Post on 15-Nov-2014
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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 Team Approach
Methodological Approach
Operations 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
ISOLATION OF
MANAGEMENT PROBLEM
PROBLEM FORMULTION
REAL WORLD
ISOLATION OF
MANAGEMENT PROBLEM
PROBLEM FORMULATION
REAL WORLD
QUALI-TATIVE MODEL
QUAN-TATIVE MODEL
MODEL BUILDING
MODEL REFINEM-
ENT
ISOLATION OF
MANAGEMENT PROBLEM
PROBLEM FORMULATION
REAL WORLD
QUALI-TATIVE MODEL
QUAN-TATIVE MODEL
MODEL BUILDING
MODEL REFINEM-
ENT
MODEL TESTING
TEST-ING
SYSTEMDATA COLLECTION
ISOLATION OF
MANAGEMENT PROBLEM
PROBLEM FORMULATION
REAL WORLD
QUALI-TATIVE MODEL
QUAN-TATIVE MODEL
MODEL BUILDING
MODEL REFINEM-
ENT
MODEL TESTING
TEST-ING
SYSTEM
ESTABLISH-ING CONTROLS
CONCLUS-IONS &
IMPLEMENTATION
DATA COLLECTION
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
. . .
. . .
am1x1+am2x2+…….amnxn(<,=,>)bm
And x1,x2,x3……….xn >0
OBJECTIVE FUNCTION
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
. . .
. . .
am1x1+am2x2+…….amnxn(<,=,>)bm
And x1,x2,x3……….xn >0
OBJECTIVE FUNCTION
CONSTRAINTS
NON-NEGATIVE RESTRICTIONS
Two Phase Procedure
Phase I1.Verbalize the problem and its structure.2.Determine Overall Structure.3.Determine restricting factors.
Phase II
1. Define Decision Variables.
2. Identify contribution coefficients(cj’s)
associated with each variable
3. Formulate the objective function.
4. Identify physical rate of substitution
coefficients(ai j’s).
5. Identify the available resources (bi’s).
6. Maintain non-negativity condition.
DECISION VARIABLE
ARTICLE HOURS ON MACHINE
HOURS ON CRAFTSMAN
PROFIT PER UNIT
X1 A 1.5 2 Rs. 50
X2 B 2.5 1.5 Rs.40
Hours Available (per week)
80Maximum
70Maximum
Objective FunctionMaximize Z=50x1 + 40x2
Constraints Time for article A + Time for article B <
Available time on M/cFor Machine-
1.5x1 + 2.5x2 <80
For Craftsman- 2x1 + 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
Minutes available per week
120 min. 60 min.