DSIMGTS
trend project
(x is time)
associate forecasting
(x=independent variable)
Steps in formulating an LP Model
1. Analyze the problem given. 2. Identify the decision variables. 3. Use the variables to formulate the objective function and the constraints. 4. State the non - negativity constraint.
Three components of the LP Model
1. Decision Variables 2. Objective Function 3. Constraints
Scientific Method Steps
1. Define the problem and gather data 2. Formulate a model 3. Develop a computer based procedure to derive solutions for the problem 4. Test the model and refine it as needed 5. Apply the model to analyze the problem and 6. Help to implement the team's recommendations
Mixed BIP model
A BIP model wherein only some variables are restricted to binary variables
Pure BIP model
A BIP model wherein the variables are restricted to binary variables
Management Science
A discipline that aids managerial decision making through applying scientific approach to managerial problems that require quantitative factors.
true
A management science team will try to conduct a systematic investigation of a problem that includes careful data gathering, developing and testing hypotheses, and then applying sound logic in the analysis. (true or false)
Linear programming
A mathematical modeling technique used by businesses to aid in planning and decision making, specifically for resource allocation.
State of nature
A possible situation that could arise due to random factors that aren't controlled by the decision maker
Alternatives
A set of options that the decision maker could choose from.
Binary Integer Programming
A special case of integer linear programming, wherein variables are binary. (0 or 1)
Single Server system
A system with just one server
Multiple Server system
A system with more than 1 server
mean absolute deviation
After determining the forecasting error in each of a number of months for any forecasting method, one common measure of the accuracy of that method is the
Queueing System
Customers arrive individually and wait in a line or queue in order to await service
analyze trends
Descriptive analytics is the process of using data to
Constant service time
Each customer has the same service time
mean square error
However, instead of assuming proportionality, there are some situations where the consequences of incurring forecasting errors somewhat larger than hoped are very serious. For such situations, another popular measure of the accuracy of a forecasting method is the average of the square of its forecasting errors
linear regression
If the sales data show a relatively constant trend in some direction, then _____ provides a reasonable forecasting method.
Decision tree
Illustration for decision analysis
contingent decision
In general, one yes-or-no decision is said to be contingent on another yes-or-no decision if it is allowed to be yes only if the other is yes
Product mix problem?
In this problem, LP is used in order to find the most realistic and practical allocation for 2 or more products that are produced with limited resources.
Queue
It is where customers wait before being served
Decision Analysis?
It provides a framework that business leaders could use whenever outcomes to situations become uncertain.
parallel proportional
Key Properties of Objective Function Lines: All objective function lines for the same problem are ______ . Furthermore, the value of W at which an objective function line intercepts the W axis is _______ to the value of P.
true
Management science is a discipline that attempts to aid managerial decision making by applying a scientific approach to managerial problems that involve quantitative factors. (true or false)
mathematics and computer science
Management science is based strongly on which of the following fields?
Infinite Queue
No definite number of customers to be held
Product mix problem
One of the most common LP application is the product mix problem
Outcome
Other term for state of nature
predict what will happen in the future.
Predictive analytics is the process of using data to
determine the best course of action for the future
Prescriptive analytics is the process of using data to
Queue discipline
Refers to the order in which members of the queue are selected to begin service. (Ex. First come, first serve)
Moving-average method
Suitable for a moderately stable time series where the last
Exponential smoothing method:
Suitable for a time series in the range from somewhat unstable to rather stable, where the value of the smoothing constant needs to be adjusted to fit the anticipated degree of stability. Refines the moving-average method by placing the greatest weight on the most recent values, but is not as readily understood by managers as the moving-average method.
last-value method
Suitable for a time series that is so unstable that even the next-to-last value is not considered relevant for forecasting the next value.
Exponential smoothing with trend
Suitable for a time series where the mean of the distribution tends to follow a trend either up or down, provided that changes in the trend occur only occasionally and gradually.
averaging method
Suitable for a very stable time series where even its first few values are considered relevant later for forecasting the next value.
false
The discovery of the simplex method in 1947 was the beginning of management science as a discipline. (true or false)
Prior Probability
The estimated probabilities of the states of nature prior to obtaining additional information through a test or survey.
two
The graphical method can be used to solve any linear programming problem having only ______ decision variables. The method uses the following steps:
true
The mathematical model of a business problem is the system of equations and related mathematical expressions that describes the essence of the problem. (true or false)
Queue capacity
The maximum number of customers that can be held in the queue.
Payoff
The quantitative measure to the consequences of each outcome.
true
The rapid growth of computing capability and power has led to a corresponding rapid growth of the management science discipline. (true or false)
Inter-arrival times
The times between consecutive arrivals to a queueing system
finite Queue
There is a definite number of customers to be held.
Maximax Criterion
This criterion gives an opportunity for the best possible outcome (the largest payoff in the entire payoff table) to occur
Maximin Criterion
This criterion provides the best possible protection against being unlucky
Maximum likelihood Criterion
Through basing our decision on the assumption that the most likely state of nature will occur, there is a higher chance of better outcome.
EMV (Expected Monetary Value)
What to use when the decision-making is under risk?
expected payoff
__-, calculate the weighted average of its payoffs by multiplying each payoff by the prior probability of the corresponding state of nature and then summing these products
Excel Solver
________________________ is used in order to find the optimal solution.
Bayes' Theorem
a formula for calculating a posterior probability of a state of nature
management science teams
a group of people who conduct larger and more formal studies. it can be hired from consulting firms or the employees of the company itself. the team may be composed of not just management scientiists but all those who can provide necessary info for the problem
objective function line
a line whose points all have the same value of the objective function
bayes 'criterion rule
a popular criterion for decision making the uses probabilties to calculate the expected payoff for each decision alter-native and then chooses the one with the largest expected payoff
moving average method
a series of arithmetic means used if little or no trend
trend projection
a time-series forecasting method that fits a trend line to a series of historical fatal points
statistical forecasting method
ability to forecast future sales of their products is particularly important for many companies
maximin criterion
always chooses the decision alternative that provides the best guarantee for its minimum possible payoff.
decision support system
an interactive computer-based system that aids managerial decision making. The system draws current data from databases or management information systems and then solves the various versions of the model specified by the manager.
operation research
another name for management science because the discipline started in WWII, when scientists were doing research on military operations. The abbreviation could be OR/MS
solution
any choice of value for the decision variables (regardless of how desirable or undesirable the choice)
model
approximate representation
Model
approximate representation of the problem
yes-on-no decisions
arises when a particular option is being considered and the only possible choices are yes go ahead with this option, or no, decline this option
maximum likelihood criterion
assumes that the most likely state of nature will occur and chooses accordingly.
analytics
attempts to provide necessary info that can aid managers in making decisions
averaging forecasting method
average of all montly sales to date as the forecast for the next month
measures of forecast accuracy
company forecast values with actual values
decision support system
computer based system that draws out current data and tests the various models
decision-making under certainty
consequences of each alternative is known
paramters
constraints in the algebraic molde
objective cell
contains the overall measure of performance for the decision in the changing cells
marginal cost
cost for each additional unit produced
fixed cost
cost that remains the same regardless of the production volume
variable cost
cost that varies with the production volume
Alternative
course of action or strategy that may be chosen by the decision maker
decision-making under risk
decision making when we know the probabilities associated with each possible states of nature
Bayes' Decision Rule
decision rule says to choose the alternative with the largest expected payoff.
overlapping
description for the systematic investigation (scientific method)
most likely state of nature
equally assumes that ____ will occur
EVwPI
expected value with perfect information
equally likely
find the average payoff for each alternative, select the alternative with the highest average
equally likely
finds the alternative with the highest average outcome
data mining software
for extracting hidden predictive informatio
exponential smoothing
form of weighted moving average
evpi = evwpi - maximum emv
formular for evpi
mathematical model
formulas, mathematical expression
decision constraints measure of performance
hat are the three questions that need to be answered to begin the process of formulating a linear programming model on a spreadsheet?
decision trees
illustration for decision analysis
measures of forecast accuracy
in choosing a, select the one with the lowest forecast error
Decision Maker
individual/group responsible for the decision making
exponential smoothing
involves little record keeping of past data
bayes' decision rule
is a particular appropriate criterion for most decision makers in most situations
Linear Programming
is a widely used mathematical modeling technique designed to help managers in planning and decision making relative to resource allocatio n
binary decision variable
is assigned a value of 1 for choosing yes and a value of 0 for choosing no.
range name
is simply a descriptive name given to a cell or range of cells that immediately identifies what is there
modeling process
is typically an evolutionary process that begins with a simple "verbal model" to define the essence of the problem and then gradually evolves into increasingly more complete mathematical mod
nodes
junction points
show formula
key to know the formula in excel
Branches
lines emanating from the nodes
Link
lines that connect nodes and allow travel in either direction
Arc
lines that connect nodes but DO NOT allow travel in either direction
maximax
locate the maximum payoff for each alternative
maximin
locate the minimum payoff for each alternative, select the alternative with the maximum value
quantitative
management science solves quantitative or qualitative
objective function
maximize or minimize, one objective only
Decision analysis
method for reducing uncertainty in the decision-making process through data analysis
bip
models that fit linear programming except that they use binary decision variables
associate forecasting
most common technique in linear regression analysis
State of nature (outcome)
occurence or situation over which the decision maker has little or no control
State of nature
occurrence or situation over which the decision maker has little or no contrl
feasible solution
one that satisfies all the constraints
emv (expected monetary value)
option for decision-making under risk
functional constraint
other constraints are referred to as
expected monetary value
other term for baye's decision rule
laplace
other term for equally likely
optimistic
other term for maximax
pessimistic
other term for maximin
income
partner of outgoing
evpi
places an upper bound on what you should pay for additional information
linear programming
planning of activities represented by a linear mathematical model
feasible region
points in the feasible region that satisfy every constraint
decision-making under risk
probability of state of nature occuring is known
Decision-making under uncertainty
probability of state of nature occurring is not known
institute for operations research and management science
professional society for the management science discipline
management science
provides recommendation and suggestions to aid managers in making decision
spreadsheet model
provides relevant data and its analysis
Payoff
quantitative result for each alternative and outcome combination
mean absolute deviation
reasonable measure of accuracy when the seriousness of a forecasting error is considered to be roughly proportional to the size of the forecasting error.
data cells
refer to cells showing the data
alternative
remember: in answering the maximax, maximin what should you answer (payoff/alternative)
event node
represented by a circle, indicates that a random event occurs at that point
decision node
represented by a square, indicates that a decision needs to be made at that point in the process
exponential smoothing
requires smoothing constant (a) ranges from 0 to 1 subjecting choosen
constraints
restrictions, identifies the limitation of production
last-value forecasting method
says simply to use the last month's sales as the forecast for the next month. it is also called 25% method
time series
series of observation over time of some quantity of interest
output cells
show quantities that are calculated from the changing cell
payoff table
shows the payoff for each combination of a decision alternative
single individual
small informal management studies are made by a ___
time-series forecasting methods.
statistical methods are available for using the historical data from a time series to forecast a future observation in the series.
decision table
tabular means of analysing the decision alternative and state of nature
profit
the ___ that the firm seeks to maximize is based on the profit contribution per unit of each product
forecasting errors
the absolute value of the difference between the actual sales and fore-casted sales
optimal solution
the best feasible solution, the one that maximizes p
payoff
the data in the decision table, the numbers there are called the
x1 + x2 = 2
the equation is true only when both variables are taken
x1 + x2 = 1
the equation is true only when one of the variables is taken
x1 + 2 >= 1
the equation is true when 1 or both of the variables are taken
x1 <= x2
the equation represents that there is a pre-quisite variable for another variable to be taken
define the problem and gather data
the it department plays a vital role in providing the necessary data/resources
Non-Linear Programming?
the model is a linear programming model except for having at least one nonlinear formula for an output cell (such as the objective cell)
relative reference
the relative position is the two cells in the same row and immediately to the left (based upon the relative position)
predictive analytics
the use of data to predict what will happen in the future
prescriptive analysis
the use of data to prescribe the course course of action (frequently using the optimization techniques)
descriptive analytics
the use use data (sometimes massive amount of data) to analyze trends
judgemental forecasting methods
these methods are especially valuable when little or no historical sales data are available or when major changes in the marketplace make these data unreliable for forecasting purposes
absolute reference
these references do not change when they are filed into other cells but instead always refer to the same absolute cell location
exponential smoothing
this latter method adjusts exponential smoothing by also directly considering any current upward or downward trend in the sales.
binary integer programming
this type of programming is commonly used for problems involving a yeas-or-no decision, or a go or no go decision
true
true or false: Bayes' decision rule provides larger payoffs in the long run than any
true
true or false: The expected payoff for a particular decision alternative can be interpreted as what the average payoff would become if the same situation were to be repeated numerous times.
true
true or false: The goal of all these methods is to estimate the mean of the underlying probability 702 distribution of the next value of the time series as closely as possible.
true
true or false: solver's sensitivity report is not available for integer programming methods
true
true or false: there is no single decision criterion that is best for every situation
decision variables
unknown variables, shows the correct product mix or combination of products to maximize allocation
arithmetic method
used often for smoothing
weighted moving average
used when some trend might be present (oldler data usually less important)
binary variables
variables who only possible values are 0 and 1
infeasible solution
violates at least one contraints
weighted moving average
weighted based on experience and invitation
exponential smoothing
weights decline exponentially, most recent data weighted cost
changing cells
what are cells containing the decision to be made (color yellow)
maximax maximin equallly likely
what are three basic approaches regarding decision-making uncertainty
net present value
what is npv
npv
what is used in bip (capital or npv)
EVPI
what to use is decision-making under certainty
George Dantzig
who created the simplex method
independent variable
x is what
dependent variable
y is what
1940-1950
year that management science started
