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8/9/2019 Product Optimization_Sunil Pillai
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Sunil Pillai
EPS-EOL-Vadinar
May 24, 2010
8/9/2019 Product Optimization_Sunil Pillai
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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
8/9/2019 Product Optimization_Sunil Pillai
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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
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Stream DHDS Blending Storage Naptha FO IFO
LK
HK
LGO
HGO
VD
HN
LCO
HG
VBVR
Slurry
Possible Options
Product Optimisation 4Sunil Pillai
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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
Product Optimisation 5Sunil Pillai
8/9/2019 Product Optimization_Sunil Pillai
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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
Product Optimisation 6Sunil Pillai
8/9/2019 Product Optimization_Sunil Pillai
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Availability
Sulphur(HSD)
KV (HSD, FO,IFO)
Flash(HSD, FO)
Density (FO)
DHDS Flow
IFO Flow
Non_Negativity
Product Optimisation 7Sunil Pillai
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=:::::8::::8∗
. +
::::::8∗
. + 64∗ℎ ∗ℎ 15 ∗ 1⍴ + 25 ∗ 2⍴ + 75 ∗ 7⍴ + 95 ∗ 9⍴ + 105 ∗ 10 ⍴ ∗+96 ∗ 9 ⍴ + 106 ∗ 10 ⍴ ∗+103∗10⍴∗
Sunil Pillai Product Optimisation 8
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Volumetric Calculations
Divide-by-Zero Error
Index Value Comparisons
Non-Linear Constraint Error
Product Optimisation 9Sunil Pillai
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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
Product Optimisation 10Sunil Pillai
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Convert all Division intoMultiplication
Instead of
×
≤ Spec_Sulphur_HSDMax
We Use × ℎ ≤ ℎ ×
Product Optimisation 11Sunil Pillai
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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
Product Optimisation 12Sunil Pillai
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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.
Sunil Pillai Product Optimisation 13
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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.
Sunil Pillai Product Optimisation 14
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Sunil Pillai Product Optimisation 15
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
8/9/2019 Product Optimization_Sunil Pillai
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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.
Product Optimisation 16Sunil Pillai
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Sunil Pillai Product Optimisation 18
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
8/9/2019 Product Optimization_Sunil Pillai
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All 27 Variablesdocumented with
their Names & CellReferences
All 25 Constraintsproperly categorized& grouped for clearunderstanding of theProblem & ease of Troubleshooting
Sunil Pillai Product Optimisation 19
DocumentationSheet
8/9/2019 Product Optimization_Sunil Pillai
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One Click Solution.
Loads the Solver &Generates Sensitivity &
Limits Reports
Automatically
Product Optimisation 20Sunil Pillai
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Maximization Problem
27 Decision Variables
25 Constraints
54 Variable Bounds (Upper & Lower)
71 Input Variables
Completely Linear Problem
Sunil Pillai Product Optimisation 21
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LP Solve
GIPALS
Project SixPap
Kestral & NEOS
Server
Kinsol
Tron
Open Office Add-
ins
Product Optimisation 22Sunil Pillai
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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
Product Optimisation 23Sunil Pillai
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Product Optimisation 24Sunil Pillai
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Disadvantages
Interface Not suitable for Dynamic Data. Variable values are written in program
Product Optimisation 25Sunil Pillai
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G eneral I nterior- P oint A lgorithm L inear
S olver
Adjustable Preprocessor
Flexible Debug Options
Constraint Editor with Error trracking
Product Optimisation 26Sunil Pillai
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Product Optimisation 27Sunil Pillai
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Disadvantage
Not Free Copy
30-Day trial Version has limitation of
15000 Variables & 15000Constraints.
Only a linear Solver
Product Optimisation 28Sunil Pillai
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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.
Product Optimisation 29Sunil Pillai
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Product Optimisation 30Sunil Pillai
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Results cannot be Exported.
Constraints to be entered in theMatrix.
Input variables are not allowed, Direct
Data to be entered into the model.
Product Optimisation 31Sunil Pillai
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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.
Sunil Pillai Product Optimisation 32
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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.
Product Optimisation 33Sunil Pillai
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Product Optimisation 34Sunil Pillai
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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
Sunil Pillai Product Optimisation 35
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Sunil Pillai Product Optimisation 36
Provides Facility to Designthe Entire Model. It can also
be exported to otherApplications
8/9/2019 Product Optimization_Sunil Pillai
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• Modeling pane of Solver
Foundation
• Introduces the Concept of
Goals.
•
Detailed Solution Report isavailable.
• Provides Better Scope for
Diagnosis
Sunil Pillai Product Optmisation 37
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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
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