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Introduction to Operations Research 10th edition Frederick S. Hillier, Gerald J. Lieberman - Solutions

Reconsider Prob. 19.2-4. (a) Formulate a linear programming model for finding an optimal policy.
Reconsider Prob. 19.2-5. (a) Formulate a linear programming model for finding an optimal policy.
Reconsider Prob. 19.2-6. (a) Formulate a linear programming model for finding an optimal policy.
Reconsider Prob. 19.2-7. (a) Formulate a linear programming model for finding an optimal policy.
Reconsider Prob. 19.2-8. (a) Formulate a linear programming model for finding an optimal policy.
During any period, a potential customer arrives at a certain facility with probability 1 2. If there are already two people at the facility (including the one being served), the potential customer leaves the facility immediately and never returns. However, if there is one person or less, he
A student is concerned about her car and does not like dents. When she drives to school, she has a choice of parking it on the street in one space, parking it on the street and taking up two spaces, or parking in the lot. If she parks on the street in one space, her car gets dented with probability
Use the uniform random numbers in cells C13:C18 of Fig. 20.1 to generate six random observations for each of the following situations. (a) Throwing an unbiased coin. (b) A baseball pitcher who throws a strike 60 percent of the time and a ball 40 percent of the time. (c) The color of a traffic light
Hugh’s Repair Shop specializes in repairing German and Japanese cars. The shop has two mechanics. One mechanic works ononly German cars and the other mechanic works on only Japanese cars. In either case, the time required to repair a car has an exponential distribution with a mean of 0.2 day. The
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 they are released. Under this plan, the monitors and printers will be brought to the inspection station one at
Read the referenced article that fully describes the OR study summarized in the application vignette presented in Sec. 20.2. Briefly describe how simulation was applied in this study. Then list the various financial and nonfinancial benefits that resulted from this study.
(a) The numbers x1, x2, . . . , xn and y1, y2, . . . , yn are random observations from the same exponential distribution.(b) The average of x1, x2, . . . , xn is equal to the average of y1, y2, . . . , yn.(c) z is a random observation from an Erlang (gamma) distribution.
Consider the discrete random variable X that is uniformly distributed (equal probabilities) on the set {1, 2, . . . , 9}. You wish to generate a series of random observations xi (i = 1, 2, . . .) of X. The following three proposals have been made for doing this. For each one, analyze whether it is
Obtaining uniform random numbers as instructed at the beginning of the Problems section, use the acceptance-rejection method to generate three random observations from the triangular distribution used to illustrate this method in Sec. 20.4.
Obtaining uniform random numbers as instructed at the beginning of the Problems section, use the acceptance-rejection method to generate three random observations from the probability density function
An insurance company insures four large risks. The number of losses for each risk is independent and identically distributed on the points {0, 1, 2} with probabilities 0.7, 0.2, and 0.1, respectively. The size of an individual loss has the following cumulative distribution function:Obtaining
A company provides its three employees with health insurance under a group plan. For each employee, the probability of incurring medical expenses during a year is 0.9, so the number of employees incurring medical expenses during a year has a binomial distribution with p = 0.9 and n = 3. Given that
Reconsider the coin flipping game introduced in Sec. 20.1 and analyzed with simulation in Figs. 20.1, 20.2, and 20.3. (a) Revise the spreadsheet model in Fig. 20.1 by using Excel’s VLOOKUP function instead of the IF function to generate each simulated flip of the coin. Then perform a simulation
The weather can be considered a stochastic system, because it evolves in a probabilistic manner from one day to the next. Suppose for a certain location that this probabilistic evolution satisfies the following description: The probability of rain tomorrow is 0.6 if it is raining today. The
Apply the inverse transformation method as indicated next to generate three random observations from the uniform distribution between –10 and 40 by using the following uniform random numbers: 0.0965, 0.5692, 0.6658. (a) Apply this method graphically. (b) Apply this method algebraically. (c) Write
Obtaining uniform random numbers as instructed at the beginning of the Problems section, generate three random observations from each of the following probability distributions.(a) The uniform distribution from 25 to 75.(b) The distribution whose probability density function is(c) The distribution
Obtaining uniform random numbers as instructed at the beginning of the Problems section, generate three random observations from each of the following probability distributions.(a) The random variable X has P{X = 0} = 1/2. Given X ‰ 0, it has a uniform distribution between €“5
Each time an unbiased coin is flipped three times, the probability of getting 0, 1, 2, and 3 heads is 1/8, 3/8, 3/8, and 1/8, respectively. Therefore, with eight groups of three flips each, on the average, one group will yield 0 heads, three groups will yield 1 head, three groups will yield 2
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 sum of 7 or 11 or, alternatively, if the first sum is 4, 5, 6, 8, 9, or 10 and the same sum reappears before a
Obtaining uniform random numbers as instructed at the beginning of the Problems section, use the inverse transformation method and the table of the normal distribution given in Appendix 5 (with linear interpolation between values in the table) to generate 10 random observations (to three decimal
Obtaining uniform random numbers as instructed at the beginning of the Problems section, generate three random observations (approximately) from a normal distribution with mean = 5 and standard deviation = 10. (a) Do this by applying the central limit theorem, using three uniform random numbers to
Obtaining uniform random numbers as instructed at the beginning of the Problems section, generate four random observations (approximately) from a normal distribution with mean = 0 and standard deviation = 1. (a) Do this by applying the central limit theorem, using three uniform random numbers to
Obtaining uniform random numbers as instructed at the beginning of the Problems section, generate two random observations from each of the following probability distributions. (a) The exponential distribution with mean = 10 (b) The Erlang distribution with mean = 10 and shape parameter k = 2 (that
Richard Collins, manager and owner of Richard€™s Tire Service, wishes to use simulation to analyze the operation of his shop. One of the activities to be included in the simulation is the installation of automobile tires (including balancing the tires). Richard estimates that the
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 inventory policy for stoves, she records the number sold each day over a period of 25 days, as summarized
Obtaining uniform random numbers as instructed at the beginning of the Problems section, generate four random observations from an exponential distribution with mean = 1. Then use these four observations to generate one random observation from an Erlang distribution with mean = 4 and shape
The results from a simulation run are inherently random. This problem will demonstrate this fact and investigate the impact of the number of trials on this randomness. Consider the example involving Freddie the newsboy that was introduced in Sec. 20.6. The spreadsheet model is available in this
The Aberdeen Development Corporation (ADC) is reconsidering the Aberdeen Resort Hotel project. It would be located on the picturesque banks of Grays Harbor and have its own championship-level golf course. The cost to purchase the land would be $1 million, payable now. Construction costs would be
The Avery Co. factory has been having a maintenance problem with the control panel for one of its production processes. This control panel contains four identical electromechanical relays that have been the cause of the trouble. The problem is that the relays fail fairly frequently, thereby forcing
For one new product to be produced by the A plus Company, bushings will need to be drilled into a metal block and cylindrical shafts inserted into the bushings. The shafts are required to have a radius of at least 1.0000 inch, but the radius should be as little larger than this as possible. With
Reconsider Prob. 20.4-6 involving the game of craps. Now the objective is to estimate the probability of winning a play of this game. If the probability is greater than 0.5, you will want to go to Las Vegas to play the game numerous times until you eventually win a considerable amount of money.
Consider the example involving Freddie the newsboy that was introduced in Sec. 20.6. The spreadsheet model is available in this chapter’s Excel files on the book’s website. The parameter analysis report generated in Sec. 20.6 for Freddie’s problem suggests that 55 is the best order quantity,
Now that Jennifer is in middle school, her parents have decided that they really must start saving for her college education. They have $10,000 to invest right now. Furthermore, they plan to save another $4,000 each year until Jennifer starts college five years from now. They plan to split their
Michael Wise operates a newsstand at a busy intersection downtown. Demand for the Sunday Times at this newsstand averages 300 copies with a standard deviation of 50 copies. (Assume a normal distribution.) Michael purchases the paper for $0.75 and sells them for $1.25. Any papers at the end of the
Road Pavers, Inc. (RPI) is considering bidding on a county road construction project. RPI has estimated that the cost of this particular project would be $5 million. In addition, the cost of putting together a bid is estimated to be $50,000. The county also will receive four other bids on the
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 area. Simulation is being used to analyze whether to have one or two clerks on duty at the box office. While
Flight 120 between Seattle and San Francisco is a popular flight among both leisure and business travelers. The airplane holds 112 passengers in a single cabin. Both a discount 7-day advance fare and a full-price fare are offered. The airline’s management is trying to decide (1) how many seats to
Reconsider case 17.1. The current and proposed queueing systems in this case were to be analyzed with the help of queueing models to determine how to reduce in-process inventory as much as possible. However, these same queueing systems also can be effectively analyzed by applying simulation with
The Adventure Toys Company manufactures a popular line of action figures and distributes them to toy stores at the wholesale price of $10 per unit. Demand for the action figures is seasonal, with the highest sales occurring before Christmas and during the spring. The lowest sales occur during the
A factory’s planer department has had a difficult time keeping up with its workload, which has seriously disrupted the production schedule for subsequent operations. At times, the work pours in and a big backlog builds up. Then there might be a long pause when not much comes in, so the planers
A client of a large investment bank is interested in purchasing a European call option for a certain stock that provides him with the right to purchase the stock at a fixed price 12 weeks from today. The client then would exercise this option in 12 weeks only if this fixed price is less than the
Use the mixed congruential method to generate the following sequences of random numbers. (a) A sequence of 10 one-digit random integer numbers such that xn + 1 ≡ (xn + 3) (modulo 10) and x0 = 2 (b) A sequence of eight random integer numbers between 0 and 7 such that xn + 1 ≡ (5xn + 1) (modulo
Reconsider Prob. 20.3-1. Suppose now that you want to convert these random integer numbers to (approximate) uniform random numbers. For each of the three parts, give a formula for this conversion that makes the approximation as close as possible. (a) A sequence of 10 one-digit random integer
Use the mixed congruential method to generate a sequence of five two-digit random integer numbers such that xn + 1 ≡ (41xn + 33) (modulo 100) and x0 = 48.
Use the mixed congruential method to generate a sequence of three three-digit random integer numbers such that xn + 1 ≡ (201xn + 503) (modulo 1,000) and x0 = 485.
You need to generate five uniform random numbers. (a) Prepare to do this by using the mixed congruential method to generate a sequence of five random integer numbers between 0 and 31 such that xn+1 ≡ (13xn + 15) (modulo 32) and x0 = 14. (b) Convert these random integer numbers to uniform random
Consider the M/M/1 queueing theory model that was discussed in Sec. 17.6 and Example 2, Sec. 20.1. Suppose that the mean arrival rate is 5 per hour, the mean service rate is 10 per hour, and you are required to estimate the expected waiting time before service begins by using simulation. (a)
You are given the multiplicative congruential generator x0 = 1 and xn+1 ≡ 7xn (modulo 13) for n = 0, 1, 2, . . . . (a) Calculate xn for n = 1, 2, . . . , 12. (b) How often does each integer between 1 and 12 appear in the sequence generated in part (a)? (c) Without performing additional
The Rustbelt Manufacturing Company employs a maintenance crew to repair its machines as needed. Management now wants a simulation study done to analyze what the size of the crew should be, where the crew sizes under consideration are 2, 3, and 4. The time required by the crew to repair a machine
While performing a simulation of a single-server queueing system, the number of customers in the system is 0 for the first 10 minutes, 1 for the next 17 minutes, 2 for the next 24 minutes, 1 for the next 15 minutes, 2 for the next 16 minutes, and 1 for the next 18 minutes. After this total of 100
View the first demonstration example (Simulating a Basic Queueing System) in the simulation area of your OR Tutor. (a) Enter this same problem into the interactive procedure for simulation in your IOR Tutorial. Interactively execute a simulation run for 20 minutes of simulated time. (b) Use the
View the second demonstration example (Simulating a Queueing System with Priorities) in the simulation area of your OR Tutor. Then enter this same problem into the interactive procedure for simulation in your IOR Tutorial. Interactively execute a simulation run for 20 minutes of simulated time.
Consider the Everglade cash flow problem discussed in this chapter. Suppose that extra cash is kept in an interest-bearing savings account. Assume that any cash left at the end of a year earns 3 percent interest the following year. Make any necessary modifications to the spreadsheet and re-solve.
Refer to the spreadsheet file named “Everglade Problem 21-10” contained in the Excel files for this chapter on the book’ website. This file contains a formulation of the Everglade problem considered in this chapter. However, there are three errors in this formulation. Use the ideas presented
Among its many financial products, the Prudent Financial Services Corporation (normally referred to as PFS) manages a well-regarded pension fund that is used by a number of companies to provide pensions for their employees. PFS€™s management takes pride in the rigorous professional
The Pine Furniture Company makes fine country furniture. The company’s current product lines consist of end tables, coffee tables, and dining room tables. The production of each of these tables requires 8, 15, and 80 pounds of pine wood, respectively. The tables are handmade, and require one
Reboot, Inc. is a manufacturer of hiking boots. Demand for boots is highly seasonal. In particular, the demand in the next year is expected to be 3,000, 4,000, 8,000, and 7,000 pairs of boots in quarters 1, 2, 3, and 4, respectively. With its current production facility, the company can produce at
The Fairwinds Development Corporation is considering taking part in one or more of three different development projects€” A, B, and C€”that are about to be launched. Each project requires a significant investment over the next few years, and then would be sold upon completion.
Refer to the scenario described in Prob. 3.4-9 (Chap. 3), but ignore the instructions given there. Focus instead on using spreadsheet modeling to address Web Mercantile’s problem by doing the following. (a) Visualize where you want to finish. What numbers will Web Mercantile require? What are the
Refer to the scenario described in Prob. 3.4-10 (Chap. 3), but ignore the instructions given there. Focus instead on using spreadsheet modeling to address Larry Edison’s problem by doing the following. (a) Visualize where you want to finish. What numbers will Larry require? What are the decisions
Refer to the scenario described in Prob. 3.4-12 (Chap.3), but ignore the instructions given there. Focus instead on using spreadsheet modeling to address Al Ferris’s problem by doing the following. (a) Visualize where you want to finish. What numbers will Al require? What are the decisions that
In contrast to the spreadsheet model for the Wyndor Glass Co. product-mix problem shown in Fig. 21.6, the spreadsheet given next is an example of a poorly formulated spreadsheet model for this same problem. Identify each of the guidelines in Sec. 21.3 that is violated by this poor model. In each
Refer to the spreadsheet file named “Everglade Problem 21-9” contained in the Excel files for this chapter on the book’s website. This file contains a formulation of the Everglade problem considered in this chapter. However, there are three errors in this formulation. Use the ideas presented
Christine Phillips is in charge of planning and coordinating next spring€™s sales management training program for her company. Christine has listed the following activity information for this project:Construct the project network for this project.
Consider Christine Phillip’s project involving planning and coordinating next spring’s sales management training program for her company as described in Prob. 22.2-1. After constructing the project network, she now is ready for the following steps. (a) Find all the paths and path lengths
Refer to the activity list given in Prob. 22.2-2 as Christine Phillips does more detailed planning for next spring’s sales management training program for her company. After constructing the project network, she now is ready for the following steps. (a) Find all the paths and path lengths through
Using the PERT three-estimate approach, the three estimates for one of the activities are as follows: optimistic estimate = 30 days, most likely estimate = 36 days, pessimistic estimate = 48 days. What are the resulting estimates of the mean and variance of the duration of the activity?
Alfred Lowenstein is the president of the research division for Better Health, Inc., a major pharmaceutical company. His most important project coming up is the development of a new drug to combat AIDS. He has identified 10 groups in his division which will need to carry out different phases of
Reconsider Prob. 22.4-2. For each of the 10 activities, here are the three estimates that led to the estimates of the mean and variance of the duration of the activity (rounded to the nearest integer) given in the table for Prob. 22.4-2.(Note how the great uncertainty in the duration of these
Bill Fredlund, president of Lincoln Log Construction, is considering placing a bid on a building project. Bill has determined that five tasks would need to be performed to carry out the project. Using the PERT three-estimate approach, Bill has obtained the estimates in the next table for how long
Sharon Lowe, vice president for marketing for the Electronic Toys Company, is about to begin a project to design an advertising campaign for a new line of toys. She wants the project completed within 57 days in time to launch the advertising campaign at the beginning of the Christmas season.Sharon
The Lockhead Aircraft Co. is ready to begin a project to develop a new fighter airplane for the U.S. Air Force. The company€™s contract with the Department of Defense calls for project completion within 100 weeks, with penalties imposed for late delivery.The project involves 10 activities
Label each of the following statements about the PERT three-estimate approach as true or false, and then justify your answer by referring to specific statements (with page citations) in the chapter. (a) Activity durations are assumed to be no larger than the optimistic estimate and no smaller than
Do Prob. 10.8-1.The Tinker Construction Company is ready to begin a project that must be completed in 12 months. This project has four activities (A, B, C, D) with the project network shown next.The project manager, Sean Murphy, has concluded that he cannot meet the deadline by performing all these
Reconsider Prob. 22.2-1. Christine has done more detailed planning for this project and so now has the following expanded activity list:Construct the new project network.
Do Prob. 10.8-2. Reconsider the Tinker Construction Co. problem presented in Prob. 10.8-1. While in college, Sean Murphy took an OR course that devoted a month to linear programming, so Sean has decided to use linear programming to analyze this problem. (a) Consider the upper path through the
Reconsider the Electronic Toys Co. problem presented in Prob. 22.4-5. Sharon Lowe is concerned that there is a significant chance that the vitally important deadline of 57 days will not be met. Therefore, to make it virtually certain that the deadline will be met, she has decided to crash the
Consider the scenario described in Prob. 10.8-3. (a) To prepare for analyzing the effect of crashing, find the earliest times, latest times, and slack for each activity when they are done in the normal way. Also identify the corresponding critical path(s) and project duration. (b) Use marginal cost
Do Prob. 10.8-4.The 21st Century Studios is about to begin the production of its most important (and most expensive) movie of the year. The movie€™s producer, Dusty Hoffmer, has decided to use PERT/CPM to help plan and control this key project. He has identified the eight major activities
Do Prob 10.8-5.The Lockhead Aircraft Co. is ready to begin a project to develop a new fighter airplane for the U.S. Air Force. The company€™s contract with the Department of Defense calls for project completion within 92 weeks, with penalties imposed for late delivery.The project involves
Reconsider Prob. 22.5-4 involving the Good Homes Construction Co. project to construct a large new home. Michael Dean now has generated the plan for how to crash this project. Since this plan causes all three paths through the project network to be critical paths, the earliest start time for each
The P-H Microchip Co. needs to undertake a major maintenance and renovation program to overhaul and modernize its facilities for wafer fabrication. This project involves six activities (labeled A, B, . . . , F) with the precedence relationships shown in the following network.The estimated durations
Reconsider Prob. 22.3-4 involving a project at Stanley Morgan Bank to install a new management information system. Ken Johnston already has obtained the earliest times, latest times, and slack for each activity. He now is getting ready to use PERT/Cost to schedule and control the costs for this
Brent Bonnin begins his senior year of college filled with excitement and a twinge of fear. The excitement stems from his anticipation of being done with it all€”professors, exams, problem sets, grades, group meetings, all-nighters. The list could go on and on. The fear stems from the
Construct the project network for a project with the following activity list.
Ken Johnston, the data processing manager for Stanley Morgan Bank, is planning a project to install a new management information system. He now is ready to start the project, and wishes to finish in 20 weeks. After identifying the 14 separate activities needed to carry out this project, as well as
You are given the following information about a project consisting of six activities:(a) Construct the project network for this project. (b) Find the earliest times, latest times, and slack for each activity. Which of the paths is a critical path? (c) If all other activities take the estimated
Reconsider the Reliable Construction Co. project introduced in Sec. 22.1, including the complete project network obtained in Fig. 22.5 at the end of Sec. 22.3. Note that the estimated durations of the activities in this figure turn out to be the same as the mean durations given in Table 22.4 (Sec.
Follow the instructions for Prob. 22.3-6 except use the optimistic estimates in Table 22.4 instead.
Follow the instructions for Prob. 22.3-6 except use the crash times given in Table 22.7 (Sec. 22.5) instead.
You and several friends are about to prepare a lasagna dinner. The tasks to be performed, their immediate predecessors, and their estimated durations are as follows:*There is none in the refrigerator. (a) Construct the project network for preparing this dinner. (b) Find all the paths and path
Suppose that the air freight charge per ton between seven particular locations is given by the following table (except where no direct air freight service is available):A certain corporation must ship a certain perishable commodity from locations 1€“3 to locations 4€“7. A total
Using the decomposition principle, begin solving the Good Foods Corp. multidivisional problem presented in Sec. 23.2 by executing the first two iterations.
Consider the following table of constraint coefficients for a linear programming problem:Show how this table can be converted into the dual angular structure for multitime period linear programming shown in Table 23.9 (with three time periods in this case) by reordering the variables and
Consider the Wyndor Glass Co. problem described in Sec. 3.1 (see Table 3.1). Suppose that decisions have been made to discontinue additional products in the future and to initiate other new products. Therefore, for the two products being analyzed, the number of hours of production time available

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