MSL 5080, Methods of Analysis for Business Operations 1 .docxgertrudebellgrove
MSL 5080, Methods of Analysis for Business Operations 1
Course Learning Outcomes for Unit I
Upon completion of this unit, students should be able to:
1. Differentiate the steps of the quantitative analysis approach.
1.1 Apply quantitative analysis in a real-world situation.
1.2 Perform a break-even analysis.
Reading Assignment
Chapter 1: Introduction to Quantitative Analysis
Unit Lesson
Quantitative Analysis
As good an opening as any to a postgraduate quantitative analysis course is to confirm that yes, mathematics
is involved to improve situations and outcomes and also to stress that leadership has always been the
foundation for quantitative analysis. The answer will not make you prosper, but leading the effort in deciding
what quantitative analysis measurements mean and what to do after seeing these numbers may indeed
benefit your organization. There will be a bit more discussion on what leaders may do with quantitative
analysis after introducing some fundamentals.
To quote the authors from the textbook, “Quantitative analysis is the scientific approach to managerial
decision-making” (Render, Stair, Hanna, & Hale, 2015, p. 2). A scientific approach means calculating with
numbers. Conversely, perhaps you have worked for leaders who used guesswork or a gut feeling to decide a
numbers-based, quantitative issue. Perhaps the leader chose fortunately, and that is good; but pursuit of
good fortune becomes hazardous if you are using hope and chance to gain a good outcome. You may have
noticed this does not work well for most Las Vegas vacationers who enjoy themselves by gambling against
high odds that favor the casinos. So, quantitative analysis can have a valuable place as a decision tool if you
can make the analysis properly fit the situation.
The use of quantitative analysis to keep track, measure, analyze totals, and forecast, is older than language
itself. Sumerians, and other peoples in the Middle East, used it for grain and livestock categories. Exploration
of mathematics theory (i.e., learning how to add, subtract, multiply, and divide) made quantitative analysis
possible. Now, apply mathematics to estimate probability to see what might happen, determine averages and
percentages to see how much might be involved, and address many specific situations. As you can imagine,
just knowing a number (e.g., how much livestock a person has) may not mean much by itself. This is where
mathematics helps: The purpose of quantitative analysis is to turn raw data into meaningful information.
Formulas turn that data into something leaders can use along with considering qualitative factors such as
weather and customer demand. In theory, good leadership should do the rest.
Business Analytics
The textbook covers the terms below that you are intended to recall throughout the course:
Business analytics uses (usually large amounts of) data to make better business decisions. There are
three catego ...
MSL 5080, Methods of Analysis for Business Operations 1 .docxpoulterbarbara
MSL 5080, Methods of Analysis for Business Operations 1
Course Learning Outcomes for Unit I
Upon completion of this unit, students should be able to:
1. Differentiate the steps of the quantitative analysis approach.
1.1 Apply quantitative analysis in a real-world situation.
1.2 Perform a break-even analysis.
Reading Assignment
Chapter 1: Introduction to Quantitative Analysis
Unit Lesson
Quantitative Analysis
As good an opening as any to a postgraduate quantitative analysis course is to confirm that yes, mathematics
is involved to improve situations and outcomes and also to stress that leadership has always been the
foundation for quantitative analysis. The answer will not make you prosper, but leading the effort in deciding
what quantitative analysis measurements mean and what to do after seeing these numbers may indeed
benefit your organization. There will be a bit more discussion on what leaders may do with quantitative
analysis after introducing some fundamentals.
To quote the authors from the textbook, “Quantitative analysis is the scientific approach to managerial
decision-making” (Render, Stair, Hanna, & Hale, 2015, p. 2). A scientific approach means calculating with
numbers. Conversely, perhaps you have worked for leaders who used guesswork or a gut feeling to decide a
numbers-based, quantitative issue. Perhaps the leader chose fortunately, and that is good; but pursuit of
good fortune becomes hazardous if you are using hope and chance to gain a good outcome. You may have
noticed this does not work well for most Las Vegas vacationers who enjoy themselves by gambling against
high odds that favor the casinos. So, quantitative analysis can have a valuable place as a decision tool if you
can make the analysis properly fit the situation.
The use of quantitative analysis to keep track, measure, analyze totals, and forecast, is older than language
itself. Sumerians, and other peoples in the Middle East, used it for grain and livestock categories. Exploration
of mathematics theory (i.e., learning how to add, subtract, multiply, and divide) made quantitative analysis
possible. Now, apply mathematics to estimate probability to see what might happen, determine averages and
percentages to see how much might be involved, and address many specific situations. As you can imagine,
just knowing a number (e.g., how much livestock a person has) may not mean much by itself. This is where
mathematics helps: The purpose of quantitative analysis is to turn raw data into meaningful information.
Formulas turn that data into something leaders can use along with considering qualitative factors such as
weather and customer demand. In theory, good leadership should do the rest.
Business Analytics
The textbook covers the terms below that you are intended to recall throughout the course:
Business analytics uses (usually large amounts of) data to make better business decisions. There are
three catego.
These slides demonstrate my experience in handling Microsoft Excel 2007 beyond just using formulae but combining the formulas with Excel\'s features to better communicate quantitative results.
Perform magic and save hours of time with Model Analyzer for Excel. Decide among multiple investment alternatives. Analyze multiple scenarios and how sensitive certain variables are.
MSL 5080, Methods of Analysis for Business Operations 1 .docxgertrudebellgrove
MSL 5080, Methods of Analysis for Business Operations 1
Course Learning Outcomes for Unit I
Upon completion of this unit, students should be able to:
1. Differentiate the steps of the quantitative analysis approach.
1.1 Apply quantitative analysis in a real-world situation.
1.2 Perform a break-even analysis.
Reading Assignment
Chapter 1: Introduction to Quantitative Analysis
Unit Lesson
Quantitative Analysis
As good an opening as any to a postgraduate quantitative analysis course is to confirm that yes, mathematics
is involved to improve situations and outcomes and also to stress that leadership has always been the
foundation for quantitative analysis. The answer will not make you prosper, but leading the effort in deciding
what quantitative analysis measurements mean and what to do after seeing these numbers may indeed
benefit your organization. There will be a bit more discussion on what leaders may do with quantitative
analysis after introducing some fundamentals.
To quote the authors from the textbook, “Quantitative analysis is the scientific approach to managerial
decision-making” (Render, Stair, Hanna, & Hale, 2015, p. 2). A scientific approach means calculating with
numbers. Conversely, perhaps you have worked for leaders who used guesswork or a gut feeling to decide a
numbers-based, quantitative issue. Perhaps the leader chose fortunately, and that is good; but pursuit of
good fortune becomes hazardous if you are using hope and chance to gain a good outcome. You may have
noticed this does not work well for most Las Vegas vacationers who enjoy themselves by gambling against
high odds that favor the casinos. So, quantitative analysis can have a valuable place as a decision tool if you
can make the analysis properly fit the situation.
The use of quantitative analysis to keep track, measure, analyze totals, and forecast, is older than language
itself. Sumerians, and other peoples in the Middle East, used it for grain and livestock categories. Exploration
of mathematics theory (i.e., learning how to add, subtract, multiply, and divide) made quantitative analysis
possible. Now, apply mathematics to estimate probability to see what might happen, determine averages and
percentages to see how much might be involved, and address many specific situations. As you can imagine,
just knowing a number (e.g., how much livestock a person has) may not mean much by itself. This is where
mathematics helps: The purpose of quantitative analysis is to turn raw data into meaningful information.
Formulas turn that data into something leaders can use along with considering qualitative factors such as
weather and customer demand. In theory, good leadership should do the rest.
Business Analytics
The textbook covers the terms below that you are intended to recall throughout the course:
Business analytics uses (usually large amounts of) data to make better business decisions. There are
three catego ...
MSL 5080, Methods of Analysis for Business Operations 1 .docxpoulterbarbara
MSL 5080, Methods of Analysis for Business Operations 1
Course Learning Outcomes for Unit I
Upon completion of this unit, students should be able to:
1. Differentiate the steps of the quantitative analysis approach.
1.1 Apply quantitative analysis in a real-world situation.
1.2 Perform a break-even analysis.
Reading Assignment
Chapter 1: Introduction to Quantitative Analysis
Unit Lesson
Quantitative Analysis
As good an opening as any to a postgraduate quantitative analysis course is to confirm that yes, mathematics
is involved to improve situations and outcomes and also to stress that leadership has always been the
foundation for quantitative analysis. The answer will not make you prosper, but leading the effort in deciding
what quantitative analysis measurements mean and what to do after seeing these numbers may indeed
benefit your organization. There will be a bit more discussion on what leaders may do with quantitative
analysis after introducing some fundamentals.
To quote the authors from the textbook, “Quantitative analysis is the scientific approach to managerial
decision-making” (Render, Stair, Hanna, & Hale, 2015, p. 2). A scientific approach means calculating with
numbers. Conversely, perhaps you have worked for leaders who used guesswork or a gut feeling to decide a
numbers-based, quantitative issue. Perhaps the leader chose fortunately, and that is good; but pursuit of
good fortune becomes hazardous if you are using hope and chance to gain a good outcome. You may have
noticed this does not work well for most Las Vegas vacationers who enjoy themselves by gambling against
high odds that favor the casinos. So, quantitative analysis can have a valuable place as a decision tool if you
can make the analysis properly fit the situation.
The use of quantitative analysis to keep track, measure, analyze totals, and forecast, is older than language
itself. Sumerians, and other peoples in the Middle East, used it for grain and livestock categories. Exploration
of mathematics theory (i.e., learning how to add, subtract, multiply, and divide) made quantitative analysis
possible. Now, apply mathematics to estimate probability to see what might happen, determine averages and
percentages to see how much might be involved, and address many specific situations. As you can imagine,
just knowing a number (e.g., how much livestock a person has) may not mean much by itself. This is where
mathematics helps: The purpose of quantitative analysis is to turn raw data into meaningful information.
Formulas turn that data into something leaders can use along with considering qualitative factors such as
weather and customer demand. In theory, good leadership should do the rest.
Business Analytics
The textbook covers the terms below that you are intended to recall throughout the course:
Business analytics uses (usually large amounts of) data to make better business decisions. There are
three catego.
These slides demonstrate my experience in handling Microsoft Excel 2007 beyond just using formulae but combining the formulas with Excel\'s features to better communicate quantitative results.
Perform magic and save hours of time with Model Analyzer for Excel. Decide among multiple investment alternatives. Analyze multiple scenarios and how sensitive certain variables are.
Microsoft Excel 101: What you must knowSwati Chhabra
Excel is the powerhouse of spreadsheet software most commonly used for business applications and thereby making your job easier and less stressful. The tool that is capable of analyzing data, performing calculations, presenting information in advanced dashboards. It also integrates information from different programs.
This webinar will help you gain the necessary skills to create, edit, format, and print basic Microsoft Excel worksheets.
what is the future of Pi Network currency.DOT TECH
The future of the Pi cryptocurrency is uncertain, and its success will depend on several factors. Pi is a relatively new cryptocurrency that aims to be user-friendly and accessible to a wide audience. Here are a few key considerations for its future:
Message: @Pi_vendor_247 on telegram if u want to sell PI COINS.
1. Mainnet Launch: As of my last knowledge update in January 2022, Pi was still in the testnet phase. Its success will depend on a successful transition to a mainnet, where actual transactions can take place.
2. User Adoption: Pi's success will be closely tied to user adoption. The more users who join the network and actively participate, the stronger the ecosystem can become.
3. Utility and Use Cases: For a cryptocurrency to thrive, it must offer utility and practical use cases. The Pi team has talked about various applications, including peer-to-peer transactions, smart contracts, and more. The development and implementation of these features will be essential.
4. Regulatory Environment: The regulatory environment for cryptocurrencies is evolving globally. How Pi navigates and complies with regulations in various jurisdictions will significantly impact its future.
5. Technology Development: The Pi network must continue to develop and improve its technology, security, and scalability to compete with established cryptocurrencies.
6. Community Engagement: The Pi community plays a critical role in its future. Engaged users can help build trust and grow the network.
7. Monetization and Sustainability: The Pi team's monetization strategy, such as fees, partnerships, or other revenue sources, will affect its long-term sustainability.
It's essential to approach Pi or any new cryptocurrency with caution and conduct due diligence. Cryptocurrency investments involve risks, and potential rewards can be uncertain. The success and future of Pi will depend on the collective efforts of its team, community, and the broader cryptocurrency market dynamics. It's advisable to stay updated on Pi's development and follow any updates from the official Pi Network website or announcements from the team.
US Economic Outlook - Being Decided - M Capital Group August 2021.pdfpchutichetpong
The U.S. economy is continuing its impressive recovery from the COVID-19 pandemic and not slowing down despite re-occurring bumps. The U.S. savings rate reached its highest ever recorded level at 34% in April 2020 and Americans seem ready to spend. The sectors that had been hurt the most by the pandemic specifically reduced consumer spending, like retail, leisure, hospitality, and travel, are now experiencing massive growth in revenue and job openings.
Could this growth lead to a “Roaring Twenties”? As quickly as the U.S. economy contracted, experiencing a 9.1% drop in economic output relative to the business cycle in Q2 2020, the largest in recorded history, it has rebounded beyond expectations. This surprising growth seems to be fueled by the U.S. government’s aggressive fiscal and monetary policies, and an increase in consumer spending as mobility restrictions are lifted. Unemployment rates between June 2020 and June 2021 decreased by 5.2%, while the demand for labor is increasing, coupled with increasing wages to incentivize Americans to rejoin the labor force. Schools and businesses are expected to fully reopen soon. In parallel, vaccination rates across the country and the world continue to rise, with full vaccination rates of 50% and 14.8% respectively.
However, it is not completely smooth sailing from here. According to M Capital Group, the main risks that threaten the continued growth of the U.S. economy are inflation, unsettled trade relations, and another wave of Covid-19 mutations that could shut down the world again. Have we learned from the past year of COVID-19 and adapted our economy accordingly?
“In order for the U.S. economy to continue growing, whether there is another wave or not, the U.S. needs to focus on diversifying supply chains, supporting business investment, and maintaining consumer spending,” says Grace Feeley, a research analyst at M Capital Group.
While the economic indicators are positive, the risks are coming closer to manifesting and threatening such growth. The new variants spreading throughout the world, Delta, Lambda, and Gamma, are vaccine-resistant and muddy the predictions made about the economy and health of the country. These variants bring back the feeling of uncertainty that has wreaked havoc not only on the stock market but the mindset of people around the world. MCG provides unique insight on how to mitigate these risks to possibly ensure a bright economic future.
how to swap pi coins to foreign currency withdrawable.DOT TECH
As of my last update, Pi is still in the testing phase and is not tradable on any exchanges.
However, Pi Network has announced plans to launch its Testnet and Mainnet in the future, which may include listing Pi on exchanges.
The current method for selling pi coins involves exchanging them with a pi vendor who purchases pi coins for investment reasons.
If you want to sell your pi coins, reach out to a pi vendor and sell them to anyone looking to sell pi coins from any country around the globe.
Below is the contact information for my personal pi vendor.
Telegram: @Pi_vendor_247
Empowering the Unbanked: The Vital Role of NBFCs in Promoting Financial Inclu...Vighnesh Shashtri
In India, financial inclusion remains a critical challenge, with a significant portion of the population still unbanked. Non-Banking Financial Companies (NBFCs) have emerged as key players in bridging this gap by providing financial services to those often overlooked by traditional banking institutions. This article delves into how NBFCs are fostering financial inclusion and empowering the unbanked.
where can I find a legit pi merchant onlineDOT TECH
Yes. This is very easy what you need is a recommendation from someone who has successfully traded pi coins before with a merchant.
Who is a pi merchant?
A pi merchant is someone who buys pi network coins and resell them to Investors looking forward to hold thousands of pi coins before the open mainnet.
I will leave the telegram contact of my personal pi merchant to trade with
@Pi_vendor_247
How to get verified on Coinbase Account?_.docxBuy bitget
t's important to note that buying verified Coinbase accounts is not recommended and may violate Coinbase's terms of service. Instead of searching to "buy verified Coinbase accounts," follow the proper steps to verify your own account to ensure compliance and security.
The Evolution of Non-Banking Financial Companies (NBFCs) in India: Challenges...beulahfernandes8
Role in Financial System
NBFCs are critical in bridging the financial inclusion gap.
They provide specialized financial services that cater to segments often neglected by traditional banks.
Economic Impact
NBFCs contribute significantly to India's GDP.
They support sectors like micro, small, and medium enterprises (MSMEs), housing finance, and personal loans.
Poonawalla Fincorp and IndusInd Bank Introduce New Co-Branded Credit Cardnickysharmasucks
The unveiling of the IndusInd Bank Poonawalla Fincorp eLITE RuPay Platinum Credit Card marks a notable milestone in the Indian financial landscape, showcasing a successful partnership between two leading institutions, Poonawalla Fincorp and IndusInd Bank. This co-branded credit card not only offers users a plethora of benefits but also reflects a commitment to innovation and adaptation. With a focus on providing value-driven and customer-centric solutions, this launch represents more than just a new product—it signifies a step towards redefining the banking experience for millions. Promising convenience, rewards, and a touch of luxury in everyday financial transactions, this collaboration aims to cater to the evolving needs of customers and set new standards in the industry.
how to sell pi coins in South Korea profitably.DOT TECH
Yes. You can sell your pi network coins in South Korea or any other country, by finding a verified pi merchant
What is a verified pi merchant?
Since pi network is not launched yet on any exchange, the only way you can sell pi coins is by selling to a verified pi merchant, and this is because pi network is not launched yet on any exchange and no pre-sale or ico offerings Is done on pi.
Since there is no pre-sale, the only way exchanges can get pi is by buying from miners. So a pi merchant facilitates these transactions by acting as a bridge for both transactions.
How can i find a pi vendor/merchant?
Well for those who haven't traded with a pi merchant or who don't already have one. I will leave the telegram id of my personal pi merchant who i trade pi with.
Tele gram: @Pi_vendor_247
#pi #sell #nigeria #pinetwork #picoins #sellpi #Nigerian #tradepi #pinetworkcoins #sellmypi
BYD SWOT Analysis and In-Depth Insights 2024.pptxmikemetalprod
Indepth analysis of the BYD 2024
BYD (Build Your Dreams) is a Chinese automaker and battery manufacturer that has snowballed over the past two decades to become a significant player in electric vehicles and global clean energy technology.
This SWOT analysis examines BYD's strengths, weaknesses, opportunities, and threats as it competes in the fast-changing automotive and energy storage industries.
Founded in 1995 and headquartered in Shenzhen, BYD started as a battery company before expanding into automobiles in the early 2000s.
Initially manufacturing gasoline-powered vehicles, BYD focused on plug-in hybrid and fully electric vehicles, leveraging its expertise in battery technology.
Today, BYD is the world’s largest electric vehicle manufacturer, delivering over 1.2 million electric cars globally. The company also produces electric buses, trucks, forklifts, and rail transit.
On the energy side, BYD is a major supplier of rechargeable batteries for cell phones, laptops, electric vehicles, and energy storage systems.
when will pi network coin be available on crypto exchange.DOT TECH
There is no set date for when Pi coins will enter the market.
However, the developers are working hard to get them released as soon as possible.
Once they are available, users will be able to exchange other cryptocurrencies for Pi coins on designated exchanges.
But for now the only way to sell your pi coins is through verified pi vendor.
Here is the telegram contact of my personal pi vendor
@Pi_vendor_247
The European Unemployment Puzzle: implications from population agingGRAPE
We study the link between the evolving age structure of the working population and unemployment. We build a large new Keynesian OLG model with a realistic age structure, labor market frictions, sticky prices, and aggregate shocks. Once calibrated to the European economy, we quantify the extent to which demographic changes over the last three decades have contributed to the decline of the unemployment rate. Our findings yield important implications for the future evolution of unemployment given the anticipated further aging of the working population in Europe. We also quantify the implications for optimal monetary policy: lowering inflation volatility becomes less costly in terms of GDP and unemployment volatility, which hints that optimal monetary policy may be more hawkish in an aging society. Finally, our results also propose a partial reversal of the European-US unemployment puzzle due to the fact that the share of young workers is expected to remain robust in the US.
Scope Of Macroeconomics introduction and basic theories
Excel Solver
1. CIVL 1112 Excel - Solver 1/7
Excel Solver Function Excel Solver Function
What is the Excel Solver good for?
What is the Excel Solver good for?
Solvers, or optimizers, are software tools that help
What must I do to use a solver? users find the best way to allocate scarce resources.
How do I define a model?
The resources may be raw materials, machine time or
What kind of solution can I expect? people time, money, or anything else in limited supply.
What makes a model hard to solve? The "best" or optimal solution may mean maximizing
profits, minimizing costs, or achieving the best possible
Can you show me step by step?
quality.
Excel Solver Function Excel Solver Function
What must I do to use a solver? What must I do to use a solver?
To use a solver, you must build a model that specifies: Spreadsheets such as Excel provide a convenient way
to build a model
Th resources to be used, using d i i variables
The t b d i decision i bl Anyone who has used a spreadsheet is already f
h h d d h l d familiar
l
The limits on resource usage, called constraints, and with the process:
The measure to optimize, called the objective. Cells on a worksheet can hold numbers, labels, or formulas that
calculate new values -- such as the objective of an optimization
The solver will find values for the decision variables Constraints are simply limits (specified with <=, = or >=
that satisfy the constraints while optimizing relations) on formula cells
(maximizing or minimizing) the objective. And the decision variables are simply input cells containing
numbers
Excel Solver Function Excel Solver Function
How do I define a model? Decision Variables How do I define a model? Decision Variables
A solver deals with numbers, so you'll need to quantify For example, if you are shipping goods from 3 different
the various elements of your model: decision variables, plants to 5 different warehouses, there are 3 x 5 = 15
constraints, and the objective -- and their relationships different routes alon which products could be shipped
along
Decision variables usually measure the amounts of So, you might have 15 variables, each one measuring the
resources, such as time and money, to be allocated to number of products shipped along that route
some purpose, or the level of some activity
For example, the number of products to be manufactured,
the number of pounds or gallons of a chemical required
for some process, etc.
2. CIVL 1112 Excel - Solver 2/7
Excel Solver Function Excel Solver Function
How do I define a model? Decision Variables How do I define a model? Objective
In addition, you might also have 4 different product Once you've defined the decision variables, the next
types, and you might want to plan shipments in each of step is to define the objective, which is a function that
the next 6 months depends on the variables
So this might lead to 15 x 4 x 6 = 360 variables
For example, suppose you were planning how many units
This illustrates how a model can become large rather to manufacture of three products:
quickly!
TV sets, stereos, and speaker
Part of the art of modeling is deciding how much detail
is really required
Excel Solver Function Excel Solver Function
How do I define a model? Objective How do I define a model? Objective
Your objective might be to maximize profit On a spreadsheet where the number of TV sets,
stereos and speakers are in cells D9, E9 and F9
Assume that:
h each TV set yields a profit of $ 5
h V ld f f $75, respectively,
respectively the formula would be:
each stereo $50, and
each speaker $35 = 75*D9 + 50*E9 + 35*F9
Then your objective function might be:
You'd be finished at this point, if the model did not
require any constraints
75*TV sets + 50*stereos + 35*speakers
Excel Solver Function Excel Solver Function
How do I define a model? Constraints How do I define a model? Constraints
In most models constraints play a key role in
determining what values can be assumed by the General Constraints
decision variables For example, the cell range A1:A5 contains the
p g
percentage of funds to be used to purchase 5
Constraints reflect real-world limits on variables different types of material
To define a constraint, you first compute a value based You could use cell B1 to calculate =SUM(A1:A5)
on the decision variables
Then define a constraint of B1 = 1 so that the
Then you place a limit (<=, = or >=) on this computed percentages allocated must sum up to 100%.
value
3. CIVL 1112 Excel - Solver 3/7
Excel Solver Function Excel Solver Function
How do I define a model? Constraints How do I define a model? Constraints
Physical Constraints
Bounds on Variables
Of course, you can also place a limit directly on a
y p y Many constraints are determined by the physical nature
decision variable, such as A1 <= 100 of the problem.
Upper and lower bounds on the variables are efficiently For example, if your decision variables measure the
handled by most optimizers and are very useful in many physical dimensions of an object, negative values for
problems. these variables would make no sense.
Excel Solver Function Excel Solver Function
How do I define a model? Constraints How do I define a model? Constraints
Physical Constraints Integer Constraints
Advanced optimization software also allows you to
This type of non-negativity constraint is very common
non negativity specify constraints that require decision variables to
assume only integer (whole number) values at the
Constraints such as A1 >= 0 must be stated explicitly, solution
because the solver has no other way to know that If you are scheduling a fleet of trucks, for example, a
negative values are disallowed solution that called for a fraction of a truck to travel a
certain route would not be useful.
Integer constraints normally can be applied only to
decision variables, not to quantities calculated from
them.
Excel Solver Function Excel Solver Function
What kind of solution can I expect?
A solution (set of values for the decision variables) for
What kind of solution can I expect?
which all of the constraints in the Solver model are A globally optimal solution is one where there are no
satisfied is called a feasible solution other feasible solutions with better objective function
values
Most solution algorithms first try to find a feasible
solution, and then try to improve it by finding another A locally optimal solution is one where there are no
feasible solution that increases the value of the other feasible solutions "in the vicinity" with better
objective function (when maximizing, or decreases it objective function values
when minimizing)
The Solver is designed to find optimal solutions --
An optimal solution is a feasible solution where the ideally the global optimum -- but this is not always
objective function reaches a maximum (or minimum) possible
value
4. CIVL 1112 Excel - Solver 4/7
Excel Solver Function Excel Solver Function
What makes a model hard to solve? Can you show me step by step?
Three major factors interact to determine how Consider the following problem:
difficult it will be to find an optimal solution to a solver Imagine that you are managing a factory that is building
model: three products TV sets, stereos and speakers
products:
The mathematical relationships between the objective and
Each product is assembled from parts in inventory, and
constraints, and the decision variables
there are five types of parts: chassis, picture tubes,
The size of the model (number of decision variables and speaker cones, power supplies and electronics units
constraints)
Your goal is to produce the mix of products which will
The use of integer variables - memory and solution time may maximize profits, given the inventory of products on
rise exponentially as you add more integer variables
hand
Excel Solver Function Excel Solver Function
Can you show me step by step? Can you show me step by step?
From this description, we can see that: To assemble a TV set, you need 1 chassis, 1 picture
The decision variables are the number of products to build tube, 2 speaker cones, 1 power supply and 2 sets of
The objective function will be (gross) profit electronics
To make a stereo, you need 1 chassis, 2 speaker cones, 1
Assume that you can sell TV sets for a gross profit of power supply and 1 set of electronics
$75 each, stereos for a profit of $50 each, and To build a speaker, all you need is 1 speaker cone and 1
speaker cones for $35 each set of electronics
The parts you have on hand are 450 chassis, 250
75*TV sets + 50*stereos + 35*speakers picture tubes, 800 speaker cones, 450 power supplies
and 600 sets of electronics
Excel Solver Function Excel Solver Function
Can you show me step by step? Can you show me step by step?
Before we implement this problem statement in either Building each product requires a certain number of
Excel, let's write out formulas corresponding to the parts of each type.
verbal description above.
p The number of parts used depends on the mix of
If we temporarily use the symbols: products built (constraint left hand side), and the
x for the number of TV sets assembled, number of parts of each type on hand (constraint right
y for the number of stereos, and hand side):
z for the number of speakers, 1 x + 1 y + 0 z <= 450 (Chassis)
1 x + 0 y + 0 z <= 250 (Picture tubes)
The total profit is: 2 x + 2 y + 1 z <= 800 (Speaker cones)
1 x + 1 y + 0 z <= 450 (Power supplies)
Maximize 75 x + 50 y + 35 z (Profit)
2 x + 1 y + 1 z <= 600 (Electronics)
5. CIVL 1112 Excel - Solver 5/7
Excel Solver Function Excel Solver Function
Can you show me step by step? Can you show me step by step?
The next step is to create a worksheet where the
formulas for the objective function and the constraints
are calculated
In the worksheet on the next slide, we have reserved
cells E4, F4, and G4 to hold our decision variables x, y
and z: the number of TV sets, stereos and speakers to
build
Excel Solver Function Excel Solver Function
Can you show me step by step? Can you show me step by step?
The objective function is: The Excel formula for the
75 x + 50 y + 35 z number of chassis used is:
=E7*$E$4+F7*$F$4+G7*$G$4
The Excel formula is: The Excel formula for the
=E4*E14+F4*F14+G4*G14 number of picture tubes used
is:
=E8*$E$4+F8*$F$4+G8*$G$4
The remaining # Used values
are computed in similar ways
Excel Solver Function Excel Solver Function
Can you show me step by step? Can you show me step by step?
The constraints are: To run Solver, click on the
Number of used parts must Data tab, in the Analysis
be less than inventory, or group, click Solver.
D7:D11 <= C7:C11
Number of TV sets, stereos,
and speakers must be non-
negative, or
E4:G4 >= 0
6. CIVL 1112 Excel - Solver 6/7
Excel Solver Function Excel Solver Function
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Set the target cell, or the Choose the “Set Target Cell”
value of the objective or the value of the objective
function, in this case, the function, in this case, the
Total Profit, cell E16
Profit Total Profit, cell E16
Profit
Excel Solver Function Excel Solver Function
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Set the “By Changing Cells” Set the inventory constraint:
or the value of the decision
variables, in this case, the D7:D11 <= C7:C11
number of TVs stereos and
TVs, stereos,
speakers: E4:G4
Excel Solver Function Excel Solver Function
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Set the non-negative Excel Solver is ready to run.
constraint: Just click on Solve
E4:G4 >= 0
7. CIVL 1112 Excel - Solver 7/7
Excel Solver Function Excel Solver Function
Can you show me step by step? Can you show me step by step?
When you click on Solve the
following window appears
Y can s l t an Answer
You select A s
Report and Excel inserts a
new sheet into the workbook
Excel Solver Function Excel Solver Function
How do I define a model? Questions?
See if you can use Solver to:
Maximize the Cost-Adjusted SWR f the reinforced
M h d d R for h f d
concrete beam project
What are the decision variables?
What is the objective function?
What are the constraints?