Solution Manual
Quantitative Analysis For Management, By Render
All Chapters 1 To 15 Reviewed
14TH EDITION
11-1
Copyright © 2024 Pearson Education, Inc.
,CHAPTER 1
Introduction to Quantitative Analysis
TEACHING SUGGESTIONS
Teaching Suggestion 1.1: Importance of Qualitative Factors.
Section 1.1 gives students an overview of quantitative analysis. In this section, a number of
qualitative factors, including federal legislation and new technology, are discussed. Students can
be asked to discuss other qualitative factors that could have an impact on quantitative analysis.
Waiting lines and project planning can be used as examples.
Teaching Suggestion 1.2: Discussing Other Quantitative Analysis Problems.
Section 1.2 covers an application of the quantitative analysis approach. Students can be asked to
describe other problems or areas that could benefit from quantitative analysis.
Teaching Suggestion 1.3: Discussing Conflicting Viewpoints.
Possible problems in the QA approach are presented in this chapter. A discussion of conflicting
viewpoints within the organization can help students understand this problem. For example, how
many people should staff a registration desk at a university? Students will want more staff to reduce
waiting time, while university administrators will want less staff to save money. A discussion of
these types of conflicting viewpoints will help students understand some of the problems of using
quantitative analysis.
Teaching Suggestion 1.4: Difficulty of Getting Input Data.
A major problem in quantitative analysis is getting proper input data. Students can be asked to
explain how they would get the information they need to determine inventory ordering or carrying
costs. Role-playing with students assuming the parts of the analyst who needs inventory costs and
the instructor playing the part of a veteran inventory manager can be fun and interesting. Students
quickly learn that getting good data can be the most difficult part of using quantitative analysis.
Teaching Suggestion 1.5: Dealing with Resistance to Change.
11-2
Copyright © 2024 Pearson Education, Inc.
,Resistance to change is discussed in this chapter. Students can be asked to explain how they would
introduce a new system or change within the organization. People resisting new approaches can
be a major stumbling block to the successful implementation of quantitative analysis. Students can
be asked why some people may be afraid of a new inventory control or forecasting system.
SOLUTIONS TO DISCUSSION QUESTIONS AND PROBLEMS
1-1. Quantitative analysis involves the use of mathematical equations or relationships in analyzing
a particular problem. In most cases, the results of quantitative analysis will be one or more numbers
that can be used by managers and decision makers in making better decisions. Calculating rates of
return, financial ratios from a balance sheet and profit and loss statement, determining the number
of units that must be produced in order to break even, and many similar techniques are examples
of quantitative analysis. Qualitative analysis involves the investigation of factors in a decision-
making problem that cannot be quantified or stated in mathematical terms. The state of the
economy, current or pending legislation, perceptions about a potential client, and similar situations
reveal the use of qualitative analysis. In most decision-making problems, both quantitative and
qualitative analysis are used. In this book, however, we emphasize the techniques and approaches
of quantitative analysis.
1-2. Quantitative analysis is the scientific approach to managerial decision making. This type of
analysis is a logical and rational approach to making decisions. Emotions, guesswork, and whim
are not part of the quantitative analysis approach. A number of organizations support the use of
the scientific approach: the Institute for Operation Research and Management Science
(INFORMS), Decision Sciences Institute, and Academy of Management.
1-3. The three categories of business analytics are descriptive, predictive, and prescriptive.
Descriptive analytics provides an indication of how things were performed in the past. Predictive
analytics uses past data to forecast what will happen in the future. Prescriptive analytics uses
optimization and other models to present better ways for a company to operate to reach goals and
objectives.
1-4. Quantitative analysis is a step-by-step process that allows decision makers to investigate
problems using quantitative techniques. The steps of the quantitative analysis process include
defining the problem, developing a model, acquiring input data, developing a solution, testing the
solution, analyzing the results, and implementing the results. In every case, the analysis begins
with defining the problem. The problem could be too many stockouts, too many bad debts, or
determining the products to produce that will result in the maximum profit for the organization.
After the problems have been defined, the next step is to develop one or more models. These
models could be inventory control models, models that describe the debt situation in the
organization, and so on. Once the models have been developed, the next step is to acquire input
data. In the inventory problem, for example, such factors as the annual demand, the ordering cost,
and the carrying cost would be input data that are used by the model developed in the preceding
step. In determining the products to produce in order to maximize profits, the input data could be
such things as the profitability for all the different products, the amount of time that is available
at the various production departments that produce the products, and the amount of time it takes
for each product to be produced in each production department. The next step is developing the
solution. This requires manipulation of the model in order to determine the best
11-3
Copyright © 2024 Pearson Education, Inc.
, solution. Next, the results are tested, analyzed, and implemented. In the inventory control problem,
this might result in determining and implementing a policy to order a certain amount of inventory
at specified intervals. For the problem of determining the best products to produce, this might mean
testing, analyzing, and implementing a decision to produce a certain quantity of given products.
1-5. Although the formal study of quantitative analysis and the refinement of the tools and
techniques of the scientific method have occurred only in the recent past, quantitative approaches
to decision making have been in existence since the beginning of time. In the early 1900s,
Frederick W. Taylor developed the principles of the scientific approach. During World War II,
quantitative analysis was intensified and used by the military. Because of the success of these
techniques during World War II, interest continued after the war.
1-6. Model types include the scale model, physical model, and schematic model (which is a picture
or drawing of reality). In this book, mathematical models are used to describe mathematical
relationships in solving quantitative problems.
In this question, the student is asked to develop two mathematical models. The student might
develop a number of models that relate to finance, marketing, accounting, statistics, or other fields.
The purpose of this part of the question is to have the student develop a mathematical relationship
between variables with which the student is familiar.
1-7. Input data can come from company reports and documents, interviews with employees and
other personnel, direct measurement, and sampling procedures. For many problems, a number of
different sources are required to obtain data, and in some cases it is necessary to obtain the same
data from different sources in order to check the accuracy and consistency of the input data. If the
input data are not accurate, the results can be misleading and very costly to the organization. This
concept is called ―garbage in, garbage out.‖
1-8. Implementation is the process of taking the solution and incorporating it into the company or
organization. This is the final step in the quantitative analysis approach, and if a good job is not
done with implementation, all of the effort expended on the previous steps can be wasted.
1-9. Sensitivity analysis and post optimality analysis allow the decision maker to determine how
the final solution to the problem will change when the input data or the model change. This type
of analysis is very important when the input data or model has not been specified properly. A
sensitive solution is one in which the results of the solution to the problem will change drastically
or by a large amount with small changes in the data or in the model. When the model is not
sensitive, the results or solutions to the model will not change significantly with changes in the
input data or in the model. Models that are very sensitive require that the input data and the model
itself be thoroughly tested to make sure that both are very accurate and consistent with the problem
statement.
1-10. There are a large number of quantitative terms that may not be understood by managers.
Examples include PERT, CPM, simulation, the Monte Carlo method, mathematical programming,
EOQ, and so on. The student should explain each of the four terms selected in his or her own
words.
1-11. Many quantitative analysts enjoy building mathematical models and solving them to find
the optimal solution to a problem. Others enjoy dealing with other technical aspects, for example,
data analysis and collection, computer programming, or computations. The
11-4
Copyright © 2024 Pearson Education, Inc.
Quantitative Analysis For Management, By Render
All Chapters 1 To 15 Reviewed
14TH EDITION
11-1
Copyright © 2024 Pearson Education, Inc.
,CHAPTER 1
Introduction to Quantitative Analysis
TEACHING SUGGESTIONS
Teaching Suggestion 1.1: Importance of Qualitative Factors.
Section 1.1 gives students an overview of quantitative analysis. In this section, a number of
qualitative factors, including federal legislation and new technology, are discussed. Students can
be asked to discuss other qualitative factors that could have an impact on quantitative analysis.
Waiting lines and project planning can be used as examples.
Teaching Suggestion 1.2: Discussing Other Quantitative Analysis Problems.
Section 1.2 covers an application of the quantitative analysis approach. Students can be asked to
describe other problems or areas that could benefit from quantitative analysis.
Teaching Suggestion 1.3: Discussing Conflicting Viewpoints.
Possible problems in the QA approach are presented in this chapter. A discussion of conflicting
viewpoints within the organization can help students understand this problem. For example, how
many people should staff a registration desk at a university? Students will want more staff to reduce
waiting time, while university administrators will want less staff to save money. A discussion of
these types of conflicting viewpoints will help students understand some of the problems of using
quantitative analysis.
Teaching Suggestion 1.4: Difficulty of Getting Input Data.
A major problem in quantitative analysis is getting proper input data. Students can be asked to
explain how they would get the information they need to determine inventory ordering or carrying
costs. Role-playing with students assuming the parts of the analyst who needs inventory costs and
the instructor playing the part of a veteran inventory manager can be fun and interesting. Students
quickly learn that getting good data can be the most difficult part of using quantitative analysis.
Teaching Suggestion 1.5: Dealing with Resistance to Change.
11-2
Copyright © 2024 Pearson Education, Inc.
,Resistance to change is discussed in this chapter. Students can be asked to explain how they would
introduce a new system or change within the organization. People resisting new approaches can
be a major stumbling block to the successful implementation of quantitative analysis. Students can
be asked why some people may be afraid of a new inventory control or forecasting system.
SOLUTIONS TO DISCUSSION QUESTIONS AND PROBLEMS
1-1. Quantitative analysis involves the use of mathematical equations or relationships in analyzing
a particular problem. In most cases, the results of quantitative analysis will be one or more numbers
that can be used by managers and decision makers in making better decisions. Calculating rates of
return, financial ratios from a balance sheet and profit and loss statement, determining the number
of units that must be produced in order to break even, and many similar techniques are examples
of quantitative analysis. Qualitative analysis involves the investigation of factors in a decision-
making problem that cannot be quantified or stated in mathematical terms. The state of the
economy, current or pending legislation, perceptions about a potential client, and similar situations
reveal the use of qualitative analysis. In most decision-making problems, both quantitative and
qualitative analysis are used. In this book, however, we emphasize the techniques and approaches
of quantitative analysis.
1-2. Quantitative analysis is the scientific approach to managerial decision making. This type of
analysis is a logical and rational approach to making decisions. Emotions, guesswork, and whim
are not part of the quantitative analysis approach. A number of organizations support the use of
the scientific approach: the Institute for Operation Research and Management Science
(INFORMS), Decision Sciences Institute, and Academy of Management.
1-3. The three categories of business analytics are descriptive, predictive, and prescriptive.
Descriptive analytics provides an indication of how things were performed in the past. Predictive
analytics uses past data to forecast what will happen in the future. Prescriptive analytics uses
optimization and other models to present better ways for a company to operate to reach goals and
objectives.
1-4. Quantitative analysis is a step-by-step process that allows decision makers to investigate
problems using quantitative techniques. The steps of the quantitative analysis process include
defining the problem, developing a model, acquiring input data, developing a solution, testing the
solution, analyzing the results, and implementing the results. In every case, the analysis begins
with defining the problem. The problem could be too many stockouts, too many bad debts, or
determining the products to produce that will result in the maximum profit for the organization.
After the problems have been defined, the next step is to develop one or more models. These
models could be inventory control models, models that describe the debt situation in the
organization, and so on. Once the models have been developed, the next step is to acquire input
data. In the inventory problem, for example, such factors as the annual demand, the ordering cost,
and the carrying cost would be input data that are used by the model developed in the preceding
step. In determining the products to produce in order to maximize profits, the input data could be
such things as the profitability for all the different products, the amount of time that is available
at the various production departments that produce the products, and the amount of time it takes
for each product to be produced in each production department. The next step is developing the
solution. This requires manipulation of the model in order to determine the best
11-3
Copyright © 2024 Pearson Education, Inc.
, solution. Next, the results are tested, analyzed, and implemented. In the inventory control problem,
this might result in determining and implementing a policy to order a certain amount of inventory
at specified intervals. For the problem of determining the best products to produce, this might mean
testing, analyzing, and implementing a decision to produce a certain quantity of given products.
1-5. Although the formal study of quantitative analysis and the refinement of the tools and
techniques of the scientific method have occurred only in the recent past, quantitative approaches
to decision making have been in existence since the beginning of time. In the early 1900s,
Frederick W. Taylor developed the principles of the scientific approach. During World War II,
quantitative analysis was intensified and used by the military. Because of the success of these
techniques during World War II, interest continued after the war.
1-6. Model types include the scale model, physical model, and schematic model (which is a picture
or drawing of reality). In this book, mathematical models are used to describe mathematical
relationships in solving quantitative problems.
In this question, the student is asked to develop two mathematical models. The student might
develop a number of models that relate to finance, marketing, accounting, statistics, or other fields.
The purpose of this part of the question is to have the student develop a mathematical relationship
between variables with which the student is familiar.
1-7. Input data can come from company reports and documents, interviews with employees and
other personnel, direct measurement, and sampling procedures. For many problems, a number of
different sources are required to obtain data, and in some cases it is necessary to obtain the same
data from different sources in order to check the accuracy and consistency of the input data. If the
input data are not accurate, the results can be misleading and very costly to the organization. This
concept is called ―garbage in, garbage out.‖
1-8. Implementation is the process of taking the solution and incorporating it into the company or
organization. This is the final step in the quantitative analysis approach, and if a good job is not
done with implementation, all of the effort expended on the previous steps can be wasted.
1-9. Sensitivity analysis and post optimality analysis allow the decision maker to determine how
the final solution to the problem will change when the input data or the model change. This type
of analysis is very important when the input data or model has not been specified properly. A
sensitive solution is one in which the results of the solution to the problem will change drastically
or by a large amount with small changes in the data or in the model. When the model is not
sensitive, the results or solutions to the model will not change significantly with changes in the
input data or in the model. Models that are very sensitive require that the input data and the model
itself be thoroughly tested to make sure that both are very accurate and consistent with the problem
statement.
1-10. There are a large number of quantitative terms that may not be understood by managers.
Examples include PERT, CPM, simulation, the Monte Carlo method, mathematical programming,
EOQ, and so on. The student should explain each of the four terms selected in his or her own
words.
1-11. Many quantitative analysts enjoy building mathematical models and solving them to find
the optimal solution to a problem. Others enjoy dealing with other technical aspects, for example,
data analysis and collection, computer programming, or computations. The
11-4
Copyright © 2024 Pearson Education, Inc.
