Decision support using linear programing

It is easy assignment this time and i hope to reduce the cost PLEASE (I am a student). Follow the requirements of the question very well I upload the slides for Q2 that you will choose a problem from ch10. PLEASE: read question 1 & 2 carefully. Best wishes.
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MINISTRY OF EDUCATION
IMAM ABDULRAHMAN BIN
FAISAL UNIVERSITY
COLLEGE OF COMPUTER SCIENCE
& INFORMATION TECHNOLOGY
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CIS 516: Decision Support & expert systems
HW #1
points: 5
Question 1. Decision support using linear programing
Select a problem of your choice and propose a linear programing or integer programming
solution to it.
Q1
The submission should contain:
• Brief description of the problem 0.25 mark
• Written description of the model 1 mark
• Working solution on a tool of your choice. 0.25 mark
Helpful sources

text book Example in page 412
2.5
points
Question 2. Discuss the applicability of one of the alternative search methods studied in
chapter 10 on a problem of your choice.
Q2
The submission should contain:
• Brief description of the problem 0.25
• The proposed solution (details depends on the selected method) 2.25
• No implementation is required
2.5
points
Potential data source
• Select your problem and discuss with your instructor before your start working.
Instructions
• Maximum number of words is 500.
•
Business Intelligence and Analytics:
Systems for Decision Support
(10th Edition)
Chapter 10:
Modeling and Analysis: Heuristic
Search Methods and Simulation
Learning Objectives
?
?
?
?
Explain the basic concepts of simulation
and heuristics, and when to use them
Understand how search methods are used
to solve some decision support models
Know the concepts behind and
applications of genetic algorithms
Explain the differences among algorithms,
blind search, and heuristics
(Continued…)
10-2
Copyright © 2014 Pearson Education, Inc.
Learning Objectives
?
?
?
10-3
Understand the concepts and applications
of different types of simulation
Explain what is meant by system
dynamics, agent-based modeling, Monte
Carlo, and discrete event simulation
Describe the key issues of model
management
Copyright © 2014 Pearson Education, Inc.
Opening Vignette
System Dynamics Allows Fluor
Corporation to Better Plan for Project
and Change Management
?
?
?
?
?
10-4
Background
Problem description
Proposed solution
Results
Answer & discuss the case questions…
Copyright © 2014 Pearson Education, Inc.
Questions for
the Opening Vignette
Explain the use of system dynamics as a
simulation tool for solving complex problems.
2. In what ways was it applied in Fluor Corporation
to solve complex problems?
3. How does a what-if analysis help a decision
maker to save on cost?
4. In your own words, explain the factors that
might have triggered the use of system
dynamics to solve change management
problems in Fluor Corporation…
1.
10-5
Copyright © 2014 Pearson Education, Inc.
Problem-Solving Search Methods
?
?
?
Search: choice phase of decision making
Search is the process of identifying the
best possible solution / course of action
[under limitations such as time, …]
Search techniques include
?
?
?
?
10-6
analytical techniques,
algorithms,
blind searching, and
heuristic searching
Copyright © 2014 Pearson Education, Inc.
Problem-Solving Search Methods
Analytical
10-7
algorithm
Copyright © 2014 Pearson Education, Inc.
Problem-Solving Search Methods
– Algorithmic/Heuristic
?
?
?
?
?
10-8
Cuts the search space (or stop
early)
Gets satisfactory solutions more
quickly and less expensively
Finds good enough feasible
solutions to complex problems
Heuristics can be
? Quantitative
? Qualitative (in ES)
Traveling Salesman Problem see
the example next >>>
Copyright © 2014 Pearson Education, Inc.
Traveling Salesman Problem
?
What is it?
?
?
10-9
A traveling salesman must visit customers in several
cities, visiting each city only once, across the country.
Goal: Find the shortest possible route.
Total number of unique routes (TNUR):
TNUR = (1/2) (Number of Cities – 1)!
Number of Cities
TNUR
5
12
6
60
9
20,160
20
1.22 1018
Copyright © 2014 Pearson Education, Inc.
Traveling Salesman Problem
10-10
Copyright © 2014 Pearson Education, Inc.
Traveling Salesman Problem
Rule 1: Starting from home base, go to the closest city
Rule 2: Always follow an exterior route
10-11
Copyright © 2014 Pearson Education, Inc.
When to Use Heuristics
?
When to Use Heuristics?
?
?
?
?
?
?
Limitations of Heuristics!
?
10-12
Inexact or limited input data
Complex reality
Reliable, exact algorithm not available
Computation time excessive
For making quick decisions
Cannot guarantee an optimal solution
Copyright © 2014 Pearson Education, Inc.
Modern Heuristic Methods
?
Tabu search
?
?
Simulated annealing
?
?
10-13
Analogy to Thermodynamics
Genetic algorithms
?
?
Intelligent search algorithm
Survival of the fittest
Ant colony and other Meta-heuristics
Copyright © 2014 Pearson Education, Inc.
Genetic Algorithms
?
?
?
It is a popular heuristic search technique
Mimics the biological process of evolution
Genetic algorithms
?
?
?
An efficient, domain-independent search heuristic
for a broad spectrum of problem domains
Main theme: Survival of the fittest
?
10-14
Software programs that “learn/search” in evolutionary
manner, similar to the way biological systems evolve
Moving toward better and better solutions by letting
only the fittest parents create the future generations
Copyright © 2014 Pearson Education, Inc.
Evolutionary Algorithm
10010110
01100010
10100100
10011001
01111101




Elitism
Selection
Reproduction
. Crossover
. Mutation
Current
generation
10-15
10010110
01100010
10100100
10011101
01111001




Next
generation
Copyright © 2014 Pearson Education, Inc.
GA Structure and GA Operators
Start
?
?
?
?
Each candidate solution is called
a chromosome (cont or bin)
A chromosome is a string of
genes
Chromosomes can copy
themselves, mate, and mutate via
evolution
Next
In GA we use specific genetic
generation
of solutions
operators
? Reproduction
? Crossover
Elites
? Mutation
Offspring
10-16
Represent problem’s
chromosome structure
Generate initial solutions
(the initial generation)
Test:
Is the solution
satisfactory?
No
Select elite solutions; carry
them into next generation
Select parents to reproduce;
apply crossover and mutation
Copyright © 2014 Pearson Education, Inc.
Yes
Stop Deploy the
solution
GA Structure and GA
Operators
Representation
Chromosomes could be:
? Bit strings
? Real numbers
? Permutations of element
? Lists of rules
? Program elements
? … any data structure …
10-17
(0101 … 1100)
(43.2 -33.1 … 0.0 89.2)
(E11 E3 E7 … E1 E15)
(R1 R2 R3 … R22 R23)
(genetic programming)
Copyright © 2014 Pearson Education, Inc.
GA Structure and GA
Operators
Initialization
?
?
?
10-18
Initially many individual solutions are randomly generated to form
an initial population. The population size depends on the nature of
the problem, but typically contains several hundreds or thousands of
possible solutions.
Traditionally, the population is generated randomly, covering the
entire range of possible solutions (the search space).
Occasionally, the solutions may be “seeded” in areas where optimal
solutions are likely to be found.
Copyright © 2014 Pearson Education, Inc.
GA Structure and GA
Operators
A fitness function
10-19
Copyright © 2014 Pearson Education, Inc.
GA Structure and GA
Operators
Selection
?
During each successive generation, a proportion of the existing
population is selected to breed a new generation.
?
Individual solutions are selected through a fitness-based process,
where fitter solutions (as measured by a fitness function) are
typically more likely to be selected.
?
10-20
roulette wheel selection and tournament selection.
Copyright © 2014 Pearson Education, Inc.
General Algorithm for GA
?
Reproduction
The next step is to generate a second generation
population of solutions from those selected through genetic
operators:
crossover (also called recombination), and/or mutation.
10-21
Copyright © 2014 Pearson Education, Inc.
GA Structure and GA
Operators
Crossover – Recombination
1010000000
Parent1
Offspring1
1011011111
1001011111
Parent2
Offspring2
1010000000
Crossover
single point random
10-22
With some high probability (crossover
rate) apply crossover to the parents.
(typical values are 0.8 to 0.95)
Copyright © 2014 Pearson Education, Inc.
GA Structure and GA
Operators
mutate
Mutation
Offspring1
1011011111
Offspring1
1011001111
Offspring2
1010000000
Offspring2
1000000000
Original offspring
Mutated offspring
With some small probability (the mutation rate) flip each bit in
the offspring (typical values between 0.1 and 0.001)
10-23
Copyright © 2014 Pearson Education, Inc.
GA Structure and GA Operators
Start
Represent problem’s
chromosome structure
What are the main parameters to be
specified?
Generate initial solutions
(the initial generation)
Next
generation
of solutions
Test:
Is the solution
satisfactory?
No
Elites
Offspring
10-24
Select elite solutions; carry
them into next generation
Select parents to reproduce;
apply crossover and mutation
Copyright © 2014 Pearson Education, Inc.
Yes
Stop Deploy the
solution
Many GA parameters to set
?
?
?
10-25
Any GA implementation needs to decide
on a number of parameters: Population
size (N), mutation rate (m), crossover rate
(c)
Often these have to be “tuned” based on
results obtained – no general theory to
deduce good values
Typical values might be: N = 50, m =
0.05, c = 0.9
Copyright © 2014 Pearson Education, Inc.
Many Variants of GA
?
Different kinds of selection (not roulette)
?
?
?
Different recombination
?
?
?
?
10-26
Multi-point crossover
3 way crossover etc.
Different kinds of encoding other than
bitstring
?
?
Tournament
Elitism, etc.
Integer values
Ordered set of symbols
Different kinds of mutation
Copyright © 2014 Pearson Education, Inc.
Genetic Algorithms
– Example: The Vector Game
?
Description of the Vector Game
?
?
?
Default Strategy: Random Trial and Error
Improved Strategy: Use of Genetic
Algorithms
?
?
10-27
Identifying a string of 5 binary digits
In an iterative fashion, using genetic
algorithm process and genetic operators, find
the opponent’s digit sequence
See your book for functional details
Copyright © 2014 Pearson Education, Inc.
A Classic GA Example:
The Knapsack Problem
?
?
?
Item:
1 2 3 4 5 6 7
Benefit: 5 8 3 2 7 9 4
Weight: 7 8 4 10 4 6 4
Knapsack holds a maximum of 22 pounds
Need to fill it for maximum benefit (one per item)
Solutions take the form of a string of 1’s
Example Solution: 1 1 0 0 1 0 0
Means choose items 1, 2, 5:
?
?
10-28
Weight = 21, Benefit = 20
Evolver solution works in
Microsoft Excel… ?
Copyright © 2014 Pearson Education, Inc.
k
? Define the
objective
function and
constraint(s)
? Identify the
decision variables
and their
characteristics
10-30
Copyright © 2014 Pearson Education, Inc.
? Observe and
analyze the
results
10-31
Copyright © 2014 Pearson Education, Inc.
? Observe and
analyze the
results
10-32
Copyright © 2014 Pearson Education, Inc.
The Knapsack Problem at Evolver
? Monitoring
the solution
generation
process…
10-33
Copyright © 2014 Pearson Education, Inc.
Genetic Algorithms
?
Limitations of Genetic Algorithms
?
?
?
?
?
?
10-34
Does not guarantee an optimal solution (often settles
in a sub optimal solution / local minimum)
Not all problems can be put into GA formulation
Development and interpretation of GA solutions
requires both programming and statistical skills
Relies heavily on the random number generators
Locating good variables for a particular problem and
obtaining the data for the variables is difficult
Selecting methods by which to evolve the system
requires experimentation and experience
Copyright © 2014 Pearson Education, Inc.
Genetic Algorithm Applications
?
?
?
?
?
?
?
?
?
10-35
Dynamic process control
Optimization of induction rules
Discovery of new connectivity topologies (NNs)
Simulation of biological models of behavior
Complex design of engineering structures
Pattern recognition
Scheduling, transportation, and routing
Layout and circuit design
Telecommunication, graph-based problems, …
Copyright © 2014 Pearson Education, Inc.
Problem-Solving Search Methods
Analytical
10-36
algorithm
Copyright © 2014 Pearson Education, Inc.
Simulation
?
?
?
?
10-37
Simulation is the “appearance” of reality
It is often used to conduct what-if analysis (and Trial
and error) on the model of the actual system
It is a popular DSS technique for conducting
experiments with a computer on a comprehensive model
of the system to assess its dynamic behavior
Often used when the system is too complex for other
DSS techniques problem is stochastic in nature
Copyright © 2014 Pearson Education, Inc.
Application Case 10.3
Simulating Effects of Hepatitis B
Interventions
Questions for Discussion
Explain the advantage of operations research methods
such as simulation over clinical trial methods in
determining the best control measure for Hepatitis B.
2. In what ways do the decision and Markov models
provide cost-effective ways of combating the disease?
3. Discuss how multidisciplinary background is an asset in
finding a solution for the problem described in the case.
4. Besides healthcare, in what other domain could such a
modeling approach help reduce cost?
1.
10-38
Copyright © 2014 Pearson Education, Inc.
Major Characteristics of
Simulation
?
Imitates reality and captures its richness
both in shape and behavior
?
?
?
?
?
10-39
“Represent” versus “Imitate”
Technique for conducting experiments
Descriptive, not normative tool
Often to “solve” [i.e., analyze] very
complex systems/problems
Simulation should be used only when a
numerical optimization is not possible
Copyright © 2014 Pearson Education, Inc.
Advantages of Simulation
?
?
?
?
?
?
?
?
10-40
The theory is fairly straightforward
Great deal of time compression
Experiment with different alternatives
The model reflects manager’s perspective
Can handle wide variety of problem types
Can include the real complexities of problems
Produces important performance measures
Often it is the only DSS modeling tool for nonstructured problems
Copyright © 2014 Pearson Education, Inc.
Disadvantages of Simulation
?
?
?
?
?
10-41
Cannot guarantee an optimal solution
Slow and costly construction process
Cannot transfer solutions and inferences to
solve other problems (problem specific)
So easy to explain/sell to managers, may lead to
overlooking analytical solutions
Software may require special skills
Copyright © 2014 Pearson Education, Inc.
Simulation Methodology
Steps:
1.
2.
3.
4.
Define problem
5. Conduct experiments
Construct the model
6. Evaluate results
Test and validate model 7. Implement solution
Design experiments
More chance for success
Define scenarios
Why
simulation
Different levels of exp.
10-42
Copyright © 2014 Pearson Education, Inc.
Sensitivity analysis
Simulation Types
(defined according to the level of abstraction)
?
Probabilistic/Stochastic vs.
Deterministic Simulation
?
?
Time-dependent (product demanded 3 times a day) vs.
Time-independent Simulation (wait line)
?
?
Uses probability distributions (cont. Vs Discrete)
Monte Carlo (language planners lab) technique (X = A + B)
[A, B, and X are all distributions]
Discrete Event vs. Continuous Simulation
Var change discretely
(customers in a shop)
?
Simulation Implementation
?
10-43
Var change continuously
(change in the temperature of a system)
Visual Simulation and/or Object-Oriented Simulation
Copyright © 2014 Pearson Education, Inc.
Visual Interactive Simulation (VIS)
Inadequacy of conventional simulation methods (confidence gap)
?
?
?
?
?
?
10-44
Visual interactive modeling (VIM), also called Visual Interactive
Simulation or Visual interactive problem solving
Uses computer graphics to present the impact of different
management decisions
Often integrated with GIS
Users can perform sensitivity analysis
Static or dynamic (animation) systems
Virtual reality, immersive, …
Copyright © 2014 Pearson Education, Inc.
Traffic at an Intersection from
the Orca Visual Simulation
10-45
Copyright © 2014 Pearson Education, Inc.
Application Case 10.4
Improving Job-Shop Scheduling
Decisions Through RFID: A
Simulation-Based Assessment
?
?
?
?
10-46
Background
Problem description
Proposed solution
Results
Copyright © 2014 Pearson Education, Inc.
SIMIO Simulation Software
10-47
Copyright © 2014 Pearson Education, Inc.
SIMIO Simulation Software
10-48
Copyright © 2014 Pearson Education, Inc.
SIMIO Simulation Software
10-49
Copyright © 2014 Pearson Education, Inc.
Simulation Software
?
A comprehensive list can be found at
?
?
?
?
?
?
?
10-50
orms-today.org/surveys/Simulation/Simulation.html
Simio LLC, simio.com
SAS Simulation, sas.com
Lumina Decision Systems, lumina.com
Oracle Crystal Ball, oracle.com
Palisade Corp., palisade.com
Rockwell Intl., arenasimulation.com …
Copyright © 2014 Pearson Education, Inc.
System Dynamics Modeling
?
?
?
?
?
10-51
Macro-level simulation models in which
aggregate values and trends are considered
Objective is to study the overall behavior of a
system over time as a whole
Evolution of the various components of the
system over time and as a result of interplay
between the components over time
First introduced by Forrester (1958)
A widely used technique in operations research
and management science
Copyright © 2014 Pearson Education, Inc.
System Dynamics Modeling

radiology
performance
+
+

medical records
storage

+
patient
treatment time –

adverse drug
event (ADE)

staff training

E-Note

E-Rx
+


+

+ Staff time saved
+
+
laboratory
performance

+
ADE correction
cost
10-52
+
Copyright © 2014 Pearson Education, Inc.
+
compliance via
+ EHR
Agent-Based Modeling
?
?
?
Agent – an autonomous computer program
that observes and acts on an environment
and directs its activity toward achieving
specific goals
Relatively new technology
Other names include
?
?
?
?
10-53
Software agents
Wizards
Knowbots, Both
Intelligent software robots (Softbots) …
Copyright © 2014 Pearson Education, Inc.
Agent-Based Modeling
?
?
?
Agent-based modeling (ABM) is a simulation
modeling technique to support complex decision
systems where a system is modeled as a set of
autonomous decision-making units called agents
A bottom-up approach to simulation modeling
Agent-based modeling platforms
?
?
?
?
10-54
SWARM (www.swarms.org),
Netlogo (http://ccl.northwestern.edu/netlogo),
RePast/Sugarscape (www.repast.sourceforge.net),
…
Copyright © 2014 Pearson Education, Inc.
Application Case 10.5
Agent-Based Simulation Helps Analyze
Spread of a Pandemic Outbreak
Questions for Discussion
1.
2.
3.
4.
10-55
What are the characteristics of an agent-based
simulation model?
List the various factors that were fed into the agentbased simulation model described in the case.
Elaborate on the benefits of using agent-based
simulation models.
Besides disease prevention, in which other situations
could agent-based simulation be employed?
Copyright © 2014 Pearson Education, Inc.
End of the Chapter
?
10-56
Questions, comments
Copyright © 2014 Pearson Education, Inc.
All rights reserved. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any
m …
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