PRACTICAL APPLICATIONS OF OR

Presented by• 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. DEBONDING DUE TO DEBRIS HITS OR A POOR BOND2. LOSING ADJACENT TILES ONCE THE FIRST IS LOST3. BURN-THROUGH4. 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– – 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 • 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 ON-TIME 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

• 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

CASE 4 : NEW HAVEN NEEDLE EXCHANGE FIGHTS 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 DECISION-SUPPORT 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 SCHOOL-

ATTENDANCE 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