Operations Management Exam 2

skepticism in the queuing example

- ten trials do not ensure steady state; unsure if random numbers replicated the actual probability because we used such few random numbers - starting conditions might be different

In formulating a mixed integer programming problem, the constraint x1 + x2 ≤ 500y1 where y1 is a 0-1 variable and x1 and x2 are continuous variables, then x1 + x2 = 500 if y1 is:

1

Conditional Constraint

Construction of one facility is conditional upon the construction of another; x2 <= x1 --> if x2 is chosen, x1 must be chosen; x2 is conditional upon x1

If the problem is maximization with constraints that are all <=, do we round up or down?

DOWN

x1 + x2 + x3 + x4 = 2

Exactly 2 of 4 facilities must be chosen

x2 + x3 = 1

Exactly one of project 2 and 3 must be selected.

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

FALSE -- mixed integer

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

FALSE -- only violated by probability

________ is not part of a Monte Carlo simulation.

Finding an optimal solution

Corequisite Constraint

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

Contingency/Mutually exclusive constraint

If one option is selected, others must be rejected

x1 + x2 + x3 + x4 <= 2

No more than 2 must be constructed.

Pseudorandom numbers

Random numbers generated by a mathematical process instead of a physical process; not true random numbers

Simulation results will not equal analytical results unless enough trials have been conducted to reach ---.

Steady State

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

TRUE

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

The solution values are always integers

Branch and Bound method

Traditional approach to solving integer programming problems: - Feasible solutions can be partitioned into smaller subsets - Smaller subsets evaluated until best solution is found - Methods is a tedious and complex mathematical process

If the problem is minimization with constraints that are all >=, do we round up or down?

UP

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

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:

X11 + X21 + X31 ≤ 250

Total Integer Model

all decision variables required to have integer solution variables x1, x2 >= and integer

0-1 Integer Model

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

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

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

detectable pattern

Confidence Limits

developed for the ananlysis of the statistical validity of simulation results

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

exactly 3 out of 5

Upper/Lower Confidence Limit

mean +/- (1.96)(SD/sqrt of sample size)

The --- periods simulated, the --- accurate the results.

more; more

Monte Carlo Process

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

what-if? analysis

one of the main attributes of simulation is its usefulness as a model for experimenting; the more complex these simulations get, they become more impossible to do manually

Analogue Simulation

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

Mixed Integer Model

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

continuous probability distribution

take the integral of the function and then square root it on both sides

Validate results of a simulation

that true steady state has been reached and the model replicates reality

Pseudorandom numbers must have the following characteristics...

uniformly distributed efficient technique sequence should reflect no pattern

Computer mathematical simulation

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

Validation is even more difficult when...

when analytical analysis is not possible and there is not analytical standard of comparison

In a "capital budgeting" problem, if either project 1 or project 2 is selected, then project 5 cannot be selected. Which of the alternatives listed below correctly models this situation?

x1 + x5 ≤ 1, x2 + x5 ≤ 1

Assume that x1, x2 and x3 are the dollars invested in three different common stocks from New York Stock Exchange. The investing company requires that more than 60% of the dollars invested should be in "stock 1". The constraint for this requirement can be written as:

x1 > .60(x1+x2+x3) 0.4x1 - 0.6x2 - 0.6x3 ≥ 0

If project 2 is selected, project 5 cannot be selected.

x2 + x5 <= 1

If project 4 is NOT selected, then project 2 must also be not selected.

x2 <= x4