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OPERATIONS RESEARCH:
THE SCIENCE OF
BETTER.
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OPERATIONS RESEARCH (ALSO KNOWN AS MANAGEMENT SCIENCE ) THE APPLICATION
OF SCIENTIFIC METHODS, TECHNIQUES AND TOOLS TO PROBLEMS INVOLVING THE
OPERATIONS OF A SYSTEM SO AS TO PROVIDE THOSE IN CONTROL OF THE SYSTEM WITH
OPTIMUM SOLUTIONS TO PROBLEMS.
Operations Research is the discipline of applying advanced analytical methods to help make
better decisions.
By using techniques such as mathematical modelling to analyze complex situations, operations
research gives executives the power to make more effective decisions and build more productivesystems based on:
More complete data
Consideration of all available options
Careful predictions of outcomes and estimates of risk
The latest decision tools and techniques
** Industrial engineering takes more of an engineering point of view, and industrial
engineers typically consider OR techniques to be a major part of their tool set.
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OPERATIONS RESEARCH:
BETTER DECISION
MAKING.
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WHY OPERATIONS RESEARCH
NEEDED?
UNIQUELY POWERFUL APPROACH TO DECISION MAKING IN A COMPLEXWORLD
You face comp lex decis ion s
Youre having problems with processes.
Youre troubled by risk.
Your organization is n ot m aking the mo st of i ts data.
You n eed to b eat st i f f competit ion.
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OR CONSISTENTLY DELIVERS SIGNIFICANT VALUESTRATEGIC TO TACTICAL, TOP-LINE TO BOTTOM-LINETO
THE ORGANIZATIONS AND EXECUTIVES WHO USE IT.
A FEW EXAMPLES:
1 SEARSUSED O.R. TO CREATE A VEHICLE ROUTING AND SCHEDULING SYSTEM TO RUN ITS DELIVERY ANDHOME SERVICE FLEETS MORE EFFICIENTLY FOR $42 MILLION IN ANNUAL SAVINGS.
2 THE PENTAGON USED O.R. TO SOLVE THE MASSIVE LOGISTICAL PROBLEMS OF SUPPLYING OPERATION
DESERT STORM, AND TO PLAN THE SUCCESSFUL LIBERATION OF KUWAIT.
3FORD USED O.R. TO OPTIMIZE THE WAY IT DESIGNS AND TESTS VEHICLE PROTOTYPES, SAVING $250
MILLION. VEHICLE PROTOTYPES, SAVING $250 MILLION.
4 DIRECTV USED O.R. TOACCURATELY FORECAST CONSUMER ADOPTION OF SATELLITE TELEVISION.
5 UPSUSED O.R. TO REDESIGN ITS OVERNIGHT DELIVERY NETWORK, FOR $87 MILLION IN SAVINGS BETWEEN
2000 AND 2002 AND ANOTHER $189 MILLION ANTICIPATED OVER THE FOLLOWING DECADE.
6 NBCUSED O.R. TO IMPROVE ADVERTISING SALES PLANS, INCREASING REVENUES BY MORE THAN $200MILLION.
7 THECITY OF NEW HAVEN, CONNECTICUT USED O.R. TO DETERMINE DEFINITIVELY IF ITS NEEDLE
EXCHANGE PROGRAM WAS REDUCING HIV INFECTION RATES.
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OPERATIONS RESEARCH:
INNOVATION OF THE 20TH
CENTURY.
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Charles
Babbage
Circa 1937, World War II
a team of British
scientists in England
Phillip
MorseTO CIVIL
SECTOR
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AND IT
IT Focuses on data as a
corporate resource
Stores, retrieves, formats,
displays data Understands business
process and transactions
OR
Uses data as input
Provides improved
solutions Gives global focus
Multiple objectives
Multiple criteria
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OR
ACTIVITIES
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ISSUES IN:
Transportation
inventory planning
production planning
communication operations
computer operations
financial assetsrisk management
revenue management
improving business productivity
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Mathematical logic,
SimulationNetwork analysis
Queuing theory
Game theory
ANALYTICAL METHODS USED IN
OPERATIONS RESEARCH:
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(1)A set of potential solutions to a problem is identified and
developed (the set may be rather large).
(2)The alternatives derived in the first step are Analyzed, and
reduced to a smaller set of solutions (the solutions have to
be feasible and workable).
(3)The alternatives derived in the second step are subjected to
simulated implementation and, if feasible, exposed to an
actual analysis in a real-world environment. It has to be
pointed out that in the final step, psychology and
management sciences often play a rather important role.
3 STEPS IN OPERATIONS REASERCH
PROCESS
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Generally speaking, OR improves the effectiveness
and the efficiency of an institution.
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METHODS IN OPERATIONS
RESEARCH
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Simulation Method
Simulationis a modeling and analysis tool widely used for the purpose of
designing, planning, and control of manufacturing systems. Simulation in general is
to pretend that one deals with
a real thing while really working with an imitation.
Goal:
Is to develop simulators that provide the decision maker with the ability to
conduct sensitivity studies to (1) search for improvements, and (2) to test and
benchmark the improvement ideas that are being made
Optimization Method
Optimization is the act of obtaining the best result under given circumstances. In
design, construction, and maintenance of any engineering system, engineers have to
take many technological and managerial decisions at several stages.
Goal:Is to identify and locate the very best choice based on certains criteria
Is either to minimize the effort required or to maximize the desired benefit.
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Probability and Statistics Method
The most important single mathematical tool of operations research is probability
and statistical theory.
Goal:Is to measure risk, mine data to find valuable connections and insights in
business analytics, test conclusions, and make reliable forecasts.
DataAnalysis Method
This method is rather useful in numerous applications including forecasting
and data mining based business environments.
Goal:
Is to aid the decision maker in detecting actual patterns and
interconnections in the data set.
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MODELS IN OPERATIONSRESEARCH
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LINEAR PROGRAMMING
Typically, a single objective function, representing either a
profit to be maximized or a cost to be minimized, and a set of
constraints that circumscribe the decision of variables.
NETWORK FLOW PROGRAMMING
A special case of the more general linear program. Includessuch problem as the transportation problem, the assignment
problem, the shortest path problem, the maximum flow
problem, and the minimum cost flow problem.
INTEGER PROGRAMMING
Some of the variables are required to take on discrete
values.
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NON-LINEAR PROGRAMMING
The objective and/or any constraints is non-linear.
In general, much more difficult to solve than linear.
DYNAMIC PROGRAMMING
A DP models describe a process in terms of states, decisions,
transition and returns. The process begin in some initial state wherea decision is made. The decision causes a transition to a new state.
Based on the starting state, ending state and a decision a return id
realized.
STOCHASTIC PROCESS
In many practical situations the attributes of a system randomly
change over time.
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MARKOV PROCESS
A continuous time stochastic process in which the duration of all
state changing activities are exponentially distributed. Time is a
continuous parameter.
SIMULATION
A general technique for estimating statistical measures of complexsystems.
A system is modeled as if the random variables are drawn randomly
from their known probability distributions. Each replication gives one
observation of the system response.
TIME-SERIES AND FORECASTING
A Time Series is a sequence of observations of a periodic random
variable.
Typically serve as input to OR decision models.
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INVENTORY THEORY
Inventories are materials stored, waiting for processing.
oWhen and how much raw material should be ordered?
oWhen should a production order should be released to the plant?
oWhat level of safety stock should be maintained at a retail outlet?
oHow is in-process inventory maintained in a production process?
RELIABILITY THEORY
Attempts to assign numbers to the propensity of systems to fail.
Estimating reliability is essentially a problem in probability modeling.
Extremely important in the telecommunications and networking industry.
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ICE
BREAKER!!!!+ =
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OPERRATONS RESEARCH IN
MANUFACTURING
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APPLICATIONS OF OR IN MANUFACTURING
SchedulingRouting
Workflow improvements
Elimination of bottlenecks
Inventory control
Business process re-
engineeringSite selection, or facility
Selection
General operational planning
Revenue management entails first to
accurately forecasting the demand, andsecondly to adjust the price structure over time
to more profitably allocate fixed capacity.
Supply chain decisions describe the who,
what, when, and where abstractions from
purchasing and transporting raw materials andparts to the costumers. The prime
management goal here may be to reduce
overall cost while processing customer orders
more efficiently than before.
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INTRODUCTION TO LINEAR PROGRAMMING
LINEAR PROGRAMMING (LP)A technique used in the optimization of a
linear objective function , subject to linear quality and linear inequalityconstraints.
- Determines the best way to achieve the best outcome ( e.g. maximum
profit or lowest cost ). In a given mathematical model and given some list of
requirements represented as linear equations.
LP is the ORistsfavorite tool because it is_ Simple,
_ Easy to understand,
_ Robust.
Simple means easy to implement, easy to
understand means easy to explain (to your boss), and
robust means that its like the Swiss Army Knife:
perfect for nothing, but good enough for everything.
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MATHEMATICAL FORMULATION OF LINEAR
PROGRAMMING MODEL
STEP 1Study the given situation
Find the key decision to be made
Identify the decision variables of the problem
STEP 2
Formulate the objective function to be optimizedSTEP 3
Formulate the constraints of the problem
STEP 4
Add non-negativity restrictions or constraints
The objective function, the set of constraints, and the non-negativity restrictions together form an LP model
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Pedro and Maria are in a Part-time business.
Pedro must work for 4 hours to complete 1
case of TV set and 2 hours for Maria to
complete a set of TV case. Pedro must work
for 3 hours to complete a case of stereo set
and 4 hours for Maria to complete a set. Theyare not to work for more than 20 hours. The
price for each TV set and Stereo set are
P80.00 and P64.00, respectively. Maximizethe Profit.
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OR PROBLEMS
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CRITICAL PATH ANALYSIS
A project-management technique that lays out all the activities needed to complete a
task, the time it will take to complete each activity and the relationships between the
activitiesThe critical path refers to the way the diagram shows those activities that must be
completed, and complete in a specific order, so that the project can be completed
successfully and on time.
FLOORPLANNING
Designing the layout of equipment in a factory or components on a computer chip to
reduce manufacturing cost.
NETWORK OPTIMIZATION
It is a special type of linear programming model. Network models have three mainadvantages over linear programming:
1. They can be solved very quickly.
2. They have naturally integer solutions.
3. They are intuitive.
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FACILITY LOCATION
The success of the organization is also depends on the decision of facility location
It refers to selection of specific site for establishment of the physical unit of
production process.Refers to the location of service organization
NEED OF FACILITY LOCATION
Selection of the location is long
term decision of organization
One selection of facility location is
very expensive and some
infeasible to alter the location
It plays a vital role in the
organization
SELECTING A WRONG
FACILITY LOCATION RESULTS:
Low profit margin
High cost of production
Poor production efficiency
High distribution cost
Labor trouble
Closure of organization
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BAYESIAN SEARCH THEORY
LOOKING FOR A TARGET
Is the application of Bayesian statistics to the search for lost objects. It has
been used several times to find lost sea vessels, for example the USS Scorpion.
It also played a key role in the recovery of the flight recorders in the Air FranceFlight 447 disaster of 2009.
OPTIMAL SEARCH
Sometimes it's OK to find just ANY path to the goal as long as you get there. But
sometimes you want to find the BEST path to the goal. The fastest, cheapest, oreasiest route to take is oftentimes more important than finding SOME path.
Thats where optimal search comes in.
ROUTING
Is the process of selecting paths in a network along which to send network
traffic. Routing is performed for many kinds of networks, including the telephone
network (circuit switching), electronic data networks (such as the Internet),
and transportation networks.
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SUPPLY CHAIN MANAGEMENT
Managing the flow of raw materials and
products based on uncertain demand
for the finished products.
AUTOMATION
Automating or integrating robotic
systems in human-driven operations
processes.
GLOBALIZATION
Globalizing operations processes in
order to take advantage of cheaper
materials, labor land, or other
productivity inputs.
TRANSPORTATION
Managing freight transportation and
delivery systems
SCHEDULING
Personnel Staffing
Manufacturing Steps
Project Tasks
Network Data TrafficSports events and their television
coverage
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Transportation: managing freight transportation and delivery systems
(Examples: LTL Shipping, intermodal freight transport)
Perfecting the Scheduled Railroad at Canadian Pacific Railway
Problem: Finding a better alternative in handling the many details and
constraints of scheduling.
The OR solution: Canadian Pacific turned to the concept of operating everyaspect of the railway on a fixed schedule. Working with Multi-Modal Applied
Systems, the railway developed an operating plan that was tightly matched to
traffic patterns.
Optimizing Production Planning and Trade at Jan de Wit Company
Problem: The company had to split the planning to control the productive
process
The OR solution: Jan de Wit implemented a decision support system based on
linear programming as a production-planning and trade tool.
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Manufacturing steps
Samsung Cuts Manufacturing Cycle Time and Inventory to Compete
Problem: Need to reduce cycle time. The huge work-in-process inventory
was expected to lose value rapidly. And a survey finding that Samsung's
cycle times were noncompetitive implied that customers might be enticed
to switch to vendors offering shorter lead times.
The OR solution: The project was named SLIM (short cycle time and low
inventory in manufacturing). SLIM delivered a set of methodologies and
scheduling applications for managing cycle time, including:
Methodology for calculating target cycle times and target work in process
levels for individual manufacturing steps
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OPERATIONS
RESEARCH IN ACTION
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Scheduling
ex. Aircrews & the fleet for airlines
Facility Planningex. Warehouse, Factory or Fire station
Planning and Forecasting
ex. Telecommunication Industry
Yield ManagementThe changing of supply and demand
Credit ScoringThe credibility of the person to pay
MarketingEvaluating the value of sale promotions
Defense and Peace KeepingFinding ways to deploy troops
rapidly
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OR BENEFITS
Decrease cost or Investment
Increase Revenue or Return on Investment
Increase Market Share
Manage & Reduce Risk
Improve Quality
Increase through output while decreasing delays
Achieve Improve Utilization from limited resources
Demonstrate Feasibility & Workability
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