Introduction To Operations Research
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- Pages: 27
Operations Research provides a quantitative technique to the executives for better decisions for operation under their control.
Developed during the World War II.
Limited military resources.
Efficient allocation of resources was required.
Large number scientists invited .
The efforts of the team helped in winning the battle.
The name “OR” directly derived from “Research on Military Operations”.
The success encouraged the scientists.
They moved to different sectors e.g., transportation, health, education, etc.
OR in India started in 1949.
Regional Research Laboratory opened in Hyderabad.
Industry Transportation Banking
and Finance
Agriculture Defense
Systems
Approach
Inter-disciplinary Methodological Operations
Team Approach
Approach
Economy
Finance, Budgeting and Investments
Purchasing, Procurement and Exploration
Production Management
Marketing Management
Personnel Management
Research and Development
Judgement Phase i. Establishment of Objectives ii. Determination of measures iii. Formulation of Problems
Research Phase i. Data Collection ii. Model formulation iii. Analysis and Predictions
Action Phase i. Making Recommendations
Better planning
Flexibility in operations
Better co-ordination
Better decisions
Better systems
Analytic Or Deductive Method
Numerical Or Iterative Method
Monte Carlo Method
PROBLEM FORMULTION
ISOLATION OF MANAGEME NT PROBLEM
REAL WORLD
PROBLEM FORMULATION
ISOLATION OF MANAGEME NT PROBLEM
REAL WORLD
MODEL BUILDING
QUALITATIVE MODEL
QUANTATIVE MODEL MODEL REFINEMENT
PROBLEM FORMULATION
ISOLATION OF MANAGEME NT PROBLEM
SYSTEM REAL WORLD
MODEL TESTING
MODEL BUILDING
QUALITATIVE MODEL
QUANTATIVE MODEL
TESTING
MODEL REFINEMENT DATA COLLE CTION
PROBLEM FORMULATION
ISOLATION OF MANAGEME NT PROBLEM
SYSTEM REAL WORLD
MODEL BUILDING
QUALITATIVE MODEL
MODEL TESTING
ESTABLISH -ING CONTROLS
TESTING
CONCLUS -IONS & IMPLEMEN TATION
QUANTATIVE MODEL MODEL REFINEMENT
DATA COLLE CTION
Linear Programming
Decision Models
Integer Programming
Dynamic Programming
Stochastic Programming
Magnitude of computation
Absence of quantification
Conventional thinking
Money and time costs
Implementation
The
analysis of problems
Linear
function of a number of
variables is to be maximized or minimized Variables
are subject to a number of
restraints in the form of linear inequalities.
Proportionality Certainty Additivity Divisibility Non-negativity
General form of a LPP Optimize (Maximize or Minimize) Z=c1x1+c2x2……cnxn
Subject to linear constraints a11x1+a12x2+…….a1nxn(<,=,>)b1 a21x1+a22x2+…….a2nxn(<,=,>)b2 . .
. .
. .
am1x1+am2x2+…….amnxn(<,=,>)bm
And x1,x2,x3……….xn >0
General form of a LPP Optimize (Maximize or Minimize) Z=c1x1+c2x2……cnxn
Subject to linear constraints a11x1+a12x2+…….a1nxn(<,=,>)b1 a21x1+a22x2+…….a2nxn(<,=,>)b2 . .
. .
. .
am1x1+am2x2+…….amnxn(<,=,>)bm
And x1,x2,x3……….xn >0
OBJECTIVE FUNCTION
General form of a LPP Optimize (Maximize or Minimize) Z=c1x1+c2x2……cnxn
Subject to linear constraints a11x1+a12x2+…….a1nxn(<,=,>)b1 a21x1+a22x2+…….a2nxn(<,=,>)b2 . .
. .
OBJECTIVE FUNCTION
. .
am1x1+am2x2+…….amnxn(<,=,>)bm
And x1,x2,x3……….xn >0
CONSTRAINTS
General form of a LPP Optimize (Maximize or Minimize) Z=c1x1+c2x2……cnxn
Subject to linear constraints a11x1+a12x2+…….a1nxn(<,=,>)b1 a21x1+a22x2+…….a2nxn(<,=,>)b2 . .
. .
OBJECTIVE FUNCTION
. .
am1x1+am2x2+…….amnxn(<,=,>)bm
And x1,x2,x3……….xn >0
CONSTRAINTS
NON-NEGATIVE RESTRICTIONS
Two Phase Procedure
Phase I 5. Verbalize
the problem and its structure. 6. Determine Overall Structure. 7. Determine restricting factors.
Phase II Define Decision Variables. Identify contribution coefficients(cj’s) associated with each variable Formulate the objective function. Identify physical rate of substitution coefficients(ai j’s). Identify the available resources (bi’s). Maintain non-negativity condition.
DECISION VARIABLE
ARTICLE
HOURS ON MACHINE
HOURS ON CRAFTSMA N
PROFIT PER UNIT
X1
A
1.5
2
Rs. 50
X2
B
2.5
1.5
Rs.40
80 Maximum
70 Maximum
Hours Available (per week)
Objective Function Maximize Z=50x1 + 40x2
Constraints Time for article A + Time for article B < Available time on M/c For Machine1.5x1 + 2.5x2 <80
For Craftsman2x1 + 1.5x2<70
Non-Negativity Constraints x1,x2 >0
DIET
DECISION VARIABLE
TIME FOR ARRANGIN G RAW MATERIALS
TIME FOR COOKING
PROFIT PER UNIT
Rice
x1
5 min.
10 min.
Rs. 2
Chapati
x2
15 min.
15 min.
Rs. 5
120 min.
60 min.
Minutes available per week
Developed during the World War II.
Limited military resources.
Efficient allocation of resources was required.
Large number scientists invited .
The efforts of the team helped in winning the battle.
The name “OR” directly derived from “Research on Military Operations”.
The success encouraged the scientists.
They moved to different sectors e.g., transportation, health, education, etc.
OR in India started in 1949.
Regional Research Laboratory opened in Hyderabad.
Industry Transportation Banking
and Finance
Agriculture Defense
Systems
Approach
Inter-disciplinary Methodological Operations
Team Approach
Approach
Economy
Finance, Budgeting and Investments
Purchasing, Procurement and Exploration
Production Management
Marketing Management
Personnel Management
Research and Development
Judgement Phase i. Establishment of Objectives ii. Determination of measures iii. Formulation of Problems
Research Phase i. Data Collection ii. Model formulation iii. Analysis and Predictions
Action Phase i. Making Recommendations
Better planning
Flexibility in operations
Better co-ordination
Better decisions
Better systems
Analytic Or Deductive Method
Numerical Or Iterative Method
Monte Carlo Method
PROBLEM FORMULTION
ISOLATION OF MANAGEME NT PROBLEM
REAL WORLD
PROBLEM FORMULATION
ISOLATION OF MANAGEME NT PROBLEM
REAL WORLD
MODEL BUILDING
QUALITATIVE MODEL
QUANTATIVE MODEL MODEL REFINEMENT
PROBLEM FORMULATION
ISOLATION OF MANAGEME NT PROBLEM
SYSTEM REAL WORLD
MODEL TESTING
MODEL BUILDING
QUALITATIVE MODEL
QUANTATIVE MODEL
TESTING
MODEL REFINEMENT DATA COLLE CTION
PROBLEM FORMULATION
ISOLATION OF MANAGEME NT PROBLEM
SYSTEM REAL WORLD
MODEL BUILDING
QUALITATIVE MODEL
MODEL TESTING
ESTABLISH -ING CONTROLS
TESTING
CONCLUS -IONS & IMPLEMEN TATION
QUANTATIVE MODEL MODEL REFINEMENT
DATA COLLE CTION
Linear Programming
Decision Models
Integer Programming
Dynamic Programming
Stochastic Programming
Magnitude of computation
Absence of quantification
Conventional thinking
Money and time costs
Implementation
The
analysis of problems
Linear
function of a number of
variables is to be maximized or minimized Variables
are subject to a number of
restraints in the form of linear inequalities.
Proportionality Certainty Additivity Divisibility Non-negativity
General form of a LPP Optimize (Maximize or Minimize) Z=c1x1+c2x2……cnxn
Subject to linear constraints a11x1+a12x2+…….a1nxn(<,=,>)b1 a21x1+a22x2+…….a2nxn(<,=,>)b2 . .
. .
. .
am1x1+am2x2+…….amnxn(<,=,>)bm
And x1,x2,x3……….xn >0
General form of a LPP Optimize (Maximize or Minimize) Z=c1x1+c2x2……cnxn
Subject to linear constraints a11x1+a12x2+…….a1nxn(<,=,>)b1 a21x1+a22x2+…….a2nxn(<,=,>)b2 . .
. .
. .
am1x1+am2x2+…….amnxn(<,=,>)bm
And x1,x2,x3……….xn >0
OBJECTIVE FUNCTION
General form of a LPP Optimize (Maximize or Minimize) Z=c1x1+c2x2……cnxn
Subject to linear constraints a11x1+a12x2+…….a1nxn(<,=,>)b1 a21x1+a22x2+…….a2nxn(<,=,>)b2 . .
. .
OBJECTIVE FUNCTION
. .
am1x1+am2x2+…….amnxn(<,=,>)bm
And x1,x2,x3……….xn >0
CONSTRAINTS
General form of a LPP Optimize (Maximize or Minimize) Z=c1x1+c2x2……cnxn
Subject to linear constraints a11x1+a12x2+…….a1nxn(<,=,>)b1 a21x1+a22x2+…….a2nxn(<,=,>)b2 . .
. .
OBJECTIVE FUNCTION
. .
am1x1+am2x2+…….amnxn(<,=,>)bm
And x1,x2,x3……….xn >0
CONSTRAINTS
NON-NEGATIVE RESTRICTIONS
Two Phase Procedure
Phase I 5. Verbalize
the problem and its structure. 6. Determine Overall Structure. 7. Determine restricting factors.
Phase II Define Decision Variables. Identify contribution coefficients(cj’s) associated with each variable Formulate the objective function. Identify physical rate of substitution coefficients(ai j’s). Identify the available resources (bi’s). Maintain non-negativity condition.
DECISION VARIABLE
ARTICLE
HOURS ON MACHINE
HOURS ON CRAFTSMA N
PROFIT PER UNIT
X1
A
1.5
2
Rs. 50
X2
B
2.5
1.5
Rs.40
80 Maximum
70 Maximum
Hours Available (per week)
Objective Function Maximize Z=50x1 + 40x2
Constraints Time for article A + Time for article B < Available time on M/c For Machine1.5x1 + 2.5x2 <80
For Craftsman2x1 + 1.5x2<70
Non-Negativity Constraints x1,x2 >0
DIET
DECISION VARIABLE
TIME FOR ARRANGIN G RAW MATERIALS
TIME FOR COOKING
PROFIT PER UNIT
Rice
x1
5 min.
10 min.
Rs. 2
Chapati
x2
15 min.
15 min.
Rs. 5
120 min.
60 min.
Minutes available per week
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