Competitive Advantage with Optimization MII

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

The Forces Driving Our Future
 Digital future
 Entrepreneurship rising
 Global marketplace
 Urban world
 Resourceful planet
 Health reimagined
Ernest & Young Megatrends 2015

 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

 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

 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

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

Anytime anywhere access to information.
Machines and software substitute humans.
How should we adapt?

Today’s Technology Buzzwords
Big Data
Data Visualization
Data Scientist
Business Intelligence
Analytics
Internet of Things
Cloud
Apps
Wearable

Big Data and Traditional Analytics
big data @ work, Thomas H. Davenport, 2014

Terminology for Using and Analyzing Data

Data Scientist?

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

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

Data Scientist at Work

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

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

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

Analytics Landscape
Descriptive
Prescriptive
Predictive
Degree of Complexity
CompetitiveAdvantage
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

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)

No Crystal Ball Required

Business Intelligence Framework
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)

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

 Simulation (predictive)
 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)
reliable forecasts

 Simulation
 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
reliable forecasts

Analytics Landscape
Descriptive
Prescriptive
Predictive
Standard Reporting
Ad hoc reporting
Query/drill down
Alerts
Simulation
Forecasting
Predictive modeling
Optimization
What happened?

Analytics Landscape
Descriptive
Prescriptive
Predictive
Standard Reporting
Ad hoc reporting
Query/drill down
Alerts
Simulation
Forecasting
Predictive modeling
Optimization
What happened?
Operations Research

Three Eras of Analytics

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)

Analytics Maturity (SAP)

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

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/

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/

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

Agenda
 Current Business and Technological Landscapes √
 Analytics Evolution √
 Introduction to Operations Research √
 A Primer on Optimization

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.
41Competitive Advantage with Optimization - Anwar Ali

LP Optimization Models
𝑚𝑎𝑥 𝑧 = 𝑐1 𝑥1 + 𝑐2 𝑥2
s.t.
𝑎11 𝑥1 + 𝑎12 𝑥2 ≤ 𝑏1
𝑎21 𝑥1 + 𝑎22 𝑥2 ≤ 𝑏2
𝑎31 𝑥1 + 𝑎32 𝑥2 ≤ 𝑏3
𝑥1 ≥ 0, 𝑥2 ≥ 0
𝑚𝑖𝑛 𝑧 = 𝑐1 𝑥1 + 𝑐2 𝑥2
s.t.
𝑎11 𝑥1 + 𝑎12 𝑥2 ≥ 𝑏1
𝑎21 𝑥1 + 𝑎22 𝑥2 ≥ 𝑏2
𝑎31 𝑥1 + 𝑎32 𝑥2 ≥ 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

Example 1: Dorian Auto
 Operations Research:
Applications and
Algorithms
 Wayne L. Winston
 Duxbury Press; 4th
edition (2003)

 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

 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

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

Graphical Solution
x (comedy ads)
y(footballads)
4 8 12 16
4
12
16
8
2
6
10
14
2 6 10 14

Graphical Solution
x (comedy ads)
y(footballads)
4 8 12 16
4
12
16
8
2
6
10
14
2 6 10 14
High-income women constraint; 7x + 2y ≥ 28

Graphical Solution
x (comedy ads)
y(footballads)
4 8 12 16
4
12
16
8
2
6
10
14
2 6 10 14
High-income men constraint; 2x + 12y ≥ 24

Unbounded
feasible region
Graphical Solution
x (comedy ads)
y(footballads)
4 8 12 16
4
12
16
8
2
6
10
14
2 6 10 14

Unbounded
feasible region
Graphical Solution
x (comedy ads)
y(footballads)
4 8 12 16
4
12
16
8
2
6
10
14
2 6 10 14
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

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

Unbounded
feasible region
Graphical Solution
x (comedy ads)
y(footballads)
4 8 12 16
4
12
16
8
2
6
10
14
2 6 10 14
Feasible integer solutions

Unbounded
feasible region
Graphical Solution
x (comedy ads)
y(footballads)
4 8 12 16
4
12
16
8
2
6
10
14
2 6 10 14
Feasible integer solutions
Optimal integer solutions
Lowest z value
in feasible region

Unbounded
feasible region
Graphical Solution
x (comedy ads)
y(footballads)
4 8 12 16
4
12
16
8
2
6
10
14
2 6 10 14
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

Example 2: Diet Problem
 Introduction to
Management Science
 Bernard W. Taylor III
 Prentice Hall, 7th edition
(2002)
 Latest is 11th edition
(2012)

 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

 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

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

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

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

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

Objective Function

Excel Solver Parameters

Excel Solver Solution

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

Model in IBM ILOG CPLEX

IBM ILOG CPLEX Solution

CPLEX Model (Integer variable)

Model in LPSolve

LPSolve Solution

LPSolve Model (Integer Variable)

LPSolve Solution (Integer Variable)

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

Conflicting Objectives
CostProfit
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

Agenda
 A Primer on Optimization √

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

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

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

Additional Reference – Williams
 Model Building in
Mathematical
Programming
 H. Paul Williams
 John Wiley & Sons, Ltd.
5th edition (2013)

Model Types (from H. Paul Williams)
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

Competitive Advantage with Optimization MII

Bin packing / knapsack problem

Cut into different sizes and shapes and minimize the waste
Cutting stock problem

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 problemCompetitive Advantage with Optimization - Anwar Ali 91

Blending problemCompetitive 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

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

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
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

Problem Formulation
 Let
 0-1 knapsack
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
𝑛
𝑖=1
𝑥𝑖
𝑛
𝑖=1
𝑥𝑖 ≤ 𝑊, 𝑥𝑖 ∈ 0, . . . , 𝑐𝑖
𝑛
𝑖=1
𝑥𝑖
𝑛
𝑖=1
𝑥𝑖 ≤ 𝑊, 𝑥𝑖 ≥ 0

Knapsack Problem Exercise
 Since the formulation has been given, let’s solve this
problem using Excel Solver
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
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

𝑛
𝑖=1
𝑥𝑖
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];
dvar boolean x[items];
subject to {
}
0-1 knapsack

int n = 5;
range items = 1..n;
int w[items] = [12,1,4,1,2];
int v[items] = [4,2,10,1,2];
dvar int+ x[items];
subject to {
}
𝑛
𝑖=1
𝑥𝑖
𝑛
𝑖=1
𝑥𝑖 ≤ 𝑊, 𝑥𝑖 ≥ 0
Unbounded

Agenda
 Formulating and Solving Optimization Models √

Waste neither time nor
money, but make the
best use of both
Benjamin Franklin

3 Classes of Business Value
 Cost reductions
 Decision improvements
 Improvements in products and services

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

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
Report by Everest Group Research 2014

Optimization in Insurance
 Product profitability
 Cost reduction
 Portfolio selection
 Manpower planning
 Site location
 Capital/assets optimization
 Scenario analysis

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

Agenda
 Formulating and Solving Optimization Models √
 Identifying Opportunities with Business Values √

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

Competencies Required
 Spreadsheet modeling
 Mathematical optimization
 Data integration
 Business acumen
 Hire consultant or upskill / train employees

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”

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

Course Outline – Fundamentals
 Introduction to Analytics and O.R.
 Algebraic Expressions
 Basic Spreadsheet Modeling
 LP and Solvers
 Model Types

Course Outline – Modeling
 Manpower Planning
 Blending
 Multi-period Inventory
 Transportation
 Assignment
 Transshipment
 Network
 Investment

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

anwarali@theoptimizationexpert.com

Competitive Advantage with Optimization MII

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