Product Optimization_Sunil Pillai

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Sunil Pillai

EPS-EOL-Vadinar

May 24, 2010



The LP Model

Objective Function, Decision Variables &Constraints.

Excel Implementation

Other Solvers

LP Solve, GIPALS, SixPap

Way Ahead

Solver Foundation Service

Sunil Pillai Product Optimisation 2



Objective:: To Maximize Revenue

Currently Max Z= Rev_HSD +Rev_FO +

Rev_Naptha +

Rev_IFO +

Rev_HSD_Strg +

Rev_FO_Strg

Product Optimisation 3Sunil Pillai



Stream DHDS Blending Storage Naptha FO IFO

LK

HK

LGO

HGO

VD

HN

LCO

HG

VBVR

Slurry

Possible Options




Symbol Stream DHDS Blending Storage Naptha FO IFO

S1 LK S11 S12 S13 S15

S2 HK S21 S22 S23 S25S3 LGO S31 S33

S4 HGO S41 S43

S5 VD S51 S53

S6 HN S62 S64

S7 LCO S71 S73 S75

S8 HG S81 S82 S83

S9 VBVR S95 S96

S10 Slurry S103 S105 S106

Model Variables




Stream DHDS Blending Storage Naptha FO IFO

LK LK_DHDS LK_Blending LK_Storage LK_FO

HK HK_DHDS HK_Blending HK_Storage HK_FO

LGO LGO_DHDS LGO_Storage

HGO HGO_DHDS HGO_Storage

VD VD_DHDS VD_Storage

HN HN_Blending HN_Naptha

LCO LCO_DHDS LCO_Storage HN_FO

HG HG_DHDS HG_Blending HG_Storage

VBVR VBVR_FO VBVR_IFO

Slurry Slurry_Storage Slurry_FO Slurry_IFO

Excel Variables ::27




Availability

Sulphur(HSD)

KV (HSD, FO,IFO)

Flash(HSD, FO)

Density (FO)

DHDS Flow

IFO Flow

Non_Negativity




=:::::8::::8∗

. +

::::::8∗

. + 64∗ℎ ∗ℎ 15 ∗ 1⍴ + 25 ∗ 2⍴ + 75 ∗ 7⍴ + 95 ∗ 9⍴ + 105 ∗ 10 ⍴ ∗+96 ∗ 9 ⍴ + 106 ∗ 10 ⍴ ∗+103∗10⍴∗




Volumetric Calculations

Divide-by-Zero Error

Index Value Comparisons

Non-Linear Constraint Error




Solver starts with zero values for all variables.

At this point the sum of the variables is also

Zero.

Any Calculation involving a Division by the Sumof Volumes will result in a Divide-by-Zero Error.

For Example:

ℎ = ×

; = 1 , 2




Convert all Division intoMultiplication

Instead of

×

≤ Spec_Sulphur_HSDMax

We Use × ℎ ≤ ℎ ×




HSD Sulphur

HSD KV

HSD Flash FO KV

FO Flash

FO Density

IFO KV IFO Flash

Output

Diesel

Sulphur

Diesel KV Diesel Flash FO KV FO Flash FO Density IFO KV IFO Flash

Output 330 2.199997 50.28787 180.0009 75.7336 0.991 40800.8 113.1402

Comparision 293008.4 50505.02 52.86698 6096.814 5.323215 254.36209 579.916549 1.12942

Min 17758.08 50505.02 87.97638 7.96854 579.916549

Max 293008.4 6.735442 6096.814 254.36209




The Functions used to convert KV &

Flash to their Index Values are Non-

Linear.

This makes the KV & Flash

Constraints unacceptable to the LP

Solver.




Linearising:: Comparisions to bemade in SAME domain (Index values)only.

Spec value to be converted into IndexValue.

This Index value of Spec Compared with the Index value of output in theConstraint.





SpecsDiesel

Sulphur

Diesel

FlashDiesel KV FO KV FO Flash FO Density IFO KV

Min 20.00 38.00 2.20 66.00

Max 330.00 100.00 180.00 0.99

Equal to 40800.00

IndexMin 0.099083 56.88 0.031046 8.528185

Index Max 0.007586 23.75

HSD Flash

HSD KV

FO KV

FO Flash

IFO KV



100% Dynamic In Nature.

No static values in any formulas in

Model.

All values are Referenced to byVariables.

In all 71 variables can be assignedvalues to model different scenarios.





Model Diagnosis

Objective Function 761787.43

Variable Count 27

1 Density_FO_CmpOp<=Density_FO_CmpMax TRUE

2 Flash_FO_CmpOp<=Flash_FO_CmpMin TRUE

3 Flash_HSD_CmpOp<=Flash_HSD_CmpMin TRUE

Diagnosis Sheet

78 VD_Strg>=0 TRUE

79 VD_Used=VD_Availability TRUE

80{32767,32767,0.000001,0.01,TRUE,FALSE,FALSE,1,1

,1,0.0001,TRUE}32767

81 {0,0,1,100,0,FALSE,TRUE,0.075,0,0,TRUE,50} 0

Separate

Diagnosis Sheet

Automatically

Displays the

status of 81Parameters of

the Problem



All 27 Variablesdocumented with

their Names & CellReferences

All 25 Constraintsproperly categorized& grouped for clearunderstanding of theProblem & ease of Troubleshooting


DocumentationSheet



One Click Solution.

Loads the Solver &Generates Sensitivity &

Limits Reports

Automatically




Maximization Problem

27 Decision Variables

25 Constraints

54 Variable Bounds (Upper & Lower)

71 Input Variables

Completely Linear Problem




LP Solve

GIPALS

Project SixPap

Kestral & NEOS

Server

Kinsol

Tron

Open Office Add-

ins




Advantages

Fastest Linear solver

Greater Control on Solver Behaviour.

Large number of Options available

Unlimited Variables & Constraints

O/p can be Transported to several other

Formats including Excel




Disadvantages

Interface Not suitable for Dynamic Data. Variable values are written in program




G eneral I nterior- P oint A lgorithm L inear

S olver

Adjustable Preprocessor

Flexible Debug Options

Constraint Editor with Error trracking




Disadvantage

Not Free Copy

30-Day trial Version has limitation of

15000 Variables & 15000Constraints.

Only a linear Solver




VB Based LP Solver

Detailed Analysis & Diagnosis Possible

Has two Algorithms:: Push-Pull & StdSimplex.

Simultaneous Computation using bothAlg.

Provides Comparision between theresults from both the Algorithms.




Results cannot be Exported.

Constraints to be entered in theMatrix.

Input variables are not allowed, Direct

Data to be entered into the model.




Kinsol & Tron work Exclusively on

Linux Platforms, not supported on

Windows.

Neos is a Server of MIT that allows

users to log in remotely & submit

their LP problems using Kestrol Client

program. Not Recommended due to

Data transfer & Security Issues.




So Far, EXCEL Add-in stands as the

best candidate as per the Input &

Interface requirement of the problem.

But its nonlinear Capacity does not

provide a reliable global optimum.




Best way to go forward lies in

continuing with Excel Interface

(Front-End) while trying to find Non-Linear Solvers that can be integrated

into Excel.

Solver Foundation Services is believed

to have the capabilities to do so with

some restrictions





Provides Facility to Designthe Entire Model. It can also

be exported to otherApplications



• Modeling pane of Solver

Foundation

• Introduces the Concept of

Goals.

•

Detailed Solution Report isavailable.

• Provides Better Scope for

Diagnosis

Sunil Pillai Product Optmisation 37



APOPT - large-scale nonlinear programming CO - nonlinear programming in the GAUSS

language. CONOPT - nonlinear programming. DONLP2 - nonlinear programming. DOT - Design Optimization Tools. Excel and Quattro Pro Solvers - spreadsheet-

based linear, integer and nonlinearprogramming.

FSQP - nonlinear and minmax constrainedoptimization, with feasible iterates.

GINO - nonlinear programming. GRG2 - nonlinear programming. HARWELL Library - linear and nonlinear

programming, nonlinear equations, datafitting.

ILOG - constraint-based programming andnonlinear optimization.

IPOPT - interior point, large-scale KNITRO -nonlinear programming.. LANCELOT - large-scale problems. LINGO - linear, integer, nonlinear

programming with modeling language. LOQO - Linear programming, unconstrained

and constrained nonlinear optimization. LSGRG2 - nonlinear programming. MINOS - linear programming and nonlinear

optimization. MOSEK - linear programming and convex

nonlinear optimization. NLPJOB - Mulicriteria optimization. NLPQL - nonlinear programming. NLPQLB - nonlinear programming with

constraints. NLPSPR - nonlinear programming. NPSOL - nonlinear programming. NOVA - nonlinear programming. OPTIMA Library - optimization and sensitivity

analysis. PROC NLP - various nonlinear optimization

capabilities. OPTPACK - constrained and unconstrained

optimization. SNOPT - large-scale quadratic and nonlinear

programming problems. SQP - nonlinear programming. SPRNLP - sparse and dense nonlinear

programming. SYNAPS Pointer - multidiscplinary design

optimization software. What's Best - Excel add-in for linear, integer,

nonlinear programming. NLopt - a variety of nonlinear-constrained

nonlinear optimization algorithms, includingalgorithms for large-scale problems


http://wiki.mcs.anl.gov/NEOS/index.php/NLopt

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/whatsbest.html

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/synaps.html

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/socs_sprnlp.html

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/sqp.html

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/sqopt_snopt.html

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/optpack.html

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/procnlp.html

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/optima.html

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/nova.html

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/npsol.html

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/nlpspr.html

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/nlpqlb.html

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/nlpql.html

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/nlpjob.html

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/mosek.html

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/minos.html

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/lsgrg2.html

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/loqo.html

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/lingo.html

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/lancelot.html

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/knitro.html

http://wiki.mcs.anl.gov/NEOS/index.php/IPOPT

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/ilog.html

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/harwell.html

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/grg2.html

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/gino.html

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/fsqp.html

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/excelqp.html

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/dot.html

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/donlp2.html

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/conopt.html

http://www-fp.mcs.anl.gov/otc/Guide/SoftwareGuide/Blurbs/co.html

http://wiki.mcs.anl.gov/NEOS/index.php/APOPT

Product Optimization_Sunil Pillai

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