −λµ λShow that for m = 1 server, the multichannel queuing model in Section 12.5, L m m P m=( ) − ( ) − +λµ λµµ λλ1 µ 2
=12-29 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 an exponential
=(b) How many are in the system, on average?
=(c) How many drills are in running order, on average?
=(d) What is the average waiting time in the queue?
=(e) What is the average wait in the system?
=12-30 A technician monitors a group of five computers that run an automated manufacturing facility. It takes an average of 15 minutes (exponentially distributed)to adjust a computer that develops a problem. The computers run for an average of 85 minutes (Poisson distributed) without requiring
=(a) average number of computers waiting for adjustment?
=(b) average number of computers not in working order?(c) probability the system is empty?(d) average time in the queue?(e) average time in the system?
=12-31 The typical subway station in Washington, D.C., has 6 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 just how many turnstiles to use for entering
=(a) How many turnstiles should be opened in each direction every morning?
=(b) Discuss the assumptions underlying the solution of this problem using queuing theory.
=12-32 The Clear Brook High School band is holding a car wash as a fundraiser to buy new equipment. The average time to wash a car is 4 minutes, and the time is exponentially distributed. Cars arrive at a rate of one every 5 minutes (or 12 per hour), and the number of arrivals per time period is
=(b) What is the average number of cars in the line?
=(c) What is the average number of cars in the system?
=(d) What is the average time in the system?
=(e) What is the probability there are more than three cars in the system?
=12-33 When additional band members arrived to help at the car wash (see Problem 12-32), it was decided that two cars should be washed at a time instead of just the one. Both work crews would work at the same rate.
=(a) What is the average time for cars waiting in the line?
=(b) What is the average number of cars in the line?
=(c) What is the average number of cars in the system?
=(d) What is the average time in the system?
=1. How much time would the new layout save?
= 2. If maintenance personnel were paid $9.50 per hour and molding personnel were paid $11.75 per hour, how much could be saved per hour with the new factory layout?
=1. Determine the average amount of time that a guest spends checking in. How would this change under each of the stated options?
=2. Which option do you recommend?
=1. Simulation is a technique usually reserved for studying only the simplest and most straightforward of problems.a. Trueb. False
=2. A simulation model is designed to arrive at a single specific numerical answer to a given problem.a. Trueb. False
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