Transcript PRESENTATION NAME

PRACTICAL
APPLICATIONS OF
OR
Presented by
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Karan Lakhani(22)
Ravi Anupam Baa(23)
Rohan Ignitius Charlie(24)
Ruhama Kachhap(25)
Vijaya Chatterjee(26)
Navya Jain(27)
Kumar Pratik(28)
Jai Thapar(29)
Ashwani Jaiswal(30)
WHAT IS OPERATIONS RESEARCH?
For convinience, and with reasonable
accuracy, we can define operations research
as the scientific method applied to problem
solving and decision making.
Contd…
Help you with the challenge of making
complex decisions by:
• Performing quantitative analysis that provides insight
• Providing sensible options and recommending
courses of action
• Reducing risk
• Improving the quality of recurring decisions
DISTINCT NATURE OF O.R.
• APPLIES LEADING-EDGE ANALYSIS
• CAN FIND THE BEST AMONG MANY CHOICES, IN
REASONABLE TIME
• CAN CONSIDER AND BALANCE MULTIPLE OBJECTIVES
• CAN HELP MEASURE, CONTROL, AND REDUCE RISK
Differences between
O.R. and IT
IT
• Focuses on data as a
corporate resource
• Stores, retrieves,
formats, displays data
• Understands business
processes and
transactions
O.R.
• Helps management select
the best decision or set of
decisions
• Applies analysis to convert
data into useful
information
• Works with management
to help gain the deepest
insights from analytical
results.
• Is typically embedded in an
information system to
provide recommended
decisions or actions
Advantages of OR
• Focuses on business impact and implementation
• Improves decision processes while reducing risk
• Helps operations become more efficient and
effective
• Establishes a disciplined, consultative approach
• Transfers technology to your department so you can
take over the project
• Uses the appropriate analytical tools
Operations Research Applications
• Inventory Theory and Models
• Waiting- line(Queueing) Models
• CPM and PERT: Networking
Inventory Theory and Models
Development of first inventory model is
credited to Harris (1915).Raymond (1931)
extended Harris’s work in the early 1930s.
Since world war II the development of
inventory theory and inventory models has
proliferated to a point of high development.
Inventory theory and models aid in the
control of inventory costs by minimizing the
total cost of purchasing, carrying, and being
short of inventory. Models useful in dealing
with quantity discounts, multiple products,
and stochastic models are discussed at some
length, along exponential smoothing, are also
presented and applied.
Waiting-Line(Queing) Models
The effort of A.K.Erlang in 1909 to analyse
telephone traffic congestion with the
objective of meeting uncertain demand for
services at Copenhagen telephone system
resulted in a new theory called queueing or
waiting line. This theory is now a valuable tool
in business because many business problems
can be characterised as arrival/departure
congestion problems.
Queing theory studies random arrivals at a
servicing or processing facility of limited
capacity. Such models have been applied to
study job shop flows, banking operations, air
traffic scheduling and control, and so on. Such
models allow management to predict lengths
of future waiting lines, average time spent in
the line or system by an individual awaiting
service, and needed facility additions.
CPM and PERT: Networking
The problem of project management came to the
forefront with the Polaris missile project, starting in
1958. A new tool was needed to schedule and
control the project. PERT was developed by the
scientists from the Navy’s Office of Special Projects,
Allen and Hamilton, the head of Missile Systems
Division of Lockheed Aircraft Corporation
At approximately the same time
Du Pont company, together with the UNIVAC division
of Remington Rand, developed the critical path
method to control the maintainence of projects for
Du Pont’s chemical plant.
Networking models enable managers to cope
with the complexities and interdependencies
involved in large projects. Much of this
application has been in the construction,
aerospace and defence industries.
The main difference between PERT and CPM is
in the manner in which the time estimates are
made. PERT assumes that the time to perform
each activities is a random variable described
by a probabilistic distribution. CPM on the
other hand infers that the activity time is
deterministically known and can be varied by
changing the level of resources used.
PERT and CPM have been widely used for a
variety of projects, including the following
types:
• Construction of a new plant.
• Research and development of a new product.
• NASA space exploration projects.
• Movie productions.
• Building of a ship.
• Government-sponsored projects for developing a
new weapons system.
• Relocation of a major facility.
• Maintenance of a nuclear reactor.
• Installation of a management information system.
• Conducting of an advertising campaign.
PERT/CPM AS AN AID TO CUTTING
COSTS
• PERT- PROGRAMME EVALUATION REVIEW
TECHNIQUE-IS A POWERFUL DYNAMIC
MANAGEMENT AID FOR COST REDUCTION.
• WHENEVER THE EXECUTION OR COMPLETION OF
PROJECTS IS DELAYED, THE BENEFITS EXPECTED
FROM THESE PROJECTS ARE POSTPONED. IN OTHER
WORDS, THE ANTICIPATED RETURN ON INVESTMENT
IN THESE PROJECTS WILL NOT BE REALIZED.
• SECONDLY, THE COST OF THESE PROJECTS WHICH
ARE NOT COMPLETED IN THE SCHEDULED TIME ARE
FOUND TO BE SEVERAL TIMES MORE, ON
COMPLETION, THAN THE ORIGINAL ESTIMATED
COSTS.
• A WAY MUST, THEREFORE, BE FOUND WHEREBY THE
TIME TAKEN TO COMPLETE THESE PROJECTS COULD
BE REDUCED OR COMPRESSED, AND THE COSTS ARE
ALSO CONTROLLED.
CASE 1: FORECASTING THE
SHUTTLE DISASTER AT NASA
• THE PROBLEM
– AFTER HE CHALLENGER SHUTTLE DISASTER IN
1986, NASA DECIDED TO CONDUCT RISK ANALYSIS
ON SPECIFIC SYSTEMS TO IDENTIFY THE GREATEST
THREATS OF A FUTURE DISASTER AND PREVENT
THEM
– CONSULTANTS AT STANFORD UNIVERSITY AND
CARNEGIE MELLON WERE CALLED IN TO ASSESS
RISK TO THE SHUTTLE TILES
• OBJECTIVES AND REQUIREMENTS
– IDENTIFY DIFFERENT POSSIBLE ACCIDENT
SCENARIOS
– COMPUTE THE PROBABILITY OF FAILURE
– SHOW HOW SAFETY COULD BE INCREASED
– PRIORITIZE RECOMMENDED SAFETY MEASURES
• THE OR SOLUTION
– MODEL WAS BASED ON A MULTIPLE PARTITION
OF THE ORBITER'S SURFACE
– FOR THE TILES IN EACH ZONE, THE OR TEAM
EXAMINED DATA TO DETERMINE THE
PROBABILITY OF:
1.
2.
3.
4.
DEBONDING DUE TO DEBRIS HITS OR A POOR BOND
LOSING ADJACENT TILES ONCE THE FIRST IS LOST
BURN-THROUGH
FAILURE OF A CRITICAL SUBSYSTEM UNDER THE SKIN
OF THE ORBITER IF A BURN-THROUGH OCCURS
– A RISK-CRITICALITY SCALE WAS DESIGNED BASED
ON THE RESULTS OF THIS MODEL
• THE EXPERTS
– FOUND THAT 15% OF THE TILES ACCOUNT FOR
ABOUT 85% OF THE RISK
– RECOMMENDED, NASA INSPECT THE BOND OF
THE MOST RISK CRITICAL TILES AND REINFORCE
INSULATION OF VULNERABLE EXTERNAL SYSTEMS
– COMPUTED THAT SUCH IMPROVEMENTS COULD
REDUCE PROBABILITY OF A SHUTTLE ACCIDENT
FROM TILE FAILURE BY 70%
– 1994 STUDY QUOTED EXTENSIVELY IN THE PRESS
AFTER THE COLUMBIA, A SECOND SHUTTLE,
EXPLODED ON REENTRY IN 2003, APPARENTLY
DUE TO TILE FAILURE
CASE 2 : MEDICARE SAVES
BILLIONS OF TAXPAYERS DOLLARS
• THE PROBLEM
– IN THE 1980S, THE U.S. FEDERAL GOVERNMENT
WAS ALREADY FACING RISING MEDICARE COSTS
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– A LEADING OPERATIONS RESEARCHER AT YALE
WAS PRESENTED WITH THE QUESTION: HOW
COULD EXPENSES BE CONTAINED?
• OBJECTIVES AND REQUIREMENTS
– MEASURE AND EVALUATE THE PERFORMANCE OF
HOSPITALS
– DEVELOP A METHODOLOGY FOR CLASSIFYING
PATIENTS
– USE THESE METHODS AS A BASIS FOR
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PERFORMANCE MEASUREMENT
RESOURCE MANAGEMENT
COST EFFECTIVENESS
QUALITY CARE
– DEFINE A PROSPECTIVE PAYMENT SCHEME FOR
REIMBURSING HOSPITALS FOR MEDICARE
PATIENTS
• THE OR SOLUTION
– DEVELOPED THE CONCEPT OF DIAGNOSTIC
RESEARCH GROUPS (DRGS)
• IDENTIFIED THE OUTPUT OF HOSPITALS AS CLASSES OF
PATIENTS, EACH CLASS RECEIVING A SIMILAR BUNDLE
OF GOODS AND SERVICES
• FOR EACH DRG, SET A RATE CONSIDERED TO BE A FAIR
PAYMENT TO THE HOSPITAL FOR DIAGNOSIS AND
TREATMENT OF A GIVEN ILLNESS
• APPLIED FULL RANGE OF INDUSTRIAL MANAGEMENT
TECHNIQUES TO REIMBURSEMENT, INCLUDING
FLEXIBLE BUDGETING AND COST AND QUALITY
CONTROL
• THE VALUE
– DRGS WERE ADOPTED BY MEDICARE IN 1983 TO
SERVE AS A BASIS FOR A PROSPECTIVE PAYMENT
SYSTEM (PPS) FOR US HOSPITALS
– BY 1990, RESULTED IN SAVINGS OF MORE THAN
$50 BILLION IN MEDICARE HOSPITAL PAYMENTS
– EXTENDED THE SOLVENCY OF THE MEDICARE
HOSPITAL TRUST FUND
CASE 3 : OPERATION DESERT
STORM AIRLIFT
• THE PROBLEM
– IN 1991, THE MILITARY AIR COMMAND (MAC) WAS
CHARGED WITH SCHEDULING AIRCRAFT, CREW, AND
MISSION SUPPORT RESOURCES TO MAXIMIZE THE ONTIME DELIVERY OF CARGO AND PASSENGERS TO THE
PERSIAN GULF
– A TYPICAL AIRLIFT MISSION CARRYING TROOPS AND
CARGO TO THE GULF REQUIRED A THREE-DAY ROUND
TRIP, VISITED 7 OR MORE DIFFERENT AIRFIELDS, BURNED
ALMOST 1 MILLION POUNDS OF FUEL, AND COST $280,000
• OBJECTIVES AND REQUIREMENTS:
– CREATE A SCHEDULING SYSTEM
– CREATE A COMMUNICATIONS SYSTEM
COORDINATING THE SCHEDULE AMONG BASES IN
THE US AND OTHER COUNTRIES
• THE OR SOLUTION
– MAC WORKED WITH THE OAK RIDGE NATIONAL
LABORATORY TO DEVELOP THE AIRLIFT
DEPLOYMENT ANALYSIS SYSTEM (ADANS)
– WITHIN THREE MONTHS, ADANS PROVIDED A SET OF
DECISION SUPPORT TOOLS TO MANAGE:
• INFORMATION ON CARGO AND PASSENGERS
• INFORMATION ON AVAILABLE RESOURCES
– ADANS ALSO DEVELOPED TOOLS FOR:
• SCHEDULING MISSIONS
• ANALYZING THE SCHEDULE
• DISTRIBUTING THE SCHEDULE TO THE MAC
WORLDWIDE COMMAND AND CONTROL SYSTEM
• THE VALUE
– BY AUGUST 1991, MORE THAN 25,000
MISSIONS HAD MOVED NEARLY 1 MILLION
PASSENGERS AND 800,000 TONS OF CARGO
TO AND FROM THE PERSIAN GULF
CASE 4 : NEW HAVEN NEEDLE
EXCHANGE FIGHTS AIDS
• THE PROBLEM
– WITH THE ADVENT OF HIV AND AIDS IN THE EARLY 1990S,
THE CITY OF NEW HAVEN INSTITUTED A NEEDLE
EXCHANGE PROGRAM AS A WAY OF REDUCING THE
SPREAD OF INFECTION AMONG INTRAVENOUS DRUG
USERS
– NEW HAVEN ASKED YALE UNIVERSITY TO DETERMINE IF
THE PROGRAM WAS ACTUALLY MAKING PROGRESS IN THE
FIGHT AGAINST HIV AND AIDS
• OBJECTIVES AND REQUIREMENTS
– DEVELOP A SYRINGE TRACKING AND TESTING SYSTEM
– MODEL HIV TRANSMISSION IN NEW HAVEN
– ESTIMATE MODEL PARAMETERS FROM THE DATA
COLLECTED IN NEW HAVEN
– DETERMINE IF THE PROGRAM IS REDUCING INFECTION
RATES AND SAVING LIVES
– RECOMMEND CONTINUATION OR DISCONTINUATION OF
THE PROGRAM.
• THE OR SOLUTION
– YALE RESEARCHERS DEVELOPED:
• A SYRINGE TRACKING AND TESTING SYSTEM TO
“INTERVIEW THE NEEDLES” RATHER THAN RELY ON
ADDICTS’ SELF-REPORTING
• A NEEDLES THAT KILL (NTK) MODEL TO FORECAST THE
INCIDENCE OF NEW HIV INFECTIONS
– THE MODELERS MADE ADJUSTMENTS TO
DETERMINE:
• FREQUENCY OF SHARED DRUG INJECTION
• PROBABILITY THAT KITS GIVEN TO ADDICTS FOR
CLEANING NEEDLES WERE EFFECTIVE
• DEPARTURE RATE FROM THE POPULATION
• INFECTIVITY PER INJECTION
• PER SYRINGE EXCHANGE RATE
• RATIO OF DRUG INJECTORS TO NEEDLES
• THE VALUE
– THE RESEARCHERS WERE ABLE TO DETERMINE THAT
NEEDLE EXCHANGE REDUCED THE HIV INFECTION RATE
AMONG PROGRAM CLIENTS BY 33%
– IN RESPONSE, THE CONNECTICUT LEGISLATURE
CONTINUED FUNDING THE PROGRAM, EXPANDED NEEDLE
EXCHANGE SERVICES TO BRIDGEPORT AND HARTFORD,
AND DECRIMINALIZED SYRINGE POSSESSION
– NEW NEEDLE EXCHANGE PROGRAMS AND LEGISLATION
WERE PROPOSED IN NEW YORK, CALIFORNIA, AND
MASSACHUSETTS AS A RESULT
CASE 5 : A NORTH CAROLINA SCHOOL
DISTRICT IMPROVES PLANNING
• THE PROBLEM
– SCHOOL PLANNING, LIKE PUBLIC SECTOR LAND-USE PLANNING,
TAKES PLACE WITHIN A COMPLEX ENVIRONMENT, INCLUDING
PERCEPTIONS OF PUBLIC EDUCATION, PUBLIC FINANCE,
TAXATION, POLITICS, AND THE COURTS
– JOHNSTON COUNTY, NC SOUGHT TO IMPROVE SCHOOL
PLANNING WHILE INTEGRATING THE CONCERNS OF
PARTICIPATING AGENCIES AND COMMUNITY GROUPS
– IT WORKED UNDER TWO CONSTRAINTS:
• INADEQUATE DATA TO SUPPORT SENSITIVE DECISIONS
• EXTERNALLY IMPOSED CONSTRAINTS ON DECISION-MAKING
• OBJECTIVES AND REQUIREMENTS
– THE SCHOOL BOARD AND ADMINISTRATION SOUGHT TO
DEVELOP A STRONG PLANNING CULTURE AND A DECISIONSUPPORT MECHANISM THAT WOULD RESTORE PUBLIC
CONFIDENCE AND WIN THE SUPPORT OF THE
COMMUNITY’S POLITICAL LEADERS
– THE OR CONSULTING GROUP WANTED TO FULFILL THESE
REQUESTS AND WHILE CREATING MODELS THAT WOULD
BE EFFECTIVE AND PORTABLE TO OTHER SCHOOL
DISTRICTS
• THE OR SOLUTION
– OR/ED LABORATORIES AND THE JOHNSTON
COUNTY SCHOOLS CREATED A PLANNING SYSTEM,
INTEGRATED PLANNING FOR SCHOOL AND
COMMUNITY, TO:
• FORECAST ENROLLMENTS
• COMPARE ENROLLMENT PROJECTIONS TO CAPACITY
• FIND THE OPTIMAL LOCATIONS FOR NEW SCHOOL
BUILDING
• SET DISTANCE-MINIMIZED BOUNDARIES FOR ALL
SCHOOLS TO AVOID OVERCROWDING AND MEET
RACIAL BALANCE GUIDELINES
• THE VALUE
– IMPLEMENTING THE SYSTEM HAS INCREASED THE
SCHOOL DISTRICT’S SUCCESS IN:
• PASSING BOND ISSUES
• REDUCING PUPIL-TRANSPORTATION COSTS
• ELIMINATING FREQUENT ADJUSTMENTS TO SCHOOLATTENDANCE BOUNDARIES
CASE 6 : US POSTAL SERVICE
AUTOMATES DELIVERY
• THE PROBLEM
• IN 1988, THE US POSTAL SERVICE FORESAW THREE
INTERLOCKING PROBLEMS:
– AN INCREASE FROM 166 BILLION TO 261 BILLION PIECES
OF MAIL HANDLED A YEAR BY THE TURN OF THE CENTURY
– INCREASED PRIVATE SECTOR COMPETITION
– A COMPLEXITY OF OPERATIONS THAT WOULD HAVE TO BE
MODELED IF AUTOMATION WERE TO RESPOND TO THE
CHALLENGES
• OBJECTIVES AND REQUIREMENTS
– CREATE A DECISION SUPPORT TOOL THAT COULD
SIMULATE POSTAL OPERATIONS AND QUANTIFY
THE EFFECTS OF AUTOMATION ALTERNATIVES
• THE OR SOLUTION
– WORKING WITH TWO OR CONSULTING GROUPS, THE
POSTAL SERVICE DEVELOPED THE MODEL FOR
EVALUATING TECHNOLOGY ALTERNATIVES (META)
– A SIMULATION MODEL THAT QUANTIFIES THE IMPACTS OF
CHANGES IN MAIL-PROCESSING AND DELIVERY
OPERATIONS
– BLENDED OR AND SOFTWARE TOOLS IN A DECISION
SUPPORT SYSTEM
• THE VALUE
– META ANALYSIS ENABLED THE POSTAL SERVICE TO
RELEASE ITS CORPORATE AUTOMATION PLAN,
INCLUDING A CUMULATIVE CAPITAL INVESTMENT
OF $12 BILLION AND LABOR SAVINGS OF $4
BILLION PER YEAR
– META SPAWNED A FAMILY OF SYSTEMS FOR USE
AT HEADQUARTERS AND FIELD LEVELS,
ACCELERATING AND ENHANCING THE USE OF OR
THROUGHOUT THE ORGANIZATION
THANK YOU