EQUIPMENT & PROCESS ALTERNATIVES

ABOVE THE BASE CASE

PROCESS OPTIONS

• NEED TO BE INVESTIGATED TO HAVE A COMPLETE SURVEY

• TECHNICAL EVALUATION TO DETERMINE RISK

• ECONOMIC EVALUATION TO DETERMINE IMPACT

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ECONOMIC EVALUATION• CAPITAL COSTS ARE BASED ON A ±20% COST

FOR PURCHASED EQUIPMENT.• OPERATING COSTS ARE BASED ON A ±5%

ACCURACY• CASH FLOW RANGES SHOULD BE DEFINED FOR

THE HIGH AND LOW END VALUE FOR THESE ESTIMATES

• RESULTING SELLING PRICE RANGE INDICATES THE LIMITS FOR CONSIDERING PROCESS REVISIONS.

• NOTE THAT THE EXTREMES OF THE PRICES BASED ON THE CASH FLOW ANALYSES ARE WHAT DETERMINES THE BASIS FOR RECOMMENDATIONS

• ALSO INCLUDE THE RISK ASSOCIATED WITH THE ALTERNATE TECHNOLOGY.

GENERAL OPTIMIZATION METHODS

• PROJECTS CAN BE OPTIMIZED ON A UNIT BY UNIT BASIS OR ON LARGER SYSTEMS

• DETERMINATION OF THE MOST SIGNIFICANT COMPONENTS IS CALLED A PARETO ANALYSIS

(http://www-personal.umich.edu/~westj/files/cds/individual/Disk2/lectures/08/08t-

pareto.pdf)• THE BASIC IDEA IS TO PUT THE EFFORT IN

THE AREA THAT HAS THE HIGHEST TOTAL RETURN POTENTIAL

1Pareto Analysis

(http://www-personal.umich.edu/~westj/files/cds/individual/Disk2/lectures/08/08t-pareto.pdf)

• Pareto* Principle provides the foundation for the concept of the “vital few” and a “trivial many”

• Examples:– Quality – a small percentage of defect categories – (causes) will constitute a high % of the total # defects.– Cost – a small percentage of components will constitute – a high % of total product cost.– Others: Inventory, absenteeism, downtime

• *Note: Wilfredo Pareto – 19th Century Italian economist studying wealth who observed that a large proportion of wealth is owned by a small percentage of the people. Pareto principle was later applied to quality by J.M. Juran

Pareto Analysis(http://www-personal.umich.edu/~westj/files/cds/individual/Disk2/lectures/08/08t-pareto.pdf)

• 80/20 Rule• In quality, this rule suggests that ~20% of defect

categories will account for ~80% of the total number of defects. Example for Bid Preparations

Pareto Analysis(http://www-personal.umich.edu/~westj/files/cds/individual/Disk2/lectures/08/08t-pareto.pdf)

• Pareto Chart

Pareto Analysis(http://www-personal.umich.edu/~westj/files/cds/individual/Disk2/lectures/08/08t-pareto.pdf)

• Pareto Analysis may be performed using:• Frequency of occurrence (expressed as a

frequency count or relative frequency %), • Or Total cost,• Or Severity, adverse outcome, or

avoidability• Note: the most frequently occurring item may not

be the most important item to address first

OPTIMIZATION PROCEDURE

• DEVELOP OBJECTIVE FUNCTION• DEVELOP CONSTRAINTS• MATHEMATICALLY OPTIMIZE

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OBJECTIVE FUNCTIONS

• CAN BE LINEAR OR NON-LINEAR AND INCLUDE MANY VARIABLES.

Y = Y (x1, x2, ..., xn) = Y ()

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CONSTRAINTS

• INCLUDE SAME VARIABLES AS THE OBJECTIVE FUNCTION

• CAN BE EQUALITIES – Φ1 = Φ1 (x1, x2, ..., xn) = Φ1 (x)– Φ2 = Φ2 (x1, x2, ..., xn) = Φ2 (x) .– Φj = Φj (x1, x2, ..., xn) = Φj (x)

• OR INEQUALITIES :– Ψ1 = Ψ1 (x1, x2, ..., xn) = Ψ1 (x) ≤ L1– Ψ2 = Ψ2 (x1, x2, ..., xn) = Ψ2 (x) ≤ L2– Ψk = Ψk (x1, x2, ..., xn) = Ψk (x) ≤ Lk

www.britannica.com/eb/art-3028?articleTypeId=1

CALCULUS METHODS

• BASED ON Y’ = 0 AT OPTIMUM • USING TOTAL DERIVATIVE

• AT THE OPTIMUM, ALL PARTIALS EQUAL ZERO

n

n

dxx

dxx

dxx

d

.....2

2

1

1

0

ix

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EXAMPLE OF APPLICATION

SOLUTION TO HX DESIGN

SOLUTION TO HX DESIGN

LA GRANGE MULTIPLIERS

• SIMULTANEOUS SOLUTION OF n EQUATIONS FOR n UNKNOWNS.

• THE FUNCTION TO BE OPTIMIZED HAS THE FORM:

• WHERE THE GRADIENT IS • AND λi IS THE LAGRANGIAN MULTIPLIER

• SET UP AN EQUATION FOR EACH VARIABLE BASED ON THE GRADIANT VECTOR FOR THE SCALAR OF THE OPTIMIZATION FUNCTION:

– WHERE THE UNIT VECTOR IS

0...2211 nny

nx

yi

x

yi

x

yy

...22

11

ii

LaGRANGE MULTIPLIER APPLIED TO HX EXAMPLE

HX LaGRANGE SOLUTION

HX LaGRANGE SOLUTION

HX LaGRANGE SOLUTION

OTHER OPTIMIZATION METHODS

• FOR MULTI-DIMENSIONAL SYSTEMS– SEARCH METHODS - EVALUATE Y AT

VARIOUS POINTS TO LOCATE THE OPTIMA (MONTE CARLO METHOD)

– TYPES - DICHOTOMOUS SEARCH, FIBONACCI SEARCH, GOLDEN SECTION, MONTE CARLO METHOD

– MAY BE THE ONLY OPTION FOR COMPLEX SYSTEMS