Questions and Answers of Introduction To Operations Research

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
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
Apply the inverse transformation method as indicated below to generate three random observations from the uniform distribution between 10 and 40 by using the following uniform random numbers:
Reconsider the coin flipping game introduced in Sec. 22.1 and analyzed with simulation in Figs. 22.1, 22.2, and 22.3.(a) Simulate one play of this game by repeatedly flipping your own coin until the
Reconsider Prob. 22.3-1.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
Read the articles about all four applications of simulation mentioned in Prob. 22.2-1.For each one, write a one-page summary of the application and the benefits it provided.
Section 22.2 introduced four actual applications of simulation that are described in articles in Interfaces. (The citations for the two that also use queueing models are given in Sec. 18.6.) Select
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
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. In
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 routine for simulation
View the first demonstration example (Simulating a Basic Queueing System) in the simulation area of your OR Tutor.D,I (a) Enter this same problem into the interactive routine for simulation in your
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
Consider the M/M/1 queueing theory model that was discussed in Sec. 17.6 and Example 2, Sec. 22.1. Suppose that the mean arrival rate is 5 per hour, the mean service rate is 10 per hour, and you are
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
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
Use the uniform random numbers in cells C10:C15 of Fig. 22.1 to generate six random observations for each of the following situations.(a) Throwing an unbiased coin.(b) A baseball pitcher who throws a
Reconsider the prototype example of Sec. 21.1. Suppose now that the production process using the machine under consideration will be used for only 4 more weeks. Using the discounted cost criterion
Reconsider Prob. 21.5-7.Suppose now that the company will be producing either of these chemicals for only 4 more months, so a decision on which pollution control process to use 1 month hence only
For Prob. 21.5-7, use two iterations of the method of successive approximations to approximate an optimal policy.
Reconsider Prob. 21.5-7.(a) Formulate a linear programming model for finding an optimal policy.C (b) Use the simplex method to solve this model. Use the resulting optimal solution to identify an
A chemical company produces two chemicals, denoted by 0 and 1, and only one can be produced at a time. Each month a decision is made as to which chemical to produce that month. Because the demand for
For Prob. 21.5-4, use three iterations of the method of successive approximations to approximate an optimal policy.
Reconsider Prob. 21.5-4.(a) Formulate a linear programming model for finding an optimal policy.C (b) Use the simplex method to solve this model. Use the resulting optimal solution to identify an
The price of a certain stock is fluctuating between $10,$20, and $30 from month to month. Market analysts have predicted that if the stock is at $10 during any month, it will be at $10 or$20 the next
For Prob. 21.5-1, use three iterations of the method of successive approximations to approximate an optimal policy.
Reconsider Prob. 21.5-1.(a) Formulate a linear programming model for finding an optimal policy.C (b) Use the simplex method to solve this model. Use the resulting optimal solution to identify an
Joe wants to sell his car. He receives one offer each month and must decide immediately whether to accept the offer.Once rejected, the offer is lost. The possible offers are $600, $800, and $1,000,
Suppose now that the number of pints of blood delivered (on a regular delivery) can be specified at the time of delivery (instead of using the old policy of receiving 1 pint at each delivery). Thus,
Consider the blood-inventory problem presented in Prob.
Use the policy improvement algorithm to find an optimal policy for Prob. 21.2-9.
Use the policy improvement algorithm to find an optimal policy for Prob. 21.2-8.
Use the policy improvement algorithm to find an optimal policy for Prob. 21.2-7.
Use the policy improvement algorithm to find an optimal policy for Prob. 21.2-6.
Use the policy improvement algorithm to find an optimal policy for Prob. 21.2-5.
Use the policy improvement algorithm to find an optimal policy for Prob. 21.2-4.
Use the policy improvement algorithm to find an optimal policy for Prob. 21.2-3.
Use the policy improvement algorithm to find an optimal policy for Prob. 21.2-2.
Use the policy improvement algorithm to find an optimal policy for Prob. 21.2-1.
Reconsider Prob. 21.2-9.(a) Formulate a linear programming model for finding an optimal policy.C (b) Use the simplex method to solve this model. Use the resulting optimal solution to identify an
Reconsider Prob. 21.2-8.(a) Formulate a linear programming model for finding an optimal policy.C (b) Use the simplex method to solve this model. Use the resulting optimal solution to identify an
Reconsider Prob. 21.2-7.(a) Formulate a linear programming model for finding an optimal policy.C (b) Use the simplex method to solve this model. Use the resulting optimal solution to identify an
Reconsider Prob. 21.2-6.(a) Formulate a linear programming model for finding an optimal policy.C (b) Use the simplex method to solve this model. Use the resulting optimal solution to identify an
Reconsider Prob. 21.2-5.(a) Formulate a linear programming model for finding an optimal policy.C (b) Use the simplex method to solve this model. Use the resulting optimal solution to identify an
Reconsider Prob. 21.2-4.(a) Formulate a linear programming model for finding an optimal policy.C (b) Use the simplex method to solve this model. Use the resulting optimal solution to identify an
Reconsider Prob. 21.2-3.(a) Formulate a linear programming model for finding an optimal policy.C (b) Use the simplex method to solve this model. Use the resulting optimal solution to identify an
Reconsider Prob. 21.2-2.(a) Formulate a linear programming model for finding an optimal policy.C (b) Use the simplex method to solve this model. Use the resulting optimal solution to identify an
Reconsider Prob. 21.2-1.(a) Formulate a linear programming model for finding an optimal policy.C (b) Use the simplex method to solve this model. Use the resulting optimal solution to identify an
Consider an infinite-period inventory problem involving a single product where, at the beginning of each period, a decision must be made about how many items to produce during that period. The setup
A person often finds that she is up to 1 hour late for work.If she is from 1 to 30 minutes late, $4 is deducted from her paycheck; if she is from 31 to 60 minutes late for work, $8 is deducted from
Buck and Bill Bogus are twin brothers who work at a gas station and have a counterfeiting business on the side. Each day a decision is made as to which brother will go to work at the gas station, and
Each year Ms. Fontanez has the chance to invest in two different no-load mutual funds: the Go-Go Fund or the Go-Slow Mutual Fund. At the end of each year, Ms. Fontanez liquidates her holdings, takes
When a tennis player serves, he gets two chances to serve in bounds. If he fails to do so twice, he loses the point. If he attempts to serve an ace, he serves in bounds with probability 38. If he
Every Saturday night a man plays poker at his home with the same group of friends. If he provides refreshments for the group(at an expected cost of $14) on any given Saturday night, the group will
A soap company specializes in a luxury type of bath soap.The sales of this soap fluctuate between two levels—low and high—depending upon two factors: (1) whether they advertise and(2) the
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,
During any period, a potential customer arrives at a certain facility with probability 12. If there are already two people at the facility (including the one being served), the potential customer
Quality Bikes is a wholesale firm that specializes in the distribution of bicycles. In the past, the company has maintained ample inventories of bicycles to enable filling orders immediately, so
Reconsider Prob. 20.7-12.The economy is beginning to boom so the management of Transcontinental Airlines is predicting that the number of people flying will steadily increase this year over the
Transcontinental Airlines maintains a computerized forecasting system to forecast the number of customers in each fare class who will fly on each flight in order to allocate the available
Reconsider Prob. 20.5-3.Ralph Billett realizes that the last-value method is considered to be the naive forecasting method, so he wonders whether he should be using another method. Therefore, he has
The Centerville Water Department provides water for the entire town and outlying areas. The number of acre-feet of water consumed in each of the four seasons of the three preceding years is shown
Follow the instructions of Prob. 20.7-15 for a product with the following sales history.
Management of the Jackson Manufacturing Corporation wishes to choose a statistical forecasting method for forecasting total sales for the corporation. Total sales (in millions of dollars)for each
Reconsider Prob. 20.7-4.Ben Swanson now has decided to use the exponential smoothing method to forecast future sales of washing machines, but he needs to decide on which smoothing constant to use.
Ben Swanson, owner and manager of Swanson’s Department Store, has decided to use statistical forecasting to get a better handle on the demand for his major products. However, Ben now needs to
The Healthwise Company produces a variety of exercise equipment. Healthwise management is very pleased with the increasing sales of its newest model of exercise bicycle. The sales during the last two
A manufacturer sells a certain product in batches of 100 to wholesalers. The following table shows the quarterly sales figure for this product over the last several years.The company incorporates
Figure 20.3 shows CCW’s average daily call volume for each quarter of the past three years, and column F of Fig. 20.4 gives the seasonally adjusted call volumes. Management now wonders what these
A company uses exponential smoothing with 1 2 to forecast demand for a product. For each month, the company keeps a record of the forecast demand (made at the end of the preceding month) and the
After graduating from college with a degree in mathematical statistics, Ann Preston has been hired by the Monty Ward Company to apply statistical methods for forecasting the company’s sales. For
Select three of the applications of statistical forecasting methods listed in Table 20.1. Read the articles describing the applications in the indicated issues of Interfaces. For each one, write a
Select one of the applications of statistical forecasting methods listed in Table 20.1. Read the article describing the application in the indicated issue of Interfaces. Write a two-page summary of
For the infinite-period model with no setup cost, show that the value of y0 that satisfies(y0) p p c(1 h )is equivalent to the value of y that satisfiesdL d(y y) c(1 ) 0, where L(y),
Find the optimal (k, Q) policy for Prob. 19.7-10 for an infinite-period model with a discount factor of 0.90.
Consider a one-period model where the only two costs are the holding cost, given by h(y D) 1 30(y D), for y D, and the shortage cost, given by p(D y) 2.5(D y), for D y.The probability
The weekly demand for a certain type of electronic calculator is estimated to be The unit cost of these calculators is $80. The holding cost is $0.70 per calculator remaining at the end of a week.
A supplier of high-fidelity receiver kits is interested in using an optimal inventory policy. The distribution of demand per month is uniform between 2,000 and 3,000 kits. The supplier’s cost for
Solve the inventory problem given in Prob. 19.7-6, but assume that the policy is to be used for only 1 year (a 12-period model). Shortages are backlogged each month, except that any shortages
Reconsider Prob. 20.7-9.Despite some fluctuations from year to year, note that there has been a basic trend upward in the annual demand for copper ore over the past 10 years. Therefore, by projecting
Determine the optimal inventory policy when the goods are to be ordered at the end of every month from now on. The cost of bringing the inventory level up to y when x already is available is given by
Solve Prob. 19.7-3 for an infinite-period model.
Solve Prob. 19.7-3 for a two-period model, assuming no salvage value, no backlogging at the end of the second period, and no discounting.
Find the optimal inventory policy for the following two-period model by using a discount factor of 0.9. The demand D has the probability density functionD()for 0 otherwise,and the costs are
Consider the following inventory situation. Demands in different periods are independent but with a common probability density function D() 5 10 for 0 50. Orders may be placed at the start of
Consider the following inventory situation. Demands in different periods are independent but with a common probability density function given byD()Orders may be placed at the start of each period
Consider the following inventory model, which is a single-period model with known density of demand D() e for 0 and D() 0 elsewhere. There are two costs connected with the model. The first
The campus bookstore must decide how many textbooks to order for a course that will be offered only once. The number of students who will take the course is a random variable D, whose distribution
The following data relate road width x and accident frequency y. Road width (in feet) was treated as the independent variable, and values y of the random variable Y, in accidents per 108 vehicle
The management of Quality Airlines has decided to base its overbooking policy on the stochastic single-period model for perishable products, since this will maximize expected profit. This policy now
A college student, Stan Ford, recently took a course in operations research. He now enjoys applying what he learned to optimize his personal decisions. He is analyzing one such decision currently,
Suppose that the demand D for a spare airplane part has an exponential distribution with mean 50, that is,5 10e /50 for 0D()0 otherwise.This airplane will be obsolete in 1 year, so all
Reconsider Prob. 19.6-4.The bakery owner, Ken Swanson, now has developed a new plan to decrease the size of shortages. The bread will be baked twice a day, once before the bakery opens (as before)
The following data are observations yi on a dependent random variable Y taken at various levels of an independent variable x. [It is assumed that E(Yixi) A Bxi, and the Yi are independent normal
A newspaper stand purchases newspapers for $0.36 and sells them for $0.50. The shortage cost is $0.50 per newspaper (because the dealer buys papers at retail price to satisfy shortages).The holding
Micro-Apple is a manufacturer of personal computers. It currently manufactures a single model—the MacinDOS—on an assembly line at a steady rate of 500 per week. MicroApple orders the floppy disk
When using the stochastic continuous-review model presented in Sec. 19.5, a difficult managerial judgment decision needs to be made on the level of service to provide to customers. The purpose of
If a particle is dropped at time t 0, physical theory indicates that the relationship between the distance traveled r and the time elapsed t is r gt k for some positive constants g and k. A
Consider a situation where a particular product is produced and placed in in-process inventory until it is needed in a subsequent production process. No units currently are in inventory, but three
MBI is a manufacturer of personal computers. All its personal computers use a 3.5-inch high-density floppy disk drive which it purchases from Ynos. MBI operates its factory 52 weeks per year, which
In the basic EOQ model, suppose the stock is replenished uniformly (rather than instantaneously) at the rate of b items per unit time until the order quantity Q is fulfilled. Withdrawals from the

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