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Operations Research

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Operations Research (MTH601)
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In its recent years of organized development, OR has entered successfully many
different areas of research for military government and industry in many countries of the world.
The basic problem in most of the developing countries in Asia and Africa is to remove poverty
and improve the standard of living of a common man as quickly as possible. So there is a great
scope for economists, statisticians, administrators, politicians and the technicians working in a
team to solve this problem by an OR approach. The possible application sectors, in Pakistan, are
as under:-
1)
Macro Economic Planning:
OR can be employed for Macro-Economic Planning of the country:
a)
Input / Output Analysis: by using LP models. This input/output analysis
can be of any duration [i.e. of short term (up to say 10 years)-Five Year
Plan; and of long term (10-30 years)].
b)
Investment Planning: OR can be employed in the Investment Planning of
the country where investment plans for the next five or ten years are
prepared. Mixed Integer Programming and Linear Programming
techniques can be used.
c)
Choice of Projects: OR can help the people in the planning in choosing the
optimal project. This sort of choice would need Integer Programming and
Quadratic Assignment techniques.
d)
OR can also be used in Simulation Modeling of the Economy of the
country.
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2)
Sectoral Planning:
OR can also be employed in a particular sector of the Economy, e.g. in
agriculture, in finance, in industry, in marketing, in production, in management
etc.
a)
Scheduling all operations within a sector can be done by using OR e.g.
production scheduling + Distribution planning + marketing + Personnel
management + maintenance + ...............
b)
Schedule of some operations within a sector can be done by employing
OR e.g. Inventory planning in agriculture or distribution of fertilizer etc.
3)
Micro Economic Planning:
This sort of activity involve for example:
Planning the operations of a Company.
Improving the layout of a workshop in a company.
Finding size of a hospital in an area etc.
There is a great potential for utilizing OR in this area of planning in our country.
POTENTIAL AREAS OF APPLICATIONS
As mentioned earlier OR can be applied in every field of life. Here are few of the many
fields where OR has potential application. This list is by no means comprehensive or exhaustive
but definitely will provide an idea of the power of OR as a separate discipline.
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Operations Research in the Public Sector
Federal, Provincial and Local Government
Development of Country Structure Plans
Manpower Planning and Career Development in Govt. Departments
Organization of Long-Term planning groups at the National Level
Corporate Planning in Local Government
Allocation of Government Houses
Estimation of Future Requirement of School/College Building
Placing of Fire Brigade in a City
Measuring the Effectiveness of Police
Timetabling in Schools and Colleges for Efficient use of Space
Health
Management policies for 120-bed nursing units
Optimum size of general hospitals
Appointment systems for hospital outpatients
Stock control for regional and area health units
National and area planning of health services
Manpower planning for nurses, radiographers, etc.
Commissioning of a new general hospital
Simulation of pathology laboratories
Organizing an ambulance service
Care provided by community nurses
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Defense
Arms control and disarmament studies
Communications network development
Logistic support in operations
Field experimentation
War games and other models of battle
Equipment procurement
Reinforcement and redeployment problems
Operations Research in Industry & Commerce
Finance and Investment
Developing the five-year plan for a food manufacturer
Development of the pipeline
Computer based financial planning
Portfolio selection
Structure for the assets of a bank
Evaluating investment in a new plant
Corporate planning in the chemical industry
Financing expansion of a small firm
Production
Production scheduling in a steel works
Meeting peak demands for electricity
Minimization of costs of power station maintenance
Scheduling newsprint deliveries
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Stock levels of steel plate
Meeting seasonal demands for products
Blending scrap metals
Stock policy for a paint manufacturer
Allowing for yarn breaks in spinning
Meeting customer requirements for carpets
Planning a quarry's output
Optimum layout for belt coal transport in a colliery
Marketing
Launching a new product
Advertising effectiveness and cost
Planning sales territories
Measurement of consumer loyalty
Buyer-seller behavior
Advertising research and media scheduling
Most profitable retail brand mix
Developing customer service policies
Pricing policies for confectionery
Personnel
Personnel shift planning
Manpower planning
Manpower for an assembly line
Effects of flexible working hours
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Distribution
Distribution of Products.
Returnable bottles: how many?
Refinery crude tank capacity
Depot location of pharmaceutical products
Trucking policy for dairy products
Distribution of newspapers to newsagents
OR in Transport
Rail
Rail freight management
Required fleet size of locomotives and rolling stock
Forecasting passenger traffic
Planning reconstruction of main-line termini
Introduction of freightliners
Road
Designing urban road networks
Forecasts of car ownership
Implementation of bus lanes
Re-routing bus services
Purchasing and maintenance of buses
Introduction of flat-fare buses
Bus services in rural areas
Preparation of crew rosters
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Air
Planning the introduction of Boeing 737/Airbus 300
Allocation of aircraft and crew to routes
Location of Islamabad Airport
Karachi-Lahore - Islamabad - Peshawer: aircraft requirements
Sea
Potential traffic for new container services
Shipbuilding requirement in the 1990's
Optimum ship size for given routes
Construction and management of a container terminal
EXAMPLE
Before proceeding further let us take an example, which will help to understand the scope
of application in various activities. Given below are some of the major activities which
OPERATIONS:
1)
Oil production from fields
2)
Transportation of Crude
from fields to refineries
from fields to export ports (Jetties)
from import ports (Jetties) to refineries
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3)
Storage of Crude
on fields
at Ports
at refineries
4)
Refinery Scheduling
Operation of CDU's
Operation of Blending Units
5)
Storage of Distilled Blended Products
at refineries
at Jetties
at distribution points
6)
Transportation of Products
from Jetties to refineries
from one refinery to another for another processing
from refinery to bulk distribution pts.
from bulk distribution points to final consumers.
At all the stages from oil production from fields to its transportation to the final consumer
OR has been employed in the developed countries of the world. Applying on macro level is not
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an easy job. This would require true and factual data computing power and trained
professionals, and perhaps at this stage we may face some problem due to limited resources in
term of manpower, money and machines, but it does not mean that we should not make a
beginning.
REQUIREMENTS FOR APPLYING SUCCESSFUL OR
In order to apply OR successfully in achieving certain objectives the following are some
of the prerequisites:
1)
Sufficient number of qualified OR personnel should be available who
should know the art of selling OR. These professional should be ready to
work in close cooperation with staff at various levels of the organization
because they have to dig out the problem from the grass roots.
2)
Normally, there is a tendency of management to give false information, in
order to create a better image, and sometime there may be a lack of
adequate communication between OR practitioner and management. To
meet these circumstances there should be a healthy interaction with the
statistical machinery so as to enhance the quality and availability of data.
3)
Satisfactory power of computer machinery along with associated support
should be available so as to analyze the data and forecast correctly. For
this management should be aware of modern techniques and tools of
management.
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4)
Last but not the least management should be ready to accept the change
and be enthusiastic to know the correct alternatives.
CONCLUSION
In the proceeding paras we traced briefly the history of OR; defined OR, and its process;
elaborated various techniques of OR; identified various areas of application and requirements for
successfully applying OR. Before concluding it will be most appropriate to quote Stafford Beer,
the famous OR Scientists.
"We call that work operational (with a large O) because it is based in the
world of genuine activity, the places where things actually happen. All good
sciences, as distinguished from all mysticism is found in empiricism. It involves
actual observation, actual measurement and actual experiment."
We call our work Research (with a capital R) because we deal with
problems to which no one knows the answer.
"Doing that thing is called RESEARCH!"
Finally I would say,
"We need OR teams of outstanding abilities, working on problems of decision &
control at the National Level. Because these problems are usually discussed in
economic terms, they are currently assumed to be purely economic problems."
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BUT THEY ARE NOT
"Interdisciplinary Scientific teams are needed to evaluate issues subject to
conflicting criteria."
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REFERENCES
Bellman, Richard E. Dynamic Programming. Princeton University. Press
Gale, David, The Theory of Linear Economic Models. McGraw-Hill
Hadley, G., Linear Programming. Addison Wesley
Ackoff, R. L., and P. Rivett, A Manager's Guide to Operations Research, Wiley
Dantzig, George B., Linear Programming and Extensions, Princeton University Press
Hadley, G., Nonlinear and Dynamic Programming, Addison Wesley
Ackoff, Russell L., and Maurice W. Sasieni, Fundamentals of Operations Research, Wiley
Beale, E. M. L., Ed. Applications of Mathematical Programming Techniques. English
University. Press
Rivett, P., Principles of Model Building, Wiley
Wagner, Harvey M. Principles of Operations Research, Prentice-Hall
Taha, Hamdy A., Operations Research: An Introduction, Macmillan
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Table of Contents:
  1. Introduction:OR APPROACH TO PROBLEM SOLVING, Observation
  2. Introduction:Model Solution, Implementation of Results
  3. Introduction:USES OF OPERATIONS RESEARCH, Marketing, Personnel
  4. PERT / CPM:CONCEPT OF NETWORK, RULES FOR CONSTRUCTION OF NETWORK
  5. PERT / CPM:DUMMY ACTIVITIES, TO FIND THE CRITICAL PATH
  6. PERT / CPM:ALGORITHM FOR CRITICAL PATH, Free Slack
  7. PERT / CPM:Expected length of a critical path, Expected time and Critical path
  8. PERT / CPM:Expected time and Critical path
  9. PERT / CPM:RESOURCE SCHEDULING IN NETWORK
  10. PERT / CPM:Exercises
  11. Inventory Control:INVENTORY COSTS, INVENTORY MODELS (E.O.Q. MODELS)
  12. Inventory Control:Purchasing model with shortages
  13. Inventory Control:Manufacturing model with no shortages
  14. Inventory Control:Manufacturing model with shortages
  15. Inventory Control:ORDER QUANTITY WITH PRICE-BREAK
  16. Inventory Control:SOME DEFINITIONS, Computation of Safety Stock
  17. Linear Programming:Formulation of the Linear Programming Problem
  18. Linear Programming:Formulation of the Linear Programming Problem, Decision Variables
  19. Linear Programming:Model Constraints, Ingredients Mixing
  20. Linear Programming:VITAMIN CONTRIBUTION, Decision Variables
  21. Linear Programming:LINEAR PROGRAMMING PROBLEM
  22. Linear Programming:LIMITATIONS OF LINEAR PROGRAMMING
  23. Linear Programming:SOLUTION TO LINEAR PROGRAMMING PROBLEMS
  24. Linear Programming:SIMPLEX METHOD, Simplex Procedure
  25. Linear Programming:PRESENTATION IN TABULAR FORM - (SIMPLEX TABLE)
  26. Linear Programming:ARTIFICIAL VARIABLE TECHNIQUE
  27. Linear Programming:The Two Phase Method, First Iteration
  28. Linear Programming:VARIANTS OF THE SIMPLEX METHOD
  29. Linear Programming:Tie for the Leaving Basic Variable (Degeneracy)
  30. Linear Programming:Multiple or Alternative optimal Solutions
  31. Transportation Problems:TRANSPORTATION MODEL, Distribution centers
  32. Transportation Problems:FINDING AN INITIAL BASIC FEASIBLE SOLUTION
  33. Transportation Problems:MOVING TOWARDS OPTIMALITY
  34. Transportation Problems:DEGENERACY, Destination
  35. Transportation Problems:REVIEW QUESTIONS
  36. Assignment Problems:MATHEMATICAL FORMULATION OF THE PROBLEM
  37. Assignment Problems:SOLUTION OF AN ASSIGNMENT PROBLEM
  38. Queuing Theory:DEFINITION OF TERMS IN QUEUEING MODEL
  39. Queuing Theory:SINGLE-CHANNEL INFINITE-POPULATION MODEL
  40. Replacement Models:REPLACEMENT OF ITEMS WITH GRADUAL DETERIORATION
  41. Replacement Models:ITEMS DETERIORATING WITH TIME VALUE OF MONEY
  42. Dynamic Programming:FEATURES CHARECTERIZING DYNAMIC PROGRAMMING PROBLEMS
  43. Dynamic Programming:Analysis of the Result, One Stage Problem
  44. Miscellaneous:SEQUENCING, PROCESSING n JOBS THROUGH TWO MACHINES
  45. Miscellaneous:METHODS OF INTEGER PROGRAMMING SOLUTION