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