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