Operations Management Exam 1

The properties of a linear programming problem are:

Proportionality, additivity, divisibility, and certainty

decision variables

mathematical symbols that represent levels of activity

proportionality (properties of LP problems)

the rate of change (slope) of the objective function and constraints is constant

sensitivity analysis

- sensitivity analysis determines the effect on the optimal solution, for example, due to changes in coefficients of the objective function and/or constraints - changes may be reactions to anticipated uncertainties related to the parameters or to new information that must be added to the model

observation

identification of a problem that exists in the system or organization

objective function

linear relationship that reflects the objective of an operation

model constraints

linear relationship that represents a restriction on decision making

parameters

numerical values that are included in the objective functions and constraints

transformation

the conversion of inputs (resources) into outputs (goods or services)

computer simulations and sensitivity analysis

- early LP used lengthy manual math solution procedure called the simplex method - steps of the simplex method have been programmed in software packages designed for linear programming problems

divisibility (properties of LP problems)

decision variables can take on any fractional value and are therefore continuous as opposed to integer in nature

Fixed cost includes

staff and management salaries

additivity (properties of LP problems)

terms in the objective function and constraints must be additive

case 2: changing the total amount of the constraint resource (right hand side)

the *sensitivity range for a right hand side* value is the range of values over which the quantity's value can change *without changing the solution variable mix, including the slack/surplus variables* the *sensitivity range* for a constraint quantity value is also the range over which the *shadow price is valid*

If one of the coefficients of the objective function is changed to a value outside of its respective sensitivity range (greater than the upper limit or lower than the lower limit), the optimal solution will be different than the one originally obtained before the change is implemented.

true

Sensitivity analysis is a way to deal with uncertainty in linear programming models.

true

graphical solutions of LP models

- limited to only two decision variables - good way to visualize and fully understand how the solution of linear programming problems is achieved

irregular LP problems

- multiple optimal solutions - infeasible solutions - unbounded solutions

slack variables

- standard form requires that all constraints should be under the form of equations (equalities) rather than inequalities - this is added to a <= constraint in order to convert it to an equation (=). They typically *represent unused resources* - contributes nothing to the objective function (Z value)

surplus variables

- subtracted from a >= constraint in order to convert it to an equation (=). - *represents excess* above constraint requirements - does not effect objective function (Z value)

cases of sensitivity analysis

1) changing the objective function coefficients 2) changing the total amount of constraint resource (constraint quantity value or the right hand side of the constraint) 3) changing constraints coefficients 4) adding new constraints 5) adding new decision variables

productivity

a measure of efficiency-- the amount of output produced compared to the amount of input required in production

linear programming

a model that consists of linear relationships representing a firm's decision(s), given an objective function and resource constraints

model implementation

actual use of the model or its solution

excel requires the standard form

all decision variables in the constraints must appear on the left hand side of the inequality (or equality) and all numeric values must be on the right-hand side

___________________ refers to the ability of an organization to sell products in a market. Please choose the option that best fits the empty space above

business competitiveness

model construction

development of the functional mathematical relationship that describes the decision variables, objective function and constraints of the problem

If the objective function slope is exactly the same as one of the constraints and this specific constraint is redundant, we have a case of multiple optimal solutions.

false

Sensitivity ranges can be computed only for the coefficients of the objective function.

false

Slack variables are only associated with maximization problems

false

The break-even point is the volume that the profit is positive (greater than zero).

false

the correct way to implement a sensitivity analysis for the second coefficient of the objective function is to vary not only the second coefficient but also the first one (at the same time).

false

If by processing the same amount of inputs used in the past a company is now capable to produce a(n) ________ amount of outputs, it means that an improvement of productivity was achieved

greater

model solution

models solved using management sciences techniques

productivity and competitiveness can be improved when

operations reduce costs, improves quality and delivers goods and services on time

The sensitivity range for an objective function coefficient is the range of values over which the current __________________ remains the same.

optimal solution

definition of the problem

problem must be clearly and consistently defined showing its boundaries and interaction with the objectives of the organization

Australian road freight company Linfox uses aerodynamic trucks and trailers to reduce fuel consumption. This is a case of generating higher

productivity

outputs

refer to the end result of an organization's efforts -- the service or product that is delivered or provided to the consumer

business competitiveness

refers to the ability of an organization to sell products in a market

inputs

resources used in the process of production

shadow price

the *marginal value* of one additional unit of resource: how much an organization is willing to pay for it also called dual variables Change in Z/Change in Qi

case 1: changing objective function coefficients

the *sensitivity range* for an objective function coefficient is the *range of values* over which the current optimal solution point *remains optimal* the sensitivity range for the Xi coefficient is designated as Ci

characteristic of LP problem

the objective function and constraints must be definable by *linear* mathematical functional relationships

certainty (properties of LP problems)

the parameters values are assumed to be known with certainty (it is a deterministic model)

break-even analysis

to determine the number of units of a product (volume) to sell or produce that will equate total revenue with total cost - zero profit

the optimal solution for a company that is able to produce two different products (x1 and x2) is x1 = 0 and x2 = 6. The best strategy for this company is to produce only x2.

true