equipment & process alternatives above the base case
TRANSCRIPT
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
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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