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