engineering optimization second edition authors: a. rabindran, k. m. ragsdell, and g. v. reklaitis...
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Engineering Optimization
Second EditionAuthors: A. Rabindran, K. M. Ragsdell,
and G. V. ReklaitisChapter-1 (Introduction)
Presenter: Pulak ChowdhuryJune 4, 2010
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Life is about Optimization
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Introduction to Optimization
Finding the best candidate from a set of alternatives without explicitly enumerate and evaluate all possible alternatives
Root of Engineering - design new, better, more efficient, and less expensive systems
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Requirements to Apply OptimizationClearly delineate the boundary of the engineering system
Define quantitative criterion - objective
Select system variables
Define a model for expressing relation of variables
Problem Formulation
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Defining System Boundaries (1)
System - A restricted portion of the Universe
System boundary - separate the system from the universe
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Defining System Boundaries (2)Initial choice may be too restrictive
Expand system boundary - increase in size and complexity
Example: A manufacturing operation has a paint shop in which finished parts are
mounted on an assembly line and painted in different colors. Optimize batch size or
color sequence.
Considering paint shop in isolation or not?
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Performance Criterion
Criteria on the basis of which the performance or design of the system can be evaluated
Examples: Total capital cost, annual cost, return on investment, cost-benefit ratio, production time, maximum production rate, etc.
Maximum/mimimum
Only one criterion
Shop foreman - design with minimum color and part changes
Sales department - design with maximized inventory of parts
Financial Officer - design that minimizes inventories
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Independent Variables
Variables adequate to characterize possible candidate designs or operating conditions of the system
Distinguishing Variables
Including all variables
To what detail?
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System Model
Describes the relations among problem variables
Simplified mathematical representation of real system
Collection of equations
Real system too expensive
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Optimization Problem
Performance Measure - Objective
A set of independent variables
A model relating the variables
Defined boundary - Constraints
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Engineering Design Process
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Application of OptimizationDesign of components or entire systems
Design of a welded beam, Design of an oxygen supply system
Planning and analysis of existing operationsRefinery production planning
Engineering analysis and data reductionNonlinear curve fitting
Control of dynamic systems
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Structure of Optimization Problems
Minimize
Subject to Constraints
Objective
Constrained Optimization ProblemProblem with no constraints, that is, Unconstrained Optimization Problem. Here,
and
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Classification of Optimization Problems
Objective
Constraints
Variables Program
Linear Linear Continuous Linear Program
Linear Linear IntegerInteger Linear
Program
nonlinear
linear N/A
Linearly Constrained Nonlinear Program
Unconstrained problems in which is a one-component vector are called single-
variable problems
Quadratic Program
Fractional Linear Program
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Refinery Production Planning: DescriptionA refinery processes crude oils to produce a number of
raw gasoline intermediates that must subsequently be blended to make two grades of motor fuel, regular and premium. Each raw gasoline has a known perform- ance rating, a maximum availability, and a fixed unit cost. The two motor fuels have a specified minimum performance rating and selling price, and their blending is achieved at a known unit cost. Contractual obligations im- pose minimum production requirements of both fuels. However, all excess fuel production or unused raw gasoline amounts can be sold in the open market at known prices. The optimal refinery production plan is to be deter- mined over the next specified planning period.
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Refinery Production Planning: Schematic
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Refinery Production Planning: Formulation
System: Raw gasoline intermediates, blending operation, fluid motor fuels
Performance Index: Net profit over planning period
Motor fuel and intermediate sales - blending costs - cost of intermediates
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Refinery Production Planning: Variables
Flows depicted as directed arcs in
the figureEach intermediate - one variable
for each intermediate = amount used for regular
= amount used for premium= amount sold directly
for each product = amount allocated to contracts= amount sold in open market
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Refinery Production Planning: Model
Material balance equations
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Refinery Production Planning: ObjectivePerformance Criterion - Net profit
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Questions?