BIT 2406 Final

Linear Programming Model Components

Proportionality Additive Divisible Certainty

most common type of forecasting method for the long-term strategic planning process

Qualitative Methods

multi-period scheduling problem the production constraint

beginning inventory - demand + production = ending inventory

Optimal Solution

best feasible solution

Hurwicz criterion multiplies the

best payoff by the coefficient of optimism

The analytic hierarchy process uses

both subjective and qualitative assessment

On an AOA diagram, a __________ represents an activity of a project

branch

Time series

category of statistical techniques that uses historical data to predict future behavior, assumes past behavior will repeat itself in the future

basic decision environment categories

certainty, uncertainty, risk

The optimal solution of a minimization problem is at the extreme point __________ the origin.

closest to

Hurwitcz Criterion

compromise between maximal and maximin

expected value

computed by multiplying each decision outcome under each state of nature by the probability of its occurrence

in shortest route problem, the constraint for each node represents

conservation of flow

If an activity cannot be delayed without affecting the entire project, then it is a __________ activity

critical

Synthesization

decision variables are prioritized within each criterion

Non-negativity constraints restrict

decision variables to zero or positive values

A systematic approach to model formulation is to first

define decision variables

Feasible Solution

does not violate any constraints

Goal programming solutions __________ achieve all goals.

doesnt always

implicit enumeration method

eliminates obviously infeasible solutions and evaluates the remaining solutions to determine which one is optimal

Constraint

equation or an inequality that expresses a resource restriction

expected opportunity loss

expected value of the regret for each decision

Undirected Branch

flow in possible either direction

Directed Branch

flow is only possible in one direction

Trend

gradual, long-term, up or down movement of demand

Technological forecasting ...

has become increasingly crucial to compete in the modern international business environment

dominant decision

has better payoff than another decision under each state of nature

Sensitivity Analysis

how a problem solution reacts to changes in one or more of the model parameters

When systematically formulating a linear program, the first step is

identify decision variables

For a maximization problem, the shadow price measures the __________ in the value of the optimal solution, per unit increase for a given __________.

improvement, resource

The linear programming relaxation contains the objective function and the original constraints of the integer programming problem, but drops all

integer restrictions

Multiple optimal solutions can occur when the objective function is __________ a constraint line

parallel to

A dummy activity is used to show a precedence relationship, but it does not represent a __________.

passage of time

The first step in solving a graphical linear programming model is

plot the model constraints as equations on the graph and indicate the feasible solution area

Decision analysis is a __________ technique

probabilistic

Conditional Probability

probability that an event will occur given that another event has already occurred

Delphi method

procedure for developing a consensus forecast about what will occur in the future

The __________ property of linear programming models indicates that the values of all the model parameters are known and are assumed to be constant

proportionality

shortest route solution technique

quickest route from source to each node

feasible solution space

region which satisfies all of the constraints in a graphical linear programming problem

Deviation variables

represent difference between targets and actual values

A decision with more than 1 objective

requires objectives be put in order of importance

The first step in the shortest route solution method is to

select the node with the shortest direct route from the origin

the transportation model method minimizes the

shipping cost

payoff table

shows the outcome for each decision alternative under the various possible states of nature

Mixed Integer Model

some integer and some non integer solutions

The linear programming model for a transportation problem has constraints for supply at each __________ and __________ at each destination.

source, demand

The difference between the assignment and the transportation problem is that

supply and demand value is 1 in the assignment problem

Deterministic Technique

technique that assumes certainty in its solution

Slack Variable

the amount by which the left side of a ≤ constraint is smaller than the right side

Utiles

units of subjective measures of utility

cyclical pattern

up-and-down repetitive movement that repeats itself over a time span of more than 1 year

Gantt Chart

valued for simplicity and shows time

Components of Break Even Analysis

volume, profit, cost

dividing each value in each column of the pairwise comparison matrix by the corresponding column sum

we get a normalized matrix

Multiple Choice

x + y = 1

Corequisite Constraint

x = y

Conditional Constraint

x ≤ y

At least one or both deviational variables in a goal constraint must equal

zero

For a resource constraint, either its slack value must be __________ or its shadow price must be __________.

zero, zero

Values with an acceptable consistency ratio are values

≤ 0.1

Best of the Worst

Maximin

Maximin

Maximum of the minimum payoffs

Do decision models consider all factors from the real world?

NO

risk averters

People who forgo a high expected value to avoid a disaster with a low probability

risk takers

People who take a chance on a bonanza with a very low probability of occurrence in lieu of a sure thing

Mutually Exclusive Constraint

one thing or another must be chosen x + y ≤ 1

In an assignment problem, one task can be done

only by one agent

work breakdown structure

A list of the tasks, broken down into modules, components, and individual tasks

A Type of Enumeration Method

Branch and Bound Method

Break Even Point is when

TC=TR

transportation problems are unique because

The solution values are always integers

Bayesian analysis

additional information is used to alter the marginal probability of the occurrence of an event

Goal constraints can include __________ deviational variables.

all

Total Integer Model

all decision variables are integers

0-1 Integer Model

all decision variables have values of 0 or 1

Posterior Probability

altered marginal probability of an event based on additional information.

Pairwise Comparison Matrix, diagonal values are

always one

Positive Deviational Variable

amount by which a goal level is exceeded

Negative Deviational Variable

amount by which goal level is underachieved

The first step of the maximal flow solution method is to

arbitrarily select any path in the network from origin to destination

first step in minimal spanning tree

arbitrarily select starting node

Binary Variables

are 0 or 1

In a transportation problem

items are allocated from sources to destinations at a minimum cost

What do managers use in forecasting?

judgement, past experience, opinion

Linear mathematical programming techniques assume that all parameters in the models are

known with certainty

critical path

longest path through the network

The quantitative analysis approach requires

mathematical expressions

The objective of the maximal flow solution approach is to

maximize the total amount of flow from an origin to a destination

expected value of perfect information

maximum amount a decision maker would pay for additional information

Maximax

maximum of the maximum payoffs

Decision Variables

measure how much or how many items to produce, purchase, hire, etc

analytical hierarchy

method for ranking decision variables using pairwise comparisons

The term opportunity loss is most closely related to

minimax

minimax regret criterion

minimizes the maximum regret

minimum spanning tree

minimum total connecting all nodes

If the feasible region for a linear programming problem is unbounded, then the solution to the corresponding linear programming problem is __________ unbounded.

never

On an AOA diagram, a __________ represents the beginning and end of activities, referred to as events

nodes

Management Science Process

observation, problem definition, model construction, model solution, implementation

Seasonal

occurs periodically