Ops Exam 2

Random numbers are equally likely to occur.

True

Transportation costs are always

integer values

0-1 integer model

All decision variables required to have integer values of zero or one

mixed integer model

Some of the decision variables (but not all) required to have integer values

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

The solution values are always integers;

corequisite constraint

ex: if one facility is constructed, the other one will also be constructed and vice versa x2 = x1

monte carlo process

*not* a type of simulation model but a technique for selecting numbers *randomly* from a probability distribution for use in trial (computer run) of a simulation model values for a random variable are generated by *sampling* from a *probability distribution*

artificially created random numbers must have the following characteristics

1. the random numbers must be *uniformly distributed* 2. the numerical technique for generating the numbers must be *efficient* 3. the sequence of random numbers should reflect *no pattern*

total integer model

All decision variables required to have integer solution values

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

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

True

computer simulation with excel spreadsheets generating random numbers

as simulation models get *more complex* they become *impossible to perform manually* in simulation modeling, random *number are generated by a mathematical process* instead of a physical process (such as spinning a wheel) random numbers are typically generated on a computer using a numerical technique and this *are not true random numbers but pseudorandom numbers*

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 sometimes

Monte Carlo is good when

complex problems no other techniques appropriate uncertainty and probability distributions stochasticity

Please indicate which one of the following options is *not* correct? Pseudorandom numbers exhibit a(n) ________ in order to be considered truly random.

detectable pattern

contingency or mutually exclusive constraint

ex: Because the swimming pool and tennis center must be built on the same part of land, only one of these two facilities can be constructed x1 + x2 <= 1 facility

conditional constraint

ex: the council knows that the tennis center has no chance of being selected if the pool is not selected first. However, even if the pool is selected, there is no guarantee that the tennis center will also be selected. Thus, the tennis center is conditional upon construction of the swimming pool x2 <= x1

The constraint (x1 + x2 + x3 + x4 + x5 = 3) means that ________ out of the ________ projects must be selected

exactly 3, 5

a large portion of the applications are for

probabilistic models

analogue simulation

replaces a physical system with an analogous physical system that is *easier to manipulate*

rounding non-integer solution values up to the nearest integer can

result in an infeasible solution (for maximization) a feasible solution is ensured by rounding down non-integer solution values but may result in a less than optimal (sub-optimal) solution

About Monte Carlo simulations

the *more periods* simulated, the *more accurate* the results simulation results will not equal analytical results unless enough trials have been conducted to reach *steady state* it is often difficult to *validate* results of simulation - that true steady state has been reached and that simulation model truly replicates reality when analytical analysis is not possible, there is no analytical standard of comparison, thus making validation even more difficult

branch and bound method

traditional approach to solving integer programming problems 1) feasible solutions can be partitioned into smaller subsets 2) smaller subsets evaluated until best solution is found 3) methods is a tedious and complex mathematical process

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

computer mathematical simulation

when a system is replaced with a mathematical model that is analyzed with the computer. it offers a means of *analyzing very complex systems* that cannot be analyzed using other techniques

ex: If the community council decides that no more than 2 facilities must be constructed

x1 + x2 + x3 + x4 <= 2

ex: if council decides exactly 2 of the 4 facilities must be built

x1 + x2 + x3 + x4 = 2