Questions and Answers of Principles Of Operations

Consider the double sampling plan for Spire CDs presented in this section.a. Suppose that the true proportion of defectives in the lot is 10 percent. On average, how many items will have to be
(Refer to Example 12.6.)
Determine a sampling plan for Spire CDs that results in .05, .05, AQL .10, and LTPD .30. Discuss the advantages and the disadvantages of the plan you obtain as compared to the current plan
Hemispherical Conductor produces the 80J84 microprocessor,which the SayleCompany plans to use in a heart–lung machine. Because of the sensitivity of the application, Sayle has established a value
A company employs the following sampling plan: It draws a sample of 10 percent of the lot being inspected. If 1 percent or less of the sample is defective, the lot is accepted. Otherwise the lot is
A producer of pocket calculators purchases the main processor chips in lots of 1,000. The producer would like to have a 1 percent rate of defectives but will normally not refuse a lot unless it has 4
If the true proportion of defectives in the lot is 5 percent, determine the probability that a lot is accepted usinga. The exact hypergeometric distribution.b. The binomial approximation to the
Samples of size 20 are drawn from lots of 100 items, and the lots are rejected if the number of defectives in the sample exceeds
What is its hourly cost?b. What are the optimal values of n and k for this process and the associated optimal cost?
A local contractor manufactures the speakers used in telephones. The phone company requires the speakers to ring at a specified noise level (in decibels). An Xchart is being designed to monitor this
Suppose that “the process going out of control” corresponds to a shift of the mean from to with probability .25, 2 with probability .25, with probability .25, and 2 with
Discuss the following pro and con positions on using optimization models to design control charts:Con: “These models are useless to me because I don’t feel I can accurately estimate the values of
Under what circumstances would the following assumptions not be accurate?a. The assumption that the probability law describing the number of periods until the process goes out of control follows the
Consider the application of the economic design of X charts for Wonderdisk presented in this section. Without actually performing the calculations, discuss what the effect on the optimal values of n
If you are doing the calculations by hand, use k 0.5, 1, 1.5, 2, 2.5, and 3.0. If you are using a computer, use k 0.1, 0.2, . . . , 2.9, 3.0.c. Determine the optimal control chart design that
A quality control engineer is considering the optimal design of an X chart. Based on his experience with the production process, there is a probability of .03 that the process shifts from an
Problem 14 required testingwhether the process was in control using a p chart. Test the hypothesis that the value of p is the same each day using classical statistical methods. That is, test the
Consider the data presented in Problem
For the company mentioned in Problem 20, a purchaser of a bag of chocolate chip cookies discovers a cookie that has no chips in it and charges the company with fraudulent advertising. Suppose the
A large national producer of cookies and baked goods uses a c chart to monitor the number of chocolate chips in its chocolate chip cookies. The company would like to have an average of six chips per
Amertron, discussed in Problem 18, has established a policy of passing rolls of wire having five or fewer defects.a. Based on the exact Poisson distribution, what is the proportion of the rolls that
Amertron produces electrical wiring in 100-foot rolls. The quality inspection process involves selecting rolls of wire at random and counting the number of defects on each roll. The last 20 rolls
Over a period of 12 consecutive production hours, samples of size 50 resulted in the following proportions of defective items:Proportion Proportion Sample Number Defective Sample Number Defective 1
Based on the estimate of the probability that a machine is sent back for rework computed from the 20 months of data, determine the following:a. If the company produces 35 machines in one particular
Consider the example of Applied Machines presented in Problem
Applied Machines produces large test equipment for integrated circuits. The machines are made to order, so the production rate varies from month to month.Before shipping, each machine is subject to
A manufacturer of photographic film produces an average of 12,000 rolls of various types of film each day. An inspector samples 25 from each day’s production and tests them for accuracy of color
A process is monitored using an X chart with UCL 13.8 and LCL 8.2.The process standard deviation is estimated to be 6.6. If the X chart is based on three-sigma limits,a. What is the estimate of
An R chart is used to monitor the variation in the weights of packages of chocolate chip cookies produced by a large national producer of baked goods. An analyst has collected a baseline of 200
What is the probability that the shift is detected on the first subgroup after the shift occurs?
A film processing service monitors the quality of the developing process with light-sensitive equipment. The accuracy measure is a number with a target value of zero. Suppose that an X chart with
Suppose that the process mean shifts to 1,011 in Problem 8.a. What is the probability that the X chart will not indicate an out-of-control condition from a single subgroup sampling? (This is
For Problem 8, suppose that the probability of concluding that the process is out of control when it is actually in control is set at .02. Find the upper and the lower control limits for the
Control charts for X and R are maintained on the shear strength of spot welds. One hundred observations divided into subgroups of size five are used as a baseline to construct the charts, and
The quality control group of a manufacturing company is planning to use control charts to monitor the production of a certain part. The specifications for the part require that each unit weigh
The members of a private golf club have handicaps that are normally distributed with mean 15 and standard deviation 3.5. In a particular event, foursomes are chosen by grouping four players chosen at
a. What is the probability that a normal variable exceeds two-sigma limits? (That is, what is the probability of observing a value of the random variable larger than 2 or less than 2?)b. If
A credit rating company recommends granting of credit cards based on several criteria. One is annual income. If the annual income of applicants is normally distributed with mean $22,000 and standard
The tensile strength of a heavy-duty plastic bag used in trash compactors is normally distributed with mean 150 pounds per square inch and standard deviation 12 pounds per square inch. An independent
The following data represent the observed number of defective disks produced each hour based on observing the system for 30 successive hours.0 3 5 2 6 8 3 5 4 6 6 9 5 1 2 1 2 5 3 3 0 1 0 7 1 7 5 4 4
Suppose that X1 and X2 are independent random variables having the uniform distribution on (0, 1, 2, 3, 4, 5). That is, f( j) PXi j for i 1, 2 and 0 j 5.a. Compute E(X1) and Var(X1). [Hint: Use
Extend the results of Problem 60 to find the optimal location of a new facility among a set of existing facilities assuming a straight-line Euclidean distance measure. Let column E correspond to
Design an electronic spreadsheet to compute the optimal solution to the gravity problem. Allow for up to 20 locations. Let column A be the location number, column B the x coordinates (a1, . . . , an)
Solve Problem 32 using an electronic spreadsheet. To do so, enter the building numbers in column A, the x coordinates in column B, and the associated weights in column C. Sort columns A, B, and C in
Solve Problem 57, assuming a Euclidean distance measure.
By systematically varying the x and y coordinates, find the optimal location of the new facility.
Design a spreadsheet to compute the total rectilinear distance from a set of up to 10 existing locations to any other location. Assume that existing locations are placed in Columns A and B and the
A company is considering where to locate its cafeteria to service six buildings. The locations of the buildings and the fraction of the company’s employees working at these locations are Fraction
Consider three locations at (0, 0), (0, 6), and (3, 3) with equal weights. Using the methods described in Appendix 11–B, find contour lines for the rectilinear location problem.
An electronics firm located near Phoenix, Arizona, is considering where to locate a new phone switch that will link five buildings. The buildings are located at (0, 0),(2, 6), (10, 2), (3, 9), and
Frank Green, an independent TV repairman, is considering purchasing a home in Ames, Iowa, that he will use as a base of operations for his repair business. Frank’s primary sources of business are
Consider the rel chart for the Meat Me fast-food restaurant, given in Figure 11–2.Assume that the areas required for each department are Department Area Required (square feet)Cooking burgers 200
An initial layout for five departments and a from-to flow data chart are given in Figure 11–34. Assuming that departments A and D are in fixed locations and cannot be moved, find the layout
An initial layout for four departments and from-to charts giving distances separating departments and unit transportation costs appear in Figure 11–33. Using the CRAFT pairwise exchange technique,
A facility has the shape shown in Figure 11–32. Using the methods described in Appendix 11–A, find the location of the centroid of this facility.
A machine shop located on the outskirts of Los Angeles accepts custom orders from a number of high-tech firms in southern California. The machine shop consists of four departments: A (lathes), B
A large supermarket chain in the Southeast requires five additional warehouses in the Atlanta area. It has identified five sites for these warehouses. The annual transportation costs (in $000) for
A real estate firm wishes to open four new offices in the Boston area. There are six potential sites available. Based on the number of employees in each office and the location of the properties that
Describe the following location problems and how they differ from those previously treated in this chapter:a. Location–allocation problemsb. Discrete location problemsc. Network location problems
Consider the University of the Far West described in Example 11.5. Suppose that the university administration has decided that two audiovisual centers are needed.Each center would have different
Consider Problem 28 of this chapter. Suppose that two new machines,A and B, are to be located in the shop. Machine A has 1, and as the expected numbers of loads transported to the existing five
For each of the location problems described, discuss which of the seven assumptions listed in this section are likely to be violated:a. Locating three new machines in a machine shop.b. Locating an
A telecommunications system is going to be installed at a company site. The switching center that governs the system must be located in one of the five buildings to be served. The goal is to minimize
Three existing facilities are located at (0, 0), (5, 5), and (10, 10). The weights applied to these facilities are 1, 2, and 3, respectively. Find the location of a new facility that minimizes the
For the situation described in Problem 28,a. Find the gravity solution.b. Use the answer obtained in part (a) as an initial solution for the Euclidean distance problem. Determine (xi, yi)
Solve Problem 32 assuming a minimax rectilinear objective.
Solve Problem 30 assuming a minimax rectilinear objective.
Solve Problem 28 assuming a minimax rectilinear objective.
Draw contour lines for this problem. (Refer to Appendix 11–B.)
Two facilities, located at (0, 0) and (0, 10), have respective weights 2 and
(Refer to Appendix 11–B.)
Draw contour lines for the location problem described in Problem
(Refer to Appendix 11–B.)
Draw contour lines for the problem of locating a machine shop described in Problem
An industrial park consists of 16 buildings. The corporations in the park are sharing the cost of construction and maintenance for a new first-aid center. Because of the park’s layout, distances
In Problem 30, suppose that Mr. Bender can park only in lots located at (1) 40th Street and 8thAvenue, (2) 46th Street and 6thAvenue, and (3) 33rd Street and 5thAvenue.Where should he plan to park?
Armand Bender plans to visit six customers in Manhattan. Three are located in a building at 34th Street and 7th Avenue. The remaining customers are at 48th and 8th, 38th and 3rd, and 42nd and 5th.
Solve the problem of locating the new audiovisual center at the University of the Far West described in Example 11.5, assuming that the weights are respectively 80, 12, 56, 104, 42, and 17 for the
A machine shop has five machines, located at (3, 3), (3, 7), (8, 4), (12, 3), and (14, 6), respectively. A new machine is to be located in the shop with the following expected numbers of loads per
For each of the seven examples of location problems listed in this section, indicate which distance measure, Euclidean or rectilinear, would be more appropriate. (Discuss how, in some cases, one or
For the situation described in Problem 25, suppose that there are only three feasible locations for the new facility: (8, 16), (6, 15), and (4, 18).a. What is the optimal location if the objective is
A coordinate system is superimposed on a map. Three existing facilities are located at (5, 15), (10, 20), and (6, 9). Compute both the rectilinear and the Euclidean distances separating each facility
Consider the problem of locating a new hospital in a metropolitan area. List the factors that can be quantified and those that cannot. Comment on the usefulness of quantitative methods in the
With which decisions related to FMS design or control can the following methods assist? Also, briefly describe how each method would be used.a. Queuing theoryb. Simulationc. Mathematical programming
For what reason might a traditional NPV (net present value) analysis not be an appropriate means for evaluating the desirability of purchasing an FMS?
For each of the case situations described, state which of the three types of manufacturing systems would be most appropriate: (1) stand-alone numerically controlled machines, (2) FMS, (3) fixed
In each case listed, state whether the factor listed is an advantage or a disadvantage of FMS. Discuss the reasons for your choice.a. Cost.b. Ability to handle different parts requirements.c.
Six departments, A, B, C, D, E, and F, consume respectively 12, 6, 9, 18, 22, and 6 squares. Based on a sweep width of 4 and a facility size of 5 by 16, use the techniques employed by ALDEP to find a
A facility consisting of eight departments has the activity relationship chart pictured in Figure 11–20. Compute the TCR for each department that would be used by CORELAP.
Consider the initial layout pictured in Figure 11–19 and the two from-to charts giving the flow and cost data. Use the CRAFT approach to obtain a final layout. Compare the total cost of each layout
Consider the initial layout and from-to chart appearing in Figure 11–18. Assuming the goal is to minimize the total distance traveled, determine the final layoutrecommended byCRAFTusing the
Determine the centroids for the six departments in the layout pictured in Figure 11–17 using the methods outlined in Appendix 11–A.
Consider the initial layout for Example 11.4, which appears in Figure 11–11. Draw a figure showing the layout obtained from exchanging the locations of A and D, and find the centroids of A and D in
For Example 11.4, which illustrated CRAFT, verify the values of the predicted costs(2,715, 3,185, 2,735, and 2,830) obtained in the first iteration.
a. Discuss the advantages and disadvantages of using computer programs to develop layouts.b. Do the results of the studies discussed in Section 11.6 suggest that human planners or computer programs
Briefly describe each of the following computerized layout techniques. In each case, indicate whether the method is a construction or improvement method.a. CRAFTb. COFADc. ALDEPd. CORELAPe. PLANET
Consider the following problem with two locations and three machines. Suppose that the costs of transporting a unit load from location j to location r are given in the following table:To location A B
University of the Atlantic is moving its business school into a new building, which has been designed to house six academic departments. The average time required for a student to get to and from
Each of four machines is to be assigned to one of five possible locations. The objective is to assign the machines to locations that will minimize the materials handling cost. The machine–location
Solve the following assignment problem:A B C D 1 21 24 26 23 2 29 27 30 29 3 24 25 34 27 4 28 26 28 25

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