A Guided Tour Through Arena
Chapter 3
Last revision June 7, 2003
Simulation with Arena, 3rd ed.
Chapter 3 A Guided Tour Through Arena
Slide 1 of 61
What We'll Do .
Start Arena Load, explore, run an existing model
Basically the same model as for the hand
IEOR 151 Lecture 2
Probability Review
1 Denitions in Probability and Their Consequences
1.1
Defining Probability
A probability space (, F, P) consists of three elements:
A sample space is the set of all possible outcomes.
The -algebra F is a set of even
IEOR 151 L 15
S C P
1
Problem Setup
e set covering problem is a specic type of a discrete location model. In this model, a facility can
serve all demand nodes that are within a given coverage distance Dc from the facility. e problem
is the place the minim
IEOR 151 L 18
R Q T
1
Generic Queues
Queueing theory is the mathematical study of waiting lines, and here we will discuss models of
queues using a stochastic processes approach to this topic. In general, we will be interested in
modeling the following asp
IEOR 151 L 22
V R P
1
Problem Formulation
In the vehicle routing problem, there are a set of depots, vehicles, and delivery locations, and the
problem is to optimally design routes for the vehicles from the depots to delivery locations. To
formally dene t
IEOR 151 L 18
R Q T II
1
Littles Law
Suppose that we dene the following variables
L average number of customers in system;
average arrival rate;
W average time in the system.
en a useful relationship for queues is Littles Law, which states that
L = W.
The Euler Tour and Chinese
Postman Problem
Professor Z. Max Shen
IEOR 151
Related Service Problems
Node routing problems:
Meal delivery, inter-library loans, school-bus
routing
Arc routing problems:
Waste collection, snow plowing, postal delivery
rout
The Traveling Salesman Problem
Professor Z. Max Shen
IEOR 151
TSP Model
Let G=(V, E) be a complete undirected
graph with vertices V, |V|= n , and the
edges E and let dij be the length of edge
(i, j).
The objective is to find a tour that visits
each vertex
IEOR 151 Lecture 14
Vertex P -Center Problem
1 Problem Setup
Location planning involves specifying the physical position of facilities that provide demanded services. Examples of facilities include hospitals, restaurants, ambulances, retail
and grocery st
IEOR 151 Lecture 15
Set Covering Problem
1 Problem Setup
The set covering problem is a specic type of a discrete location model. In this model, a
facility can serve all demand nodes that are within a given coverage distance Dc from the
facility. The probl
IEOR 151 Lecture 18
Savings Algorithm
1 Problem Formulation
Recall our formulation of the vehicle routing problem: There are a set of depots, vehicles,
and delivery locations, and the problem is to optimally design routes for the vehicles from
the depots
IEOR 151 Lecture 16
Capacitated Location Planning
1 Mathematical Model
We will consider extensions of dierent location planning models to the situation in which the
facilities have a maximum capacity of demand that the facility is able to serve. The model
IEOR 151 L 14
V P -C P
1
Problem Setup
Location planning involves specifying the physical position of facilities that provide demanded services. Examples of facilities include hospitals, restaurants, ambulances, retail and grocery stores,
schools, and re
IEOR 151 L 13
P -M P
1
Problem Setup
Location planning involves specifying the physical position of facilities that provide demanded services. Examples of facilities include hospitals, restaurants, ambulances, retail and grocery stores,
schools, and re st
IEOR 151 L 8
S M G
1
Kidney Exchanges
Recall the model for a kidney exchange1 : ere are k groups of donor-recipients (DRs), and the
market is described by a directed graph G = (V, E) with edge weights. ere is a vertex vi V
for each DR and an edge ei,j = (
IEOR 151 Lecture 3
Risk in Decision Making
1 Motivating Example
Suppose there is a chain of fast food restaurants that only oers lunch/dinner options on
its menu. Given the potential for a new revenue source, the chain is deciding whether it
should begin
IEOR 151 Lecture 5
Newsvendor Model
1 Classical Newsvendor Model
Suppose we would like to pick the inventory level for a perishable good, where the demand
is stochastic and the costs are deterministic. Here, the demand X is a random variable
drawn from a
IEOR 151 Lecture 6
Multiple Testing
1 Example: Comparing Restaurant Quality
Consider the following hypothetical situation: There is a chain of fast food restaurants that is
facing decreased customer satisfaction and revenues, and management believes the p
IEOR 151 Lecture 4
Composite Minimax
1 Numerical Example for Point Gaussian Example
1.1
Computing
Suppose Xi N (, 2 ) (for n = 20 data points) is iid data drawn from a normal distribution
with mean and variance 2 = 20. Here, the mean is unknown, and we w
IEOR 151 Lecture 1
Service Systems
1 Simplied View of Systems Engineering
Thursday, August 28, 2014
1.1
10:00 AM
Modeling and Abstraction
An important step in the engineering of service systems is to create an abstraction of both
(i) the system and (ii) r
IEOR 151 Lecture 7
Matching Markets
1 Resource Allocation without Money
In a typical market, resources (including goods and services) are allocated on the basis of
payments. However, there are many instances when payments cannot be used to allocate
goods.
IEOR 151 L 1
P R
1
1.1
Denitions in Probability and eir Consequences
D P
A probability space (, F, P) consists of three elements:
A sample space is the set of all possible outcomes.
e -algebra F is a set of events, where an event is a set of outcomes.
IEOR 151 L 3
S T
1
Kidney Stone Treatment Example
1.1
S P
In a study1 comparing the eectiveness of two classes of treatments for kidney stones, the following
success rates for each class of treatment were obtained:
Stone size
Open surgery
< 2cm
2cm
Overa
IEOR 151 L 7
M G
1
Resource Allocation with Friction
Matching games are found in many markets in which there is a resource to be allocated, but there
is some friction that prevents ecient allocation of the resources. It may be the case that the resource
i
IEOR 151 L 6
M C
1
Example: Comparing Service Rates
Consider a situation in which there are four healthcare providers performing triage for an emergency room in a hospital. Triage is the process of evaluating the severity of a patients condition
and then
IEOR 151 Lecture 11
Adverse Selection
1 Sandwich Example
Consider the following hypothetical situation: A company is holding a picnic and would like
to purchase grilled cheese sandwiches with tomatoes and swiss cheese on sourdough bread
with a toasted par
IEOR 151 Lecture 10
Nonlinear Programming
1 First-Order Optimality Conditions
We will consider the following optimization problem (P):
min f (x)
s.t. x Rn
gi (x) 0, i = 1, . . . , m
hi (x) = 0, i = 1, . . . , k
where f (x), gi (x), hi (x) are continuously
IEOR 151 Lecture 22
Square Root Rule
1 M/M/ Queue
Recall that the M/M/ queue is a model with an innite number of servers. In this model,
the service rate is state-dependent and is given by n where n is the number of customers
in line, and is the service r
IEOR 151 Lecture 9
Residency Matching
1 National Resident Matching Program (NRMP)
1.1
Model
There are m residency programs and n applicants. We will denote the i-th applicant as vi
and the j-th program as pj . Let si be the number of open positions in pi
IEOR 151 Midterm
October 21, 2015
Name:
Overall:
/50
Instructions:
1. Show all your intermediate steps.
2. You are allowed a single 8.5x11 inch note sheet.
3. Calculators are allowed.
4. Normal probability table is given on last page.
1
/10
2
/10
3
/10
4
IEOR 151 M
O 23, 2013
Name:
Problem 1:
/8
Problem 2:
/8
Problem 3:
/8
Problem 4:
/8
Problem 5:
/8
Problem 6:
/8
Overall:
/48
Instructions:
1. Show all your intermediate steps.
2. You are allowed a single 8.5x11 inch note sheet.
3. Calculators are NOT allo