Engineering Optimization Second Edition Authors: A. Rabindran, K. M. Ragsdell, and G. V. Reklaitis Chapter-1 (Introduction) Presenter: Pulak Chowdhury June 4, 2010

2 Life is about Optimization

3 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

4 Requirements to Apply Optimization Clearly delineate the boundary of the engineering system Define quantitative criterion - objective Select system variables Define a model for expressing relation of variables Problem Formulation

5 Defining System Boundaries (1) System - A restricted portion of the Universe System boundary - separate the system from the universe

6 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?

7 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

8 Independent Variables Variables adequate to characterize possible candidate designs or operating conditions of the system Distinguishing Variables Including all variables To what detail?

9 System Model Describes the relations among problem variables Simplified mathematical representation of real system Collection of equations Real system too expensive

10 Optimization Problem Performance Measure - Objective A set of independent variables A model relating the variables Defined boundary - Constraints

11 Engineering Design Process

12 Application of Optimization Design of components or entire systems Design of a welded beam, Design of an oxygen supply system Planning and analysis of existing operations Refinery production planning Engineering analysis and data reduction Nonlinear curve fitting Control of dynamic systems

13 Structure of Optimization Problems Minimize Subject to Constrai nts Objective Constrained Optimization Problem Problem with no constraints, that is, Unconstrained Optimization Problem. Here, and

14 Classification of Optimization Problems Objective Constrain ts VariablesProgram Linear ContinuousLinear Program Linear Integer Integer Linear Program nonlinearlinearN/A Linearly Constrained Nonlinear Program Unconstrained problems in which is a one- component vector are called single-variable problems Quadratic Program Fractional Linear Program

15 Refinery Production Planning: Description A 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.

16 Refinery Production Planning: Schematic

17 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

18 Refinery Production Planning: Variables Flows depicted as directed arcs in the figure Each 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

19 Refinery Production Planning: Model Material balance equations

20 Refinery Production Planning: Objective Performance Criterion - Net profit

21 Questions?