ops hw 1,2,3,4 + study guide Theory question

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<___x

"At Most limit to "

x>__

"At least "

Certainty Hypothesis

: mathematical programming assumes that all parameters are known with certainty

if Xab= the production of product a in period b, then to indicate that the limit on production of the company's 3 products in period 1 is 250, we write which of the following: A) X31 ≤ 250 B) X11 + X21 + X31 ≤ 250 C) X11 + X12 + X13 ≤ 250 D) X11 + X21 + X31 ≥ 250

Answer: (B) X11 + X21 + X31 ≤ 250 Explanation: As per the given information, Xab indicates the production of product a in period b. Therefore, X11 = Production of product 1 in period 1 X21 = Production of product 2 in period 1 X31 = Production of product 3 in period 1 To indicate that the limit on the production of the company's 3 products (1,2,3) in period 1 is 250 (less than or equal to 250), it will be written as: X11 + X21 + X31 ≤ 250

A long period of real time cannot be represented by a short period of simulated time.

False

Simulation results will always equal analytical results if 1000 trials of the simulation have been conducted.

False

The "certainty" linear programming (LP) hypothesis (LP are deterministic models) is violated by integer programming.

False

The constraint x1 + x2 ≤ 1 is named as "conditional constraint" in 0-1 integer programming problems.

False

The constraint x1 ≤ x2 is named as "mutually exclusive" constraint in 0-1 integer programming problems.

False

The three types of integer programming models are total, 0-1, and binary

False

________ is not part of a Monte Carlo simulation.

Finding an optimal solution

integer programming solutions

Integer( whole number) -excel generated with an integer constraint ( optimal solution ) relaxed- excel generated without an integer constraint ( unrealistic solution AKA does not use whole number ) rounded- relaxed solution rounded to the nearest appropriated whole number "integer" ( sup-optimal problem )

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

Productivity

The properties of a linear programming problem are

Proportionality, additivity, divisibility, and certainty

Fixed cost includes:

SALARIES

excess or unused resources associated with Less Than or Equal To Constraints

Slack

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

round down

The problem is MAX Z with constraints that are less than or equal to

round up

The problem is is MIN Z with constraints that are greater than or equal to

Compared to blending and product mix problems, transportation problems are unique because:

The solution values are always integers;

In a 0-1 integer programming model, if the constraint x1 - x2 ≤ 0, it means when project 2 is selected, project 1 ________ be selected.

can always

Pseudorandom numbers exhibit a(n) ________ in order to be considered truly random

detectable pattern

A table of random numbers must be:

efficiently generated.

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

Surplus→

mount over the minimum unit associated with Greater Than or Equal To Constraints

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

optimal solution

Business competitiveness

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

Validation of a simulation model occurs when the true ___________ average results have been reached.

steady state

Lagrange Multiplier

the dual value of a constraint. Analogous to the shadow price. It reflects the approximate change in the objective function resulting from a unit change in the quantity (right-hand-side) value of the constraint equation.

0-1 integer model

the solution values of the decision variables are zero or one.

Random numbers are equally likely to occur.

true

Random numbers generated by a mathematical process instead of a physical process are pseudorandom number

true

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

true

The three types of integer programming models are total, 0-1, and mixed.

true

For a minimization integer linear programming problem, a feasible solution is ensured by rounding ________ non-integer solution values if all of the constraints are the greater-than-or-equal-to type.

up

Conditional Constraint

→ 2 projects, if you choose X1, then you must choose X2 → not vice versa → Possible Scenarios: X1 = 1, X2 = 1 X2 = 1, X1 = 0 X1 = 0, X2 = 0 THUS: X2 will never be less than X1

Mutually Exclusive Constraint:

→ 2 projects, only one can be chosen at a time → Possible Scenarios: X1 = 1, X2 = 0 X1 = 0, X2 = 1 X1 = 0, X2 = 0 THUS: your mutually exclusive constraint X1 + X2 <= 1

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

total integer

all decision variables required to have integer values of 0 or 1 the non negativity constraint is ex: x1,x2,>= 0 AND INTEGER

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

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

Multiple Optimal Solutions

more than one solution satisfies the objective function, often found in cases where a constraint line has the same slope as the objective function.

Certainty Hypothesis

→ probability techniques violate this → what we've learned thus far does not violate this


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