ManagementScienceExam2

uniform, efficiently generated, and absent patterns

A table of random numbers must be __________, __________ __________, and ______________ _______________ .

Undefined (or general)

Constant service times are a special case of the single-server model with __________ service times.

Shortest Route Problem

Determines the shortest distance between an originating point and several destination points.

random number ranges.

Developing the cumulative probability distribution helps to determine ______________ _____________ _________________

1) they provide a picture of a system 2) a large number of systems can be easily modeled as networks

Give two reasons why networks are a popular management science technique.

probability distribution

In the Monte Carlo process, values for a random variable are generated by sampling from a _____________ _______________ .

reality

It is often difficult to validate that the results of a simulation truly replicate ____________ .

real time

Manual simulation is limited because of the amount of ________ _____________ required to simulate even one trial.

Random Numbers

Numbers that are equally likely to occur

steady state (constant, over time)

Queuing system operating statistics are ______ _____________ .

operating statistics

Simulation does not usually provide a recommended decision as does an optimization model; it provides ________________ _________________ .

validated

Simulation models must be __________ to make sure they are accurately replicating the system being simulated

Increases

The cost of service increases or decreases as the level of service improves?

Maximal Flow Problem

The network solution method used to maximize the amount of flow of items from an origin to a destination.

negative exponential probability distribution

The service rate (µ) can often be described by the

the derivative of the curve's function

The slope of a curve at any point is equal to ___ __________ __ ___ ______ ________.

zero

The slope of a curve at its highest point equals ____ .

distance, time, or cost

The values assigned to branches typically represent what 3 things?

False

True or False? In nonlinear programming you are guaranteed a solution.

True (σ=0)

True or False? In the constant service time model, there is no variability in service times.

True

True or False? In the minimal spanning tree solution approach, we can start at any node in the network.

True

True or False? Simulation has certain limitations.

True

True or False? The first step in the Maximal Flow Solution Approach is to choose any path arbitrarily from origin to destination and ship as much as possible on that path.

multiple-server models

Two or more independent servers in parallel serve a single waiting line.

first-come, first served; last-in, last out; random; appointment

Types of queue disciplines

1. An infinite calling population 2. a first-come, first-served queue discipline 3. Poisson arrival rate 4. Exponential service times

What are the 4 assumptions of the basic single-server model?

1. Arbitrarily select any path in the network from origin to destination. 2. Adjust the capacities at each node by subtracting the maximal flow for the path selected in step 1. 3. Add the maximal flow along the path in the opposite direction at each node. 4. Repeat steps 1, 2, and 3 until there are no more paths with available flow capacity.

What are the 4 steps of the maximal flow solution method?

1. Select any starting node (conventionally, node 1 is selected). 2. Select the node closest to the starting node to join the spanning tree. 3. Select the closest node not currently in the spanning tree. 4. Repeat step 3 until all nodes have joined the spanning tree.

What are the 4 steps of the minimal spanning tree solution?

1. Select the node with the shortest direct route from the origin. 2. Establish a permanent set with the origin node and the node that was selected in step 1. 3. Determine all nodes directly connected to the permanent set nodes. 4. Select the node with the shortest route (branch) from the group of nodes directly connected to the permanent set nodes. 5. Repeat steps 3 and 4 until all nodes have joined the permanent set.

What are the 5 steps of the shortest route solution method?

starting conditions

What factor can affect simulation results?

an infinitely large queue will build up

What happens if customer are not served faster than they arrive?

manual simulation of several trials

What is a good way to validate a simulation?

constrained optimization model

What is more commonly referred to as a nonlinear programming model?

simulation

What is one of the most important and widely used managerial science techniques?

With machinery and automated equipment

When do constant service times occur?

Nonlinear Programming

When problems fit the general linear programming format but include nonlinear functions.

Finite Calling Population

When the customers from which arrivals originate are limited

simulation

Which managerial science technique provides a laboratory for experimentation on a real system?

Networks

_____________ are popular because they provide a picture of a system and because a large number of systems can be easily modeled as networks.

Nonlinear Programming

a form of mathematical programming in which the objective function or constraints, or both, are nonlinear functions.

What-if? analysis

a form of model experimentation using a computer to ascertain the results of making changes in a model.

simulated time

a long period of real time is represented by a short period of ____________ _______ .

Computer mathematical simulation

a system is replicated with a mathematical model that is analyzed by using the computer

Monte Carlo

a technique for selecting numbers randomly from a probability distribution

queue

a waiting line

Network

an arrangement of paths connected at various points, through which items move.

operating characteristics

average values for characteristics that describe the performance of a waiting line system

Nodes

denoted by circles, represent junction points connecting branches.

Network flow models

describes the flow of items through a system.

unconstrained optimization model

includes a nonlinear objective function and no constraints.

constrained optimization model

includes a nonlinear objective function and one or more constraints.

Permanent Set

indicates the nodes for which the shortest route to has been found

Random Numbers

numbers equally likely to be chosen from a large population of numbers.

numerical technique

random numbers are typically generated by typically generated on the computer by using a ________________ _______________ .

pseudorandom numbers

random numbers generated by a mathematical process instead of a physical process are ___________________ _____________ .

Analogue simulation

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

Branches

represented as lines, connect nodes and show flow from one point to another.

steady state

simulation results will not equal analytical results unless enough trials of the simulations have been conducted to reach _______________ ________________ .

Poisson distribution

the arrival rate (λ) is mostly frequently distributed by a ___________ ________________

service rate

the average number of customers who can be be served during a time period.

Local Optimal

the highest point in the immediate area

Global Optimal

the highest point of all

minimal spanning tree problem

the objective of this network method is to connect all nodes in a network so that the total branch lengths are minimized

queue discipline

the order in which customers are served

queuing analysis

the probabilistic analysis of waiting lines

utilization factor

the probability that a server is busy

arrival rate

the rate at which customers arrive at the service facility

calling population

the source of customers; may be finite or infinite

classical optimization

the use of calculus to determine the optimal value of a variable

finite or infinite

two types of calling populations

arrivals, servers, and the waiting line structure

what are the 3 components of a waiting line system?

mean service rate

µ

Mean arrival rate

λ