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OPERATIONS RESEARCH
Presented By
Gayathri Devi M K,
M.Tech Dairy Technology,
CFDT, TANUVAS, Chennai-52.
gdkrishnan97@gmail.com
OR
Operations:
The activities carried out in an organization.
Research:
The process of observation and testing
characterized by the scientific method.
OPERATIONS RESEARCH
 OR is an art & science.
 OR is the scientific study of operations for
the purpose of making better decisions.
According to WHO (2003), The use of
systematic research techniques for program
decision making to achieve a specific
outcome.
HISTORY
 It was initiated in England during world war
II(1930).
 At the same time , A.K.Erlang , a Danish
engineer carried out experiment to supply the
fluctuation in demand for telephone facilities
using a automatic dialing experiment.
 OR has been studied in Health Care Settings
since 1952.
PROPERTIES
Characteristics of OR
 OR technique is multidisciplinary.
 It is used to solve complex management
problems.
 It is a continuous process.
 It is a team activity.
 It is a set of mathematical techniques
Phases of OR
Benefits of OR
 Effective decisions
 Better coordination
 Improves productivity
 Decrease cost
 Increase revenue
 Manage and reduce risks
 Improve utilization from limited resources
Limitations of OR
 Formulation of an industrial problem to an OR
set programme is a difficult task.
 A non-linear relationship is changed to linear,
this may disturb the solution.
 When the basic data is subject to frequent
changes, the cost of changing programmes
manually is a costly affair.
Applications
 Airline industry
 Telecommunications
 Manufacturing industry
 Health care
 Transportation
OR Models
Determinstic Model:
Linear program(Transportation & Assignment)
Non-linear program
Network Model:
PERT,CPM
Stochastic Model:
Queuing, Inventory, Simulation
Linear Programming Problem
 LPP is a mathematical programming technique
to optimize performance (profit or cost) under
a set of resource constraints as specified by
organization.
 Concept
- Objective function
-Set of constraints
-Non-negativity restrictions
LPP
 Graphical method
 Simplex method
 Two phase method
 Big M method
Graphical Solution Method
 In equality constraints Equation
 Plot the lines on the graph
 Identify the feasible solution region
 Plot 2 objective function lines to determine the
direction of improvement.
 Locate the solution point.
Feasible region: containing all the points that satisfy all the
inequalities in a system.
Operations Research
Simplex Method
 Simplex method is the basic building blocks
for all other methods.
 Solves the LPP in iterations to improve the
value of the objective function.
Slack variables:
refer to the amount of unused resources like
raw material, money and labour.
Steps:
1)Formulate LP
2)Introduce slack variables
3)Establish a simplex table
If objective function is max- enter the opposite
sign of coefficient, if min enter without
changing the sign.
4)Take the minimum positive value in Cj-Zj.
5)The intersection element of the key column
and key row is pivot element.
6)Construct the new iteration table by
eliminating the leaving variable and
introducing the entering variable
7)Old value-(new value  opposite value of pivot
element)
Operations Research
Softwares used
 TORA(Henrick Johnson)
 Design Expert( Stastistical optimization)
 SAS
 MATLAB
 MATHMATICA
Applications
 Manufacturing problem
 Diet problems: Minimize the cost of the
desired at such that it contains a certain
minimum amount of each nutrients.
 Transportation : to find a cheapest way to
transport product
Operations Research
Operations Research
Thank You

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Operations Research

  • 1. OPERATIONS RESEARCH Presented By Gayathri Devi M K, M.Tech Dairy Technology, CFDT, TANUVAS, Chennai-52. gdkrishnan97@gmail.com
  • 2. OR Operations: The activities carried out in an organization. Research: The process of observation and testing characterized by the scientific method.
  • 3. OPERATIONS RESEARCH OR is an art & science. OR is the scientific study of operations for the purpose of making better decisions. According to WHO (2003), The use of systematic research techniques for program decision making to achieve a specific outcome.
  • 4. HISTORY It was initiated in England during world war II(1930). At the same time , A.K.Erlang , a Danish engineer carried out experiment to supply the fluctuation in demand for telephone facilities using a automatic dialing experiment. OR has been studied in Health Care Settings since 1952.
  • 6. Characteristics of OR OR technique is multidisciplinary. It is used to solve complex management problems. It is a continuous process. It is a team activity. It is a set of mathematical techniques
  • 8. Benefits of OR Effective decisions Better coordination Improves productivity Decrease cost Increase revenue Manage and reduce risks Improve utilization from limited resources
  • 9. Limitations of OR Formulation of an industrial problem to an OR set programme is a difficult task. A non-linear relationship is changed to linear, this may disturb the solution. When the basic data is subject to frequent changes, the cost of changing programmes manually is a costly affair.
  • 10. Applications Airline industry Telecommunications Manufacturing industry Health care Transportation
  • 11. OR Models Determinstic Model: Linear program(Transportation & Assignment) Non-linear program Network Model: PERT,CPM Stochastic Model: Queuing, Inventory, Simulation
  • 12. Linear Programming Problem LPP is a mathematical programming technique to optimize performance (profit or cost) under a set of resource constraints as specified by organization. Concept - Objective function -Set of constraints -Non-negativity restrictions
  • 13. LPP Graphical method Simplex method Two phase method Big M method
  • 14. Graphical Solution Method In equality constraints Equation Plot the lines on the graph Identify the feasible solution region Plot 2 objective function lines to determine the direction of improvement. Locate the solution point.
  • 15. Feasible region: containing all the points that satisfy all the inequalities in a system.
  • 17. Simplex Method Simplex method is the basic building blocks for all other methods. Solves the LPP in iterations to improve the value of the objective function.
  • 18. Slack variables: refer to the amount of unused resources like raw material, money and labour. Steps: 1)Formulate LP 2)Introduce slack variables 3)Establish a simplex table If objective function is max- enter the opposite sign of coefficient, if min enter without changing the sign.
  • 19. 4)Take the minimum positive value in Cj-Zj. 5)The intersection element of the key column and key row is pivot element. 6)Construct the new iteration table by eliminating the leaving variable and introducing the entering variable 7)Old value-(new value opposite value of pivot element)
  • 21. Softwares used TORA(Henrick Johnson) Design Expert( Stastistical optimization) SAS MATLAB MATHMATICA
  • 22. Applications Manufacturing problem Diet problems: Minimize the cost of the desired at such that it contains a certain minimum amount of each nutrients. Transportation : to find a cheapest way to transport product