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 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 13
P -Median 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 stores, s
IEOR 151 Lecture 20
Queues
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 follow
IEOR151 Homework 7
Fall 2013
Due: Wednesday, November 13, 2013
Problem 1:
Solve a P-median problem with the heuristic algorithm: allocate 2 facilities among 7 demand
nodes (demand nodes set and candidate sites set are the same). The demand and distance
in
IEOR 151 Lecture 8
Kidney Exchanges
1 Graph Model
We will consider a graph model for a kidney exchange1 : There are k groups of donorrecipients (DRs), and the market is described by a directed graph G = (V, E) with edge
weights. There is a vertex vi V for
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 Midterm
October 22, 2014
Name:
Overall:
/48
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
/16
3
/10
4
IEOR 151 Homework 2
Due Friday, October 17, 2014 in class
1. Consider the following graph representation of a kidney exchange. Find the social welfare
maximizing exchange under the constraint that all cycles can have length less than or
equal to L = 3. (5
IEOR 151 Homework 1
Due Friday, September 26, 2013 in class
1. For each the following scenarios, would you (i) accept the null hypothesis, (ii) reject the
null hypothesis, or (iii) gather additional data and information before making a decision?
Explain y
IEOR 151 Lecture 23
Longterm Stang
1 Static Model with Single Skill
In the rst model we consider, there are a set of projects that each require a certain number
of person-months of labor. Each project requires the use of multiple skills, but each employee
IEOR 151 Lecture 21
Littles Law
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.
Then a useful relationship for queues is Littles Law, which states t
IEOR 151 Lecture 19
Markov Processes
1 Denition
A Markov process is a process in which the probability of being in a future state conditioned
on the present state and past states is equal to the probability of being in a future state
conditioned only on t
IEOR 151 Lecture 17
Vehicle Routing Problem
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
locat
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 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 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 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 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 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 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 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
IE 0R 263A: Applied Stochastic Processes I
Course Syllabus
ADMINISTRUIVE INFORMATION
Instructor: Rhonda Righter Ofce: Etcheverry 4187
email: RRightergaxlEOR.Berkeley.edu
Cell Phone: (510) 6843767 Good way to reach me during the day if Im not in my ofce.
IEOR 172: Probability and Risk Analysis for Engineers Course Syllabus
ADMINISTRATIVE INFORMATION
Instructor:
Rhonda Righter
e-mail:
Cell Phone:
(510) 6843767
Office Hours: Tu/Th 3:30 and by appointment.
[email protected]
(Use this instead of bcou