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 e
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 ev
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
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. I
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 candid
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
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 s
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 probab
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
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 d
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
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
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 proba
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 ro
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,
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
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
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
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, am
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,
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
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 gener
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 fr
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 relationsh
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
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).
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 ho
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
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 op
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