Breakfast Talk, Malaysian Insurance Institute 20th April 2017 Kuala Lumpur
Dr. Anwar Ali
www.theoptimizationexpert.com
My Background Studied engineering and worked as an engineer
Bachelor in Mechanical Eng, major in Industrial Engineering (IE) Held various engineering positions including process, machine
vision, equipment development, factory IE, systems IE
27 years in American multinational companies (1988-2015) 2 years at Texas Instruments KL 25 years at Intel Penang & Kulim, including 2 years in Arizona
Created in-house Operations Research group in 2002 Have done simulation, math optimization, and the relevant data
integration to enable simulation and optimization
Completed 2 post graduate degrees while working full time M.Sc. in Decision Science, UUM in 2005 Doctor in Engineering (Eng Biz Mgt), UTM KL in 2014
Competitive Advantage with Optimization - Anwar Ali 2
Agenda Current Business and Technological Landscapes
Analytics Evolution
Introduction to Operations Research
A Primer on Optimization
Formulating and Solving Optimization Models
Identifying Opportunities with Business Values
How to Get Started
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The Forces Driving Our Future Digital future
Entrepreneurship rising
Global marketplace
Urban world
Resourceful planet
Health reimagined
Competitive Advantage with Optimization - Anwar Ali 4 Ernest & Young Megatrends 2015
The Forces Driving Our Future Digital future
Convergence of social, mobile, cloud, big data
Growing demand for anytime anywhere access to information
Entrepreneurship rising Technology enabling machines and software to
substitute for humans
High-impact entrepreneurs are building innovative and scalable enterprises
Many new enterprises are digital from birth with young faces
Competitive Advantage with Optimization - Anwar Ali 5 Ernest & Young Megatrends 2015
The Forces Driving Our Future Global marketplace
Innovation will increasingly take place in rapid-growth markets
War for talent; greater workforce diversity providing competitive advantage
Urban world
More cities across the globe
Competitive Advantage with Optimization - Anwar Ali 6 Ernest & Young Megatrends 2015
The Forces Driving Our Future Resourceful planet
Increasing global demand for natural resources
Growing concern over environmental degradation
Health reimagined
Increasing cost pressure require more sustainable approach
Explosion in big data and mobile health technologies
From delivery of health care to management of health
Competitive Advantage with Optimization - Anwar Ali 7 Ernest & Young Megatrends 2015
Digital Future Technology is also changing the ways people work, and
is increasingly enabling machines and software to substitute for humans. Enterprises and individuals who can seize the opportunities offered by digital advances stand to gain significantly, while those who cannot may lose everything
Competitive Advantage with Optimization - Anwar Ali 8 Ernest & Young Megatrends 2015
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Anytime anywhere access to information. Machines and software substitute humans.
How should we adapt?
Today’s Technology Buzzwords
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Big Data Data Visualization
Data Scientist
Business Intelligence
Analytics
Internet of Things
Cloud
Apps
Wearable
Big Data and Traditional Analytics
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big data @ work, Thomas H. Davenport, 2014
Terminology for Using and Analyzing Data
Competitive Advantage with Optimization - Anwar Ali 12 big data @ work, Thomas H. Davenport, 2014
Data Scientist?
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Data Science Data Science is an interdisciplinary field about processes and systems to extract knowledge or insights from large volumes of data in various forms, either structured or unstructured, which is a continuation of some of the data analysis fields such as data mining and predictive analytics, as well as Knowledge Discovery in Databases
Wikipedia Competitive Advantage with Optimization - Anwar Ali 15
Data Scientist Similar training like business/data analyst
Computer science, modeling, statistics, analytics, math
Somebody who can stare at data and spot trends, discovering previously hidden insights, which can provide a competitive advantage or address a problem
Data scientists are inquisitive: exploring, asking questions, doing “what if” analysis, questioning existing assumptions and processes. Armed with data and analytical results, a top-tier data scientist will then communicate informed conclusions and recommendations across an organization.
IBM Competitive Advantage with Optimization - Anwar Ali 16
Data Scientist at Work
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Business Intelligence Business intelligence (BI) is a broad category of
applications, technologies, and processes for gathering, storing, accessing, and analyzing data to help business users make better decisions
The term was first used in 1865
Business Analytics (BA), a newer term, is a subset of BI, focusing on statistics, prediction, and optimization, rather than the reporting functionality
BI / BA are used interchangeably by different vendors with their own definition
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Analytics The extensive use of data, statistical and quantitative analysis, explanatory and predictive models, and fact-based management to drive decisions and actions
Competing on Analytics: The New Science of Winning, Davenport and Harris, 2007
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Business Analytics Business analytics can be defined as the broad use of data and quantitative analysis for decision-making within organizations. It encompasses query and reporting, but aspires to greater levels of mathematical sophistication. It includes analytics, of course, but involves harnessing them to meet defined business objectives. Business analytics empowers people in the organization to make better decisions, improve processes and achieve desired outcomes. It brings together the best of data management, analytic methods, and the presentation of results – all in a closed-loop cycle for continuous learning and improvement
The New World of “Business Analytics”, Thomas H. Davenport, March 2010
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Analytics Landscape
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Descriptive
Prescriptive
Predictive
Degree of Complexity
Com
petitive A
dvanta
ge
Standard Reporting
Ad hoc reporting
Query/drill down
Alerts
Simulation
Forecasting
Predictive modeling
Optimization
What exactly is the problem?
What will happen next if ?
What if these trends continue?
What could happen…. ?
What actions are needed?
How many, how often, where?
What happened?
Stochastic Optimization
How can we achieve the best outcome?
How can we achieve the best outcome
including the effects of variability?
Source: IBM, Based on: Competing on Analytics,
Davenport and Harris, 2007
Analytics Descriptive analytics (what has occurred)
The simplest class of analytics, condense big data into smaller, more useful nuggets of information e.g. counts, likes, posts, views, sales, finance
Predictive analytics (what will occur) Use available data to predict data we don’t have using variety
of statistical, modeling, data mining, and machine learning techniques
Prescriptive analytics (what should occur) Recommend one or more courses of action and showing the
likely outcome of each decision so that the business decision-maker can take this information and act
Adapted from Information Week, definitions by Dr Michael Wu http://www.informationweek.com/big-data/big-data-analytics/big-data-analytics-descriptive-vs-predictive-vs-prescriptive/d/d-id/1113279
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MS Excel Examples Descriptive aggregate functions:
SUM(), MIN/MAX(), COUNT(), STDEV(), AVERAGE()
Pivot tables
Predictive: FORECAST(), TREND()
Analysis ToolPak add-in (comes with Excel)
Data Mining add-in (downloadable from Microsoft)
XLMiner add-in (need to purchase from FrontlineSolvers)
Prescriptive: Solver add-in (comes with Excel, limited capability)
Open Solver add-in (open source, unlimited capability)
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No Crystal Ball Required
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Business Intelligence Framework
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Back in Business, by Ronald K. Klimberg and Virginia Miori, OR/MS Today, Vol 37, No 5, October 2010, [http://www.informs.org/ORMS-Today/Public-Articles/October-Volume-37-Number-5/Back-in-Business]
OR/MS = Operations Research/ Management Science
What is Operations Research? O.R. is the discipline of applying advanced analytical
methods to help make better decisions
Also called Management Science or Decision Science, O.R. is the science of Decision-Making
Employing techniques from mathematical sciences, O.R. arrives at optimal or near-optimal solutions to complex decision-making problems
Determine the maximum (e.g. profit, performance, or yield) or minimum (e.g. loss, risk, or cost)
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O.R. Leading Edge Techniques Simulation
Giving you the ability to try out approaches and test ideas for improvement
Optimization Narrowing your choices to the very best where there are
virtually innumerable feasible options and comparing them is difficult
Probability and statistics Helping you measure risk, mine data to find valuable
connections and insights, test conclusions, and make reliable forecasts
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O.R. Leading Edge Techniques Simulation (predictive)
Giving you the ability to try out approaches and test ideas for improvement
Optimization (prescriptive) Narrowing your choices to the very best where there are
virtually innumerable feasible options and comparing them is difficult
Probability and statistics (predictive) Helping you measure risk, mine data to find valuable
connections and insights, test conclusions, and make reliable forecasts
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O.R. Leading Edge Techniques Simulation
Giving you the ability to try out approaches and test ideas for improvement
Optimization – THIS TALK Narrowing your choices to the very best where there
are virtually innumerable feasible options and comparing them is difficult
Probability and statistics Helping you measure risk, mine data to find valuable
connections and insights, test conclusions, and make reliable forecasts
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Analytics Landscape
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Descriptive
Prescriptive
Predictive
Degree of Complexity
Com
petitive A
dvanta
ge
Standard Reporting
Ad hoc reporting
Query/drill down
Alerts
Simulation
Forecasting
Predictive modeling
Optimization
What exactly is the problem?
What will happen next if ?
What if these trends continue?
What could happen…. ?
What actions are needed?
How many, how often, where?
What happened?
Stochastic Optimization
How can we achieve the best outcome?
How can we achieve the best outcome
including the effects of variability?
Source: IBM, Based on: Competing on Analytics,
Davenport and Harris, 2007
Analytics Landscape
Descriptive
Prescriptive
Predictive
Degree of Complexity
Com
petitive A
dvanta
ge
Standard Reporting
Ad hoc reporting
Query/drill down
Alerts
Simulation
Forecasting
Predictive modeling
Optimization
What exactly is the problem?
What will happen next if ?
What if these trends continue?
What could happen…. ?
What actions are needed?
How many, how often, where?
What happened?
Stochastic Optimization
How can we achieve the best outcome?
How can we achieve the best outcome
including the effects of variability?
Source: IBM, Based on: Competing on Analytics,
Davenport and Harris, 2007
Operations Research
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Three Eras of Analytics
Competitive Advantage with Optimization - Anwar Ali 32 big data @ work, Thomas H. Davenport, 2014
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In 2013 Gartner called prescriptive analytics 'the final frontier for big data’, where companies can finally turn the unprecedented levels of data in the enterprise into powerful action
Analytics Maturity (Gartner)
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Analytics Maturity (SAP)
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Examples of Optimization Application
Deciding where to invest capital in order to grow
Figuring out the best way to run a call center
Locating a warehouse or depot to deliver materials over shorter distances at reduced cost
Solving complex scheduling problems
Deciding when to discount, and how much
Getting more out of manufacturing equipment
Optimizing a portfolio of investments
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What are the Benefits? Operations Research is called “The Science of Better”,
i.e. using science to make:
bold decisions and run everyday operations with less risk and better outcomes (no more gut-feel)
repeatable, quantitative decision analysis
Adapted from: The Guide to Operational Research, http://www.scienceofbetter.co.uk/
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Signs O.R. Could Be Beneficial The management face complex decision making
The management is not sure what the main problem is
The management is uncertain about potential outcomes
The organization is having problems with decision making processes
Management is troubled by risk
The organization is not making the most of its data
The organization needs to beat stiff competition
The Guide to Operational Research, http://www.scienceofbetter.co.uk/
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Key Messages Seize the opportunities offered by digital advances
Anytime anywhere access to information
Machines and software substitute humans
Be part of analytics initiatives
Optimization is at the top of Analytics
Optimization is the final frontier for big data
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Agenda Current Business and Technological Landscapes √
Analytics Evolution √
Introduction to Operations Research √
A Primer on Optimization
Formulating and Solving Optimization Models
Identifying Opportunities with Business Values
How to Get Started
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Optimization Modeling Optimization models have
Objective function
Decision variables
Constraints
Formulated as mathematical equations
Solved graphically (if 2 decision variables) or using Excel Solver, CPLEX, LPSolve, LINDO/LINGO, etc.
41 Competitive Advantage with Optimization - Anwar Ali
LP Optimization Models
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𝑚𝑎𝑥 𝑧 = 𝑐1𝑥1 + 𝑐2𝑥2
s.t.
𝑎11𝑥1 + 𝑎12𝑥2 ≤ 𝑏1
𝑎21𝑥1 + 𝑎22𝑥2 ≤ 𝑏2
𝑎31𝑥1 + 𝑎32𝑥2 ≤ 𝑏3
𝑥1 ≥ 0, 𝑥2 ≥ 0
𝑚𝑖𝑛 𝑧 = 𝑐1𝑥1 + 𝑐2𝑥2
s.t.
𝑎11𝑥1 + 𝑎12𝑥2 ≥ 𝑏1
𝑎21𝑥1 + 𝑎22𝑥2 ≥ 𝑏2
𝑎31𝑥1 + 𝑎32𝑥2 ≥ 𝑏3
𝑥1 ≥ 0, 𝑥2 ≥ 0
Objective function
Subject to
Constraints
Decision variables
Linear Programming A linear programming (LP) problem is an optimization
problem which Attempt to maximize (or minimize) a linear function
(called the objective function) of the decision variables
The values of the decision variables must satisfy a set of constraints. Each constraint must be a linear equation or inequality
A sign restriction is associated with each variable. For any variable xi, the sign restriction specifies either that xi must be nonnegative (xi ≥ 0) or that xi may be unrestricted in sign
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Example 1: Dorian Auto Operations Research:
Applications and Algorithms
Wayne L. Winston
Duxbury Press; 4th edition (2003)
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Example 1: Dorian Auto Dorian Auto manufactures luxury cars and trucks
The company believes that its most likely customers are high-income women and men
To reach these groups, Dorian Auto has embarked on an ambitious TV advertising campaign and will purchase 1-minute commercial spots on two type of programs: comedy shows and football games
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Example 1: Dorian Auto Each comedy commercial is seen by 7 million high
income women and 2 million high-income men and costs $50,000
Each football game is seen by 2 million high-income women and 12 million high-income men and costs $100,000
Dorian Auto would like for commercials to be seen by at least 28 million high-income women and 24 million high-income men
We will use LP to determine how Dorian Auto can meet its advertising requirements at minimum cost
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Example 1: Solution Decision variables:
x = the number of 1-minute comedy ads
y = the number of 1-minute football ads
The objective is to minimize advertising cost Minimize z = 50x + 100y
Constraints: Ads must be seen by at least 28 million high-income
women; 7x + 2y ≥ 28
Ads must be seen by at least 24 million high-income men; 2x + 12y ≥ 24
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Graphical Solution
x (comedy ads)
y (f
oo
tbal
l ad
s)
4 8 12 16
4
12
16
8
2
6
10
14
2 6 10 14
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Graphical Solution
x (comedy ads)
y (f
oo
tbal
l ad
s)
4 8 12 16
4
12
16
8
2
6
10
14
2 6 10 14
Competitive Advantage with Optimization - Anwar Ali 49
High-income women constraint; 7x + 2y ≥ 28
Graphical Solution
x (comedy ads)
y (f
oo
tbal
l ad
s)
4 8 12 16
4
12
16
8
2
6
10
14
2 6 10 14
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High-income women constraint; 7x + 2y ≥ 28
High-income men constraint; 2x + 12y ≥ 24
Unbounded feasible region
Graphical Solution
x (comedy ads)
y (f
oo
tbal
l ad
s)
4 8 12 16
4
12
16
8
2
6
10
14
2 6 10 14
Competitive Advantage with Optimization - Anwar Ali 51
High-income women constraint; 7x + 2y ≥ 28
High-income men constraint; 2x + 12y ≥ 24
Unbounded feasible region
Graphical Solution
x (comedy ads)
y (f
oo
tbal
l ad
s)
4 8 12 16
4
12
16
8
2
6
10
14
2 6 10 14
Competitive Advantage with Optimization - Anwar Ali 52
High-income women constraint; 7x + 2y ≥ 28
High-income men constraint; 2x + 12y ≥ 24
Unbounded feasible region
Graphical Solution
x (comedy ads)
y (f
oo
tbal
l ad
s)
4 8 12 16
4
12
16
8
2
6
10
14
2 6 10 14
Competitive Advantage with Optimization - Anwar Ali 53
High-income women constraint; 7x + 2y ≥ 28
High-income men constraint; 2x + 12y ≥ 24
x = 3.6 y = 1.4
Optimal Answer To minimize advertising cost, purchase
3.6 slots of comedy ads (x)
1.4 slots of football ads (y)
The total advertising cost (in thousands) is z = 50x + 100 y
z = 50(3.6) + 100(1.4)
z = 320
But in reality, it is not possible to purchase fractional number of 1-minute ads. The decision variables x and y must be integers
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Integer Programming When an LP model has integer decision variable(s), it is
called integer linear programming (ILP). Why ILP? We cannot buy 3.6 slots of ads, must be either 3 or 4
Yes/no decisions can be modeled as 0 or 1 variables
When an LP model has mixture of continuous and integer variables, it is called mixed integer linear programming (MILP)
ILP and MILP models are harder and take longer to solve compared to LP models
We will use the term “math programming” to represent LP, ILP, and MILP
Competitive Advantage with Optimization - Anwar Ali 55
Unbounded feasible region
Graphical Solution
x (comedy ads)
y (f
oo
tbal
l ad
s)
4 8 12 16
4
12
16
8
2
6
10
14
2 6 10 14
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Feasible integer solutions
Unbounded feasible region
Graphical Solution
x (comedy ads)
y (f
oo
tbal
l ad
s)
4 8 12 16
4
12
16
8
2
6
10
14
2 6 10 14
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Feasible integer solutions
Optimal integer solutions
Lowest z value in feasible region
Unbounded feasible region
Graphical Solution
x (comedy ads)
y (f
oo
tbal
l ad
s)
4 8 12 16
4
12
16
8
2
6
10
14
2 6 10 14
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2 solutions with z = 400
x = 6, y = 1 x = 4, y = 2
Graphical Integer Solutions There are 2 solutions with z = 400
4 slots of comedy ads (x) and 2 slots of football ads (y); z = 50(4) + 100(2) = 400
6 slots of comedy ads (x) and 1 slot of football ads (y); z = 50(6) + 100(1) = 400
For more complex problems which cannot be solve graphically, branch-and-bound method is used
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Example 2: Diet Problem Introduction to
Management Science
Bernard W. Taylor III
Prentice Hall, 7th edition (2002)
Latest is 11th edition (2012)
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Example 2: Diet Problem Breakfast to include at least 420 calories, 5 milligrams
of iron, 400 milligrams of calcium, 20 grams of protein, 12 grams of fiber, and must have no more than 20 grams of fat and 30 milligrams of cholesterol
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Example 2: Diet Problem The objective is to minimize meal cost while meeting
the following nutritional requirement:
Calories ≥ 420
Iron ≥ 5
Calcium ≥ 400
Protein ≥ 20
Fiber ≥ 12
Fat ≤ 20
Cholesterol ≤ 30
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Example 2: Decision Variables x1 = cups of bran cereal
x2 = cups of dry cereal
x3 = cups of oatmeal
x4 = cups of oat bran
x5 = eggs
x6 = slices of bacon
x7 = oranges
x8 = cups of milk
x9 = cups of orange juice
x10 = slices of wheat toast
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Example 2: Problem Formulation Minimize 0.18x1 + 0.22x2 + 0.10x3 + 0.12x4 + 0.10x5 + 0.09x6 + 0.40x7 + 0.16x8 + 0.50x9 + 0.07x10
Subject to: 90x1 + 110x2 + 100x3 + 90x4 + 75x5 + 35x6 + 65x7 + 100x8 + 120x9 + 65x10 ≥ 420 6x1 + 4x2 + 2x3 + 3x4 + x5 + x7 + x10 ≥ 5 20x1 + 48x2 + 12x3 + 8x4 + 30x5 + 52x7 + 250x8 + 3x9 + 26x10 ≥ 400 3x1 + 4x2 + 5x3 + 64 + 7x5 + 2x6 + x7 + 9x8 + x9 + 3x10 ≥ 20 5x1 + 2x2 + 3x3 + 4x4 + x7 + 3x10 ≥ 12 2x2 + 2x3 + 2x4 + 5x5 + 3x6 + 4x8 + x10 ≤ 20 270x5 + 8x6 + 12x8 ≤ 30
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Example 2: Solution The diet problem cannot be solved graphically as it has
10 decision variables
We will use ‘Solver’ to find solution for the problem
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Solver Mathematical software, either stand-alone or library,
that 'solves' a mathematical programming problem
Uses algorithms such as SIMPLEX and branch-and-bound to solve the problem
May include Integrated Development Environment (IDE), e.g. GUI and editor
Solvers used in this presentation: Excel Solver add-in (free, limited capability)
Excel OpenSolver add-in (free, open source)
IBM ILOG CPLEX Optimization Studio
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Objective Function
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Excel Solver Parameters
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Excel Solver Solution
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Example 2: Problem Formulation Minimize 0.18x1 + 0.22x2 + 0.10x3 + 0.12x4 + 0.10x5 + 0.09x6 + 0.40x7 + 0.16x8 + 0.50x9 + 0.07x10
Subject to: 90x1 + 110x2 + 100x3 + 90x4 + 75x5 + 35x6 + 65x7 + 100x8 + 120x9 + 65x10 ≥ 420 6x1 + 4x2 + 2x3 + 3x4 + x5 + x7 + x10 ≥ 5 20x1 + 48x2 + 12x3 + 8x4 + 30x5 + 52x7 + 250x8 + 3x9 + 26x10 ≥ 400 3x1 + 4x2 + 5x3 + 64 + 7x5 + 2x6 + x7 + 9x8 + x9 + 3x10 ≥ 20 5x1 + 2x2 + 3x3 + 4x4 + x7 + 3x10 ≥ 12 2x2 + 2x3 + 2x4 + 5x5 + 3x6 + 4x8 + x10 ≤ 20 270x5 + 8x6 + 12x8 ≤ 30
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Model in IBM ILOG CPLEX
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IBM ILOG CPLEX Solution
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CPLEX Model (Integer variable)
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Model in LPSolve
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LPSolve Solution
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LPSolve Model (Integer Variable)
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LPSolve Solution (Integer Variable)
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Key Take Away In university, we were taught how to model and then
solve the problem by hand
In practice, solvers like Excel Solver, ILOG CPLEX and LPSolve can find the solution(s) very quickly
It is important to understand the modeling concepts and able to formulate the problems correctly
But real-world models are a lot more complex than the textbook examples May have multiple conflicting objectives
Many (thousands) decision variables and constraints
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Conflicting Objectives
Competitive Advantage with Optimization - Anwar Ali 79
Cost Profit Labor
Service Time
Regulations Policy Laws
Process
Quality Systems
Safety
Compliance
Choice of Solver The choice of solver depends on the problem size and
the ability to integrate with enterprise system
Excel Solver is recommended for rapid prototyping and quick-wins Demonstrate the concept to users and management
Can be used if the problem is small When all data is local and no database interface is required
IBM ILOG CPLEX is very good for integrating the solver solution with large enterprise system Scalable with powerful database interfaces
Competitive Advantage with Optimization - Anwar Ali 80
Agenda Current Business and Technological Landscapes √
Analytics Evolution √
Introduction to Operations Research √
A Primer on Optimization √
Formulating and Solving Optimization Models
Identifying Opportunities with Business Values
How to Get Started
Competitive Advantage with Optimization - Anwar Ali 81
Problem Formulation Problem formulation is the most challenging part in
math programming
Once the problem has been formulated correctly, putting the problem into solvers is easy
Need to use the correct approach in developing the mathematical equations of a problem
The more experience we have in problem formulation, the easier it becomes
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The formulation of a problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill
Albert Einstein
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Recommended Modeling Approach First, must understand the problem well
e.g. business rules, objective(s), constraints, input data and output/decisions required
Talk to the experts how decisions are made without a model
Relate the problem to the relevant model types
Look at examples of the relevant model types Many Excel Solver examples are downloadable from Frontline
Systems
IBM ILOG CPLEX has examples of different complexity
Develop and refine the model until it represents the problem faithfully
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Additional Reference – Williams Model Building in
Mathematical Programming
H. Paul Williams
John Wiley & Sons, Ltd. 5th edition (2013)
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Model Types (from H. Paul Williams)
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Network models - Transportation problem - Assignment problem - Transhipment problem - Minimim cost problem - Shortest path problem - Maximum flow through a network - Critical path analysis
Integer programming models - Set covering problems - Set packing problems - Set partitioning problems - Knapsack problem - Travelling salesman problem - Vehicle routing problem
Bin packing / knapsack problem
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Cut into different sizes and shapes and minimize the waste
Cutting stock problem
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Start from a city, visit each city only once, and return to the original city after all cities visited. Minimize the travel distance / cost
Traveling salesman problem (TSP) Competitive Advantage with Optimization - Anwar Ali 90
Assign gates to planes considering plane type, schedule, domestic/international, airlines Assignment problem Competitive Advantage with Optimization - Anwar Ali 91
Blending problem Competitive Advantage with Optimization - Anwar Ali 92
Minimize breakfast cost and include at least 420 calories, 5 milligrams of iron, 400 milligrams of
calcium, 20 grams of protein, 12 grams of fiber, and must have no more than 20 grams of fat and 30
milligrams of cholesterol
Diet problem which is blending problem Competitive Advantage with Optimization - Anwar Ali 93
Summary of Problems Linear Programming
Blending problem
Integer Programming
Bin packing / knapsack problem
Cutting stock problem
Traveling salesman problem (TSP)
Assignment problem
We pick the interesting knapsack problem and demonstrate how it is formulated and solved
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Knapsack Problem The original name came from a problem where a hiker tries
to pack the most valuable items without overloading the knapsack. Each item has a certain value/benefit and weight. An overall weight limitation gives the single constraint
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Picture from Wikipedia
Knapsack Problem This is a combinatorial optimization problem and has
been studied since 1897. Several algorithms have been developed to solve this problem
Application examples:
Stocking warehouse to the space limit
Finding the least wasteful way to cut raw materials
Portfolio selection in investment decision
Capital budgeting allocation decision
Project selection
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Problem Formulation Let
0-1 knapsack
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𝑥𝑖 = 𝑐𝑜𝑝𝑖𝑒𝑠 𝑜𝑓 𝑒𝑎𝑐ℎ 𝑘𝑖𝑛𝑑 𝑜𝑓 𝑖𝑡𝑒𝑚
𝑣𝑖 = 𝑣𝑎𝑙𝑢𝑒
𝑤𝑖 = 𝑤𝑒𝑖𝑔ℎ𝑡
𝑊 = 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑤𝑒𝑖𝑔ℎ𝑡 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦
𝑖 = 𝑖𝑡𝑒𝑚𝑠 𝑛𝑢𝑚𝑏𝑒𝑟𝑒𝑑 1. . 𝑛
𝑚𝑎𝑥𝑖𝑚𝑖𝑧𝑒 𝑣𝑖
𝑛
𝑖=1
𝑥𝑖
𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 𝑤𝑖
𝑛
𝑖=1
𝑥𝑖 ≤ 𝑊, 𝑥𝑖 ∈ 0,1
Other Types of Knapsack Bounded
Unbounded
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𝑚𝑎𝑥𝑖𝑚𝑖𝑧𝑒 𝑣𝑖
𝑛
𝑖=1
𝑥𝑖
𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 𝑤𝑖
𝑛
𝑖=1
𝑥𝑖 ≤ 𝑊, 𝑥𝑖 ∈ 0, . . . , 𝑐𝑖
𝑚𝑎𝑥𝑖𝑚𝑖𝑧𝑒 𝑣𝑖
𝑛
𝑖=1
𝑥𝑖
𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 𝑤𝑖
𝑛
𝑖=1
𝑥𝑖 ≤ 𝑊, 𝑥𝑖 ≥ 0
Knapsack Problem Exercise Since the formulation has been given, let’s solve this
problem using Excel Solver
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Items Weight Value Take?
1 12 4
2 1 2
3 4 10
4 1 1
5 2 2
Weight of items taken 0
Weight limit 15
Total value 0
From math model to OPL model
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int n = 5;
range items = 1..n;
int w[items] = [12,1,4,1,2];
int v[items] = [4,2,10,1,2];
int W = 15; // weight limit
dvar boolean x[items];
maximize sum(i in items) v[i]*x[i];
subject to {
sum(i in items) w[i]*x[i] <= W;
}
𝑥𝑖 = 𝑐𝑜𝑝𝑖𝑒𝑠 𝑜𝑓 𝑒𝑎𝑐ℎ 𝑘𝑖𝑛𝑑 𝑜𝑓 𝑖𝑡𝑒𝑚
𝑣𝑖 = 𝑣𝑎𝑙𝑢𝑒
𝑤𝑖 = 𝑤𝑒𝑖𝑔ℎ𝑡
𝑊 = 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑤𝑒𝑖𝑔ℎ𝑡 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦
𝑖 = 𝑖𝑡𝑒𝑚𝑠 𝑛𝑢𝑚𝑏𝑒𝑟𝑒𝑑 1. . 𝑛 Items Weight Value Take?
1 12 4
2 1 2
3 4 10
4 1 1
5 2 2
Weight of items taken 0
Weight limit 15
Total value 0
From math model to OPL model
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𝑚𝑎𝑥𝑖𝑚𝑖𝑧𝑒 𝑣𝑖
𝑛
𝑖=1
𝑥𝑖
𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 𝑤𝑖
𝑛
𝑖=1
𝑥𝑖 ≤ 𝑊, 𝑥𝑖 ∈ 0,1
int n = 5;
range items = 1..n;
int w[items] = [12,1,4,1,2];
int v[items] = [4,2,10,1,2];
int W = 15; // weight limit
dvar boolean x[items];
maximize sum(i in items) v[i]*x[i];
subject to {
sum(i in items) w[i]*x[i] <= W;
}
0-1 knapsack
From math model to OPL model
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int n = 5;
range items = 1..n;
int w[items] = [12,1,4,1,2];
int v[items] = [4,2,10,1,2];
int W = 15; // weight limit
dvar int+ x[items];
maximize sum(i in items) v[i]*x[i];
subject to {
sum(i in items) w[i]*x[i] <= W;
}
𝑚𝑎𝑥𝑖𝑚𝑖𝑧𝑒 𝑣𝑖
𝑛
𝑖=1
𝑥𝑖
𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 𝑤𝑖
𝑛
𝑖=1
𝑥𝑖 ≤ 𝑊, 𝑥𝑖 ≥ 0
Unbounded
Agenda Current Business and Technological Landscapes √
Analytics Evolution √
Introduction to Operations Research √
A Primer on Optimization √
Formulating and Solving Optimization Models √
Identifying Opportunities with Business Values
How to Get Started
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Waste neither time nor money, but make the best use of both
Benjamin Franklin
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3 Classes of Business Value Cost reductions
Decision improvements
Improvements in products and services
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Examples Cost reductions
Capital dollars (e.g. fixed assets, buildings)
Manpower optimization (e.g. call centre)
Decision improvements
What-if analyses speed
Pricing decisions
Improvements in products and services
Customers retention
New products
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The capability to conduct Advanced Analytics will no longer be viewed as a competitive advantage – it will become a necessity for
survival and a requirement to stay competitive in the marketplace
2016 Big Data Survey Respondent, North American Chief Risk Officers Council
Analytics in Insurance
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Optimization in Insurance Product profitability
Cost reduction
Portfolio selection
Manpower planning
Site location
Capital/assets optimization
Scenario analysis
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Identifying Opportunities Whenever there is a need to iterate many possibilities
or scenarios before making recommendation to the management, it means there is opportunity to use Optimization
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Agenda Current Business and Technological Landscapes √
Analytics Evolution √
Introduction to Operations Research √
A Primer on Optimization √
Formulating and Solving Optimization Models √
Identifying Opportunities with Business Values √
How to Get Started
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Getting Started with Optimization Get management sponsors
Convince management the benefits of optimization
Identify the challenges in decision making process Unable to predict the outcome?
Complexity in decision making
Drill down the decision making process Objectives, rules, and boundary conditions
Input data required
What kind of outcomes/decisions needed
Build and demo quick-win optimization model(s) Refine it until it can replace the current process
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Competencies Required Spreadsheet modeling
Mathematical optimization
Data integration
Business acumen
Hire consultant or upskill / train employees
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Training Offering Current offering of SBL claimable training
1-day “Decision Optimization for Managers”
3-day “Decision Optimization”
Upcoming courses
“Decision Optimization Non-Linear Programming”
“Decision Optimization Stochastic Programming”
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Expected Learning Outcome You will learn:
Where O.R. fits in the analytics big picture and how it helps decision making
Algebraic expressions and spreadsheet modeling techniques
Linear Programming (LP) concepts and modeling techniques
How to formulate decision-making problems as LP models and solve with various solvers
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Course Outline – Fundamentals Introduction to Analytics and O.R.
Algebraic Expressions
Basic Spreadsheet Modeling
LP and Solvers
Model Types
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Course Outline – Modeling Manpower Planning
Blending
Multi-period Inventory
Transportation
Assignment
Transshipment
Network
Investment
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Course Outline – Modeling Integer Programming (IP)
0-1 IP
Knapsack, Investment
Fixed-charge and Facility Location
Set Covering
Either-Or constraints
Traveling Salesman Problem (TSP)
Goal Programming
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