OPTEX MATHEMATICAL MODELING AND MANAGEMENT SYSTEM
is a META-FRAMEWORK for Mathematical Programming.
Oriented towards the design, implementation and setup of decision support systems based in mathematical programming with special emphasis in the development of final user apps:
- The algebraic formulation is independent from any programming language
- The models can be connected with any data server
Thereby generating apps using multiple commercial or noncommercial tech according to clients’ needs
2. OUR MISSION:
BRING THE BENEFITS OF OPTIMIZATION TECHNOLOGY
TO SOCIETY:
ENABLING PEOPLE TO APPLY OPTIMIZATION TECHNOLOGY
SUCCESSFULLY INTO THEIR ORGANIZATIONS
BEING ENTREPRENEURS OF NEW COMPANIES
THAT BRING THE BENEFITS OF OPTIMIZATION TECHNOLOGY TO SOCIETY
3. Why do you choose to
programming in any
specific optimization
technology when you can
programming in all tools
at the same time with
only one effort ?FICO™
XPRESS-MOSEL
CPLEX-OPL-ODM
IMPRESS
4. Why do you choose to
programming in any
specific optimization
technology when you can
programming in all tools
at the same time with
only one effort ?
The best way is to have
the mathematical models
in a meta-platform and in
a second phase go to any
specific commercial
platform.
5. As a part of its process of
technological innovation,
DW has developed an
optimization technology
called
OPTEX
Mathematical Modeling
Management System
which is oriented to
designing, implementing
and setting up large scale
optimization models for
the real word .
6. OPTEX IS A META-FRAMEWORK
ORIENTED TOWARDS THE DESIGN, IMPLEMENTATION AND SETUP OF DECISION
SUPPORT SYSTEMS BASED IN MATHEMATICAL PROGRAMMING WITH SPECIAL
EMPHASIS IN THE DEVELOPMENT OF FINAL USER APPS:
ALGEBRAIC FORMULATION IS INDEPENDENT FROM ANY PROGRAMMING
LANGUAGE
CAN BE CONNECTED WITH ANY DATA SERVER
THEREBY GENERATING APPS USING MULTIPLE COMMERCIAL OR NONCOMMERCIAL
TECH ACCORDING TO CLIENTS’ NEEDS
7. OPTEX Mathematical Modeling System,
was developed to support
DecisionWare’s mathematical modeling
projects since 1991.
15. A DECISION SUPPORT SYSTEM
IS AS A DECISION MAKING CHAIN
INTEGRATED BY A COLLECTION
OF MODELS AND DATA FLOW
16. PTA
Industrial Operations
Tactical Planning
DEM
Long/Medium/Short
Demand Planning
INV
Inventory
Policy
Medium / Short Term
Demand Projections
Inventory
Policy
Production
Goals
POD
Production
Schedule
DIS
Distribution
Schedule
Distribution
Goals
PCO
Sourcing
Sourcing
Goals
Production
Orders
Distribution
Orders
Sourcing
Orders
PES
Supply Chain Design
Short / Medium Term
Market Scenarios
Expansion
Plans
DSS
Short / Medium Term
Market Scenarios
21. ALGEBRAIC LANGUAGES
• Algebraic Programming Language
• Database Algebraic Language
USER INTERFACE
• Based in database tables
• Operates in LANs and WANs (“Cloud Computing”)
• Visual Interface (MS-Windows)
• Filling the blanks parameterization
SERVICES
• Data-Model Generator
• Final User Interface Generator
• General Language Model Generator (C, Java …), includes Matrix Generator
• Algebraic Language Model Generator (GAMS, IBM ILOG OPL, MOSEL , AIMMS … )
PROBLEM SOLUTION
• Basic problems: LP, MIP, QP, MIQP, NLP
• Large Scale Theory: Benders Partition, Lagrangean Relaxation, Disjunctive Programming, …
• Links to multiple optimization libraries (GUROBI, IBM CPLEX, XPREXX, COIN-MP, … )
• Automatic Generation of Non-anticipative Multistage Stochastic Programming (MSP)
• Parallel solution in computers grids
CONNECTIVITY
• ERP/WMS/TMS/AMS: Enterprise Information Systems
• GIS: Geographic Information Systems
• ASP: Applications Service Provider (MS-Project, Google MAPS, …)
ELEMENTS
23. ALGEBRAIC LANGUAGES OBJECTS
MATHEMATICAL DEFINITIONS
• Index, Sets, Parameters, Variables, Equations,
Objective Functions, Planning Horizons, Decision
Trees
DECISION SUPPORT SYSTEMS
• Problems = (Equations, Variables, Objective
Functions)
• Model = (Problems, Data Flows)
• DSS = (Models, Data Flows)
DATA MODEL
• DSN, Data Tables, Fields, Shell Windows, Data
Windows, Menus
25. OPTEX- DATABASE ALGEBRAIC LANGUAGE
SQL
Server
Internet - Intranet
0
2 0
4 0
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1 s t Q t r 2 n d Q t r
0
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1 s t Q t r 2 n d Q t r
0
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4 0
6 0
8 0
1 s t Q t r 2 n d Q t r
0
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6 0
8 0
1 s t Q t r 2 n d Q t r
MM
Server
MATHEMATICAL
MODEL
SERVER
INFORMATION
SYSTEM
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EASY DEVELOPMENT MATHEMATICAL MODELS
IN A LAN-WAN ENVIRONMENT USING THE POWER
OF THE DATABASE SERVERS
26. OPTEX- DATABASE ALGEBRAIC LANGUAGE
SQL
Server
Internet - Intranet
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1 s t Q t r 2 n d Q t r
0
2 0
4 0
6 0
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1 s t Q t r 2 n d Q t r
0
2 0
4 0
6 0
8 0
1 s t Q t r 2 n d Q t r
MM
Server
MATHEMATICAL
MODEL
SERVER
INFORMATION
SYSTEM
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THE IMPLEMENTATION OF A
DECISION SUPPORT SYSTEMS IS BASED IN
A FILLING THE BLANKS PROCESS
34. TIPO DE SERIE INTERPRETACIÓN
E
ESCALÓN
()
I
IMPULSO
(PULSE)
P
POLI LÍNEA
(POLY LINE)
OPTEX- DATABASE ALGEBRAIC LANGUAGE
MULTIPLES FORMS OF
DATA INTERPRETATION
35. JVB-08/94OPTEX
Min t j h CTt(GTjth)
sujeto a:
GDzth = uTN(z) LDuzth
GDzth + GHAzth + DEFzth = DEMzth
ENuth - jL1(u) GTEjuth
- vL2(u) LLvuth = 0
. . . .
z NOD
t = 1,T
h = 1,NH
z NOD
t = 1,T
h = 1,NH
u LIN
t = 1,T
h = 1,NH
VARIABLES
OPTEX- DATABASE ALGEBRAIC LANGUAGE
36. JVB-08/94OPTEX
Min t j h CTt(GTjth)
sujeto a:
GDzth = uTN(z) LDuzth
GDzth + GHAzth + DEFzth = DEMzth
ENuth - jL1(u) GTEjuth
- vL2(u) LLvuth = 0
. . . .
z NOD
t = 1,T
h = 1,NH
z NOD
t = 1,T
h = 1,NH
u LIN
t = 1,T
h = 1,NH
CONSTRAINTS
OPTEX- DATABASE ALGEBRAIC LANGUAGE
39. MO
IL
MO
WO MO
Tiempo
OPTEX- DATABASE ALGEBRAIC LANGUAGE
FOR DISCRETE TIME MOODELS, THE
PLANNING HORIZON MAY BE IN YEARS,
MONTHS, DAY, HOURS, MINUTES, …
40. PROBLEMS
MODELS
OPTEX – DECISION SUPPORT SYSTEM ELEMENTS
A PROBLEM IS A COLLECTION OF CONSTRAINTS
A MODEL IS A COLLECTION OF PROBLEMS
CONNECTED BY A DATA FLOW AND A MODEL CONTROL
41. A DECISION SUPPORT SYSTEM IS A COLLECTION OF
MODELS AND DATA FLOW ALL USING THE SAME DATA MODEL
AND THE SAME FRAMEWORK
PTA
Aggregated Industrial
Operations
Tactical Plannings
DEM
Demand
Long/Medium/Short
Term
INV
Inventory
Policies
Demand Forecasting
Medium/Short Term
Demand Stages
Medium/Short Term
Inventory
Policies
Production
Goals
POD
Production
Scheduling
DIS
Distribution
scheduling
Distribution
Goals
PCO
Sourcing
Scheduling
Consumption
Goals
Production
Orders
Distriution
Orders
Purchase
Orders
PES
Supply Chain Design
Marjet Stages
Long/Medium Term
Expansion
Plans
DSS
DSS
MODELS
OPTEX – DECISION SUPPORT SYSTEMS ELEMENTS
42. ADVANCED OPTIMIZATION
INVESTMENTS COORDINATOR
INTERZONE
COORDINATOR
SECTOR 1
STOCHASTIC 1
INTERZONE
COORDINATOR
SECTOR 1
STOCHASTIC 1
INTERSECTOR OPERATIONS
COORDINATOR
STOCHASTIC CONDITION 1
DYNAMIC
COORD.
ZONA S.1
DYNAMIC
COORD.
ZONA S.ZS
DYNAMIC
COORD.
ZONE 1.1
DYNAMIC
COORD.
ZONA 1.Z1
1 T2 T-1 1 T2 T-1 1 T2 T-1 1 T2 T-1
TIME
PARTITION
INVESTMENTS
SECTOR
ZONE
DECOMPOSITION
MULTILEVEL
SYSTEM
INTERZONE
COORDINATOR
SECTOR 1
STOCHASTIC H
INTERZONE
COORDINATOR
SECTOR 1
STOCHASTIC H
INTERSECTOR OPERATIONS
COORDINATOR
STOCHASTIC CONDITION H
DYNAMIC
COORD.
ZONA S.1
DYNAMIC
COORD.
ZONA S.ZS
DYNAMIC
COORD.
ZONE 1.1
DYNAMIC
COORD.
ZONA 1.Z1
1 T2 T-1 1 T2 T-1 1 T2 T-1 1 T2 T-1
RANDOM
OPERATIONS
53. Scenario H
Scenario 1
Scenario 2
ARBOL DE DECISIONES DE
MULTIPLES ETAPAS
t = 1 t = 2 t = 3 t = 4
OPTEX- MULTISTAGE STOCHASTIC OPTIMIZATION
OPTEX HAS TOOLS ORIENTED TO DEVELOP
MULTISTAGE STOCHASTIC OPTIMIZATION MODELS
AUTOMATIC CONVERSION OF A
DETERMINISTIC MODEL INTO STOCHASTIC
MULTI-STAGE
DECISION TREE
54. MULTI-STAGE
DECISION TREE
N1
e = 1 e = 2 e = 3
t
1 13 25 36
N21
N22
N21
N22
N21
N22
N21
N22
Hidrology 1988
Hidrology 1992
Hidrology 1985
Hidrology 1990
High Demand High Price
Hidrology 1988 Low Demand Low Price
High Demand High Price
Low Demand Low PriceHidrology 1990
High Demand High Price
Low Demand Low PriceHidrology 1992
High Demand Low Price
High PriceLow Demand
High Demand High Price
Hidrology 1988
Hidrology 1988
0.125
0.0625
UNCERTAINTY DIMENSIONS
• Demand
• Fuel Prices
• Water Inflows
• Others
55. OPTEX HAS TOOLS ORIENTED TO DEVELOP
MULTISTAGE STOCHASTIC OPTIMIZATION
INCLUDING MULTIPLES TYPES OF RISK CONSTRAINTS
Conditional Value-at-Risk (CVaR)
Cost Probability Function
Desvío
Estándar
(s)
VaR
b=0.05
1.645 s
Cost - f(x|w)a(b)
f ( f(x|w) )
jb( f(x|w) )
OPTEX- MULTISTAGE STOCHASTIC OPTIMIZATION
57. DETERMINISTIC CASE
t = 1 t = 2
Mean
Demand
Deterministics
Investment
Decisions
Deterministics
Future Operations
Decisions
58. TWO-STAGE DECISION TREE FOR
DEMAND: UNCERTAINTY DIMENSION
t = 1 t = 2
Scenario
Demand 10
Scenario
Demand 1
Scenario
Demand 2
Deterministics
Investment
Decisions
0.10
0.10
Uncertainty
Future Operations
Decisions
59. Demand 10
Demand 1
Demand 2
0.10
0.10
Demand 10
Demand 1
Demand 2
0.10
0.10
WITHOUT Extrem Event
0.90
0.10
t = 1 t = 2
Deterministics
Investment
Decisions Uncertainty
Future Operations
Decisions
TWO-STAGE DECISION TREE FOR
DEMAND: UNCERTAINTY DIMENSION 1
EXTREME EVENT: UNCERTAINTY DIMENSION 2
WITH Extrem Event
60. THE AUTOMATIC CONVERSION IMPLIES:
1. TO INCLUDE THE INDEXES RELATED WITH THE
UNCERTAINTY DIMENSIONS
61. THE AUTOMATIC CONVERSION IMPLIES:
2. TO DEFINE A DECISION TREE
3. TO SPECIFY THE NON ANTICIPATIVE VARIABLES
4. TO SPECIFY THE PARAMETERS WITH THE
UNCERTAINTY DIMENSIONS
2.
3.
4.
73. Internet-Intranet
0
2 0
4 0
6 0
8 0
1 s t Q t r 2 n d Q t r
SERVIDOR
MODELOS
MATEMÁTICOS
OPTEX
WIDE AREA NETWORK
DOCUMENTATION
OPTEX generates automatically the following documentation:
Algebraic Formulation
Information system data model
Connectivity with other data models
Remote Access Server
Connectivity
79. MODELS
GAMS – MPS
IBM ILOG OPL
MOSEL – AIMMS - …
MODEL RESULTS
(PRIMAL – DUAL)
PROGRAMMING
ALGEBRAIC LANGUAGE
DATABASE
ALGEBRAIC LANGUAGE
OPTEX
PROCESSOR
MODELS
C PROGRAMS
LIB or DDL LIBRARY
80. OPTEX
WIDE AREA NETWORK
Internet-Intranet
0
2 0
4 0
6 0
8 0
1 s t Q t r 2 n d Q t r
SERVIDOR
MODELOS
MATEMÁTICOS
Remote access
server connectivity
CLOUD SERVER
ALGEBRAIC
LANGUAGE
SOLVER
C ANSI
SOLVER
CLOUD LINK
82. Internet
0
2 0
4 0
6 0
8 0
1 s t Q t r 2 n d Q t r
MATHEMATICAL
MODEL’S
ERVER
OPTEX
ERP
DATABASE
Remote Access Server
Connectivity
OPTEX
Graphic User Interface
OPTEX
Mathematical Modeling
Processor
ODBC
USUARIOS
ILIMITADOS
OPTIMIZATION LIBRARY
CPLEX
FICO™
XPRESS
84. OPTEX – C DSS PROGRAM STRUCTURE
I/O
Routines
MODELs
Routines
Main
OPTEX-COINLP
LINK
Routine
COINLP
Routines
CPLEX
Routines
CONSTRAINTs
Routines
OPTEX-CPLEX
LINK
Routine
OPTEX-xxxxx
LINK
Routine
XXXXX
Routines
PROBLEMs
Routines
LARGE SCALE OPTIMIZATION
Routines
DSS.LIB or DSS.DLL
DSS
DATABASE
85. OPTEX – C DSS PROGRAM STRUCTURE
MODELs
Routines
OPTEX-COINLP
LINK
Routine
COINLP
Routines
CPLEX
Routines
CONSTRAINTs
Routines
OPTEX-CPLEX
LINK
Routine
OPTEX-xxxxx
LINK
Routine
XXXXX
Routines
PROBLEMs
Routines
LARGE SCALE OPTIMIZATION
Routines
DSS.LIB or DSS.DLL
DSS
DATABASE
USER
Routines
OPTEX-USER
LINK
Routine
Customized Visual User Interface
USER
ERP
91. Internet
0
2 0
4 0
6 0
8 0
1 s t Q t r 2 n d Q t r
OPTEX
ERP
DATABASE
Remote Access Server
Connectivity
OPTEX
Graphic User Interface
ODBC
OPTEX
Mathematical Modeling
Processor
CPLEX
FICO™
Xpress
MATHEMATICAL
MODEL’S
ERVER
92. Internet
0
2 0
4 0
6 0
8 0
1 s t Q t r 2 n d Q t r
OPTEX
ERP
DATABASE
OPTEX
Graphic User Interface
ODBC
OPTEX
Mathematical Modeling
Processor
CPLEX
MATHEMATICAL
MODEL’S
ERVER
Remote Access Server
Connectivity
FICO™
Xpress
115. INFORMATION
SYSTEM
Min t j h CTt(GTjth)
sujeto a:
GDzth - uTN(z) LDuzth = 0
GDzth + GHAzth + DEFzth = DEMzth
ENuth - jL1(u) GTEjuth
- vL2(u) LLvuth = 0
Sistema Descripción
Capacidad
Térmica (MW)
EEB.
ISA.
EPM
COR
Energía Eléctrica de Bogotá
Interconexión Eléctrica S.A.
Empresas Públicas de Medellín
CORELCA
45
67
0
78
MATHEMATICAL MODEL
INFORMATION SYSTEM
INDUSTRIAL DATA
INFORMATION SYSTEM
117. RELACIÓN SIMM - SIDI
INDEX
Parameter
Restricción
IndexesVariable
Indexes
Indexes
ENTITY
ENTITIES
RELATIONS
SIMM:
MATHEMATICAL
MODEL
INFORMATION
SYSTEM
SIDI:
INDUSTRIAL
DATA
INFORMATION
SYSTEM
IndexesSets
118. IN OPTEX THE IMPLEMENTATION OF THE
INDUSTRIAL DATA INFORMATION SYSTEM IS
BASED IN A FILLING THE BLANKS GUIDED
PROCESS, SIMILAR TO THE PROCESS TO
IMPLEMENTATION OF THE MATHEMATICAL
MODELS.
THE MODELER DOESN’T NEED TO BE AN SPECIALIST
IN DATABASES LANGUAGES AND INFORMATION
SYSTEMS
IMPLEMENTATION INDUSTRIAL DATA INFORMATION SYSTEM
119. IN OPTEX THE IMPLEMENTATION OF THE
INDUSTRIAL DATA INFORMATION SYSTEM IS
BASED IN A FILLING THE BLANKS GUIDED
PROCESS, SIMILAR TO THE PROCESS TO
IMPLEMENTATION OF THE MATHEMATICAL
MODELS.
THE MODELER DOESN’T NEED TO BE AN SPECIALIST
IN DATABASES LANGUAGES AND INFORMATION
SYSTEMS
IMPLEMENTATION INDUSTRIAL DATA INFORMATION SYSTEM
122. INDUSTRIAL DATA
INFORMATION SYSTEM
IS A COLLECTION OF:
DATA TABLES, SHELL WINDOWS, DATA
WINDOWS AND MENUS ORIENTED TO THE
FINAL USER
INDUSTRIAL DATA INFORMATION SYSTEM
123. INDUSTRIAL DATA INFORMATION SYSTEM
THE DATABASE OF THE INFORMATION SYSTEM
IS A COLLECTION OF RELATIONAL DATA TABLES
ORIENTED TO MANAGE LARGE AMOUNT OF DATA, LIKE IN
THE REAL WORLD MODELS.
124. OPTEX GENERATES, ON-LINE, DATA
WINDOWS WITH A COLLECTION OF
WINDOWS-TOOLS THAT HELP THE USER IN
THE LABOR OF DATA CAPTURE.
THE DATA WINDOWS ARE JOINT IN A SHELL
WINDOWS IN A RELATIONAL APPROACH.
INDUSTRIAL DATA INFORMATION SYSTEM
125. HIERARCHIC INFORMATION SYSTEM FOR MODELS RESULTS
SCENARIO FAMILY
ROOT DIRECTORY
Family
No. 1
Directory
Family
No. E
Directory
Family
No. n
Directory
Scenario
No. E-X
Directory
Scenario
No. E-X
Directory
Tables
Parameters
Tables
Resulting
Parameters
Tables
Variable
Results
Tables
Parameters
Results
Tables
Variable
Results
Scenario
No. E-X
Directory
Tables
Parameter
Results
Tables
Variable
Results
AUTOMATICALLY, OPTEX GENERATES A HIERARCHIC INFORMATION
SYSTEM TO STORE THE RESULTS OF THE MODELS USING THE
CONCEPTS OF SCENARIOS AND FAMILY OF SCENARIOS.
126. OPTEX STORES IN TABLES
THE MATRIX AND THE
VECTORS RESULT OF THE
MATRIX GENERATION.
THIS ALLOWS THE
DEVELOPER TO VISUALIZE
AND CHECK THE VALIDITY
OF HIS MODELING
INDUSTRIAL DATA INFORMATION SYSTEM
127. OPTEX STORES
THE RESULTS
IN DATA
TABLES
AND/OR IN
TEXT FILES
AND/OR IN
EXCEL FILES
INDUSTRIAL DATA INFORMATION SYSTEM
128. OPTEX STORES
THE RESULTS
IN DATA
TABLES
AND/OR IN
TEXT FILES
AND/OR IN
EXCEL FILES
INDUSTRIAL DATA INFORMATION SYSTEM
129. OPTEX STORES
THE RESULTS
IN DATA
TABLES
AND/OR IN
TEXT FILES
AND/OR IN
EXCEL FILES
INDUSTRIAL DATA INFORMATION SYSTEM
130. OPTEX PROVIDES TOOLS
FOR VISUALIZATION OF
LITTLE MODELS.
FOR LARGE SCALE MODELS
THE STRUCTURE OF
RESULTS TABLES ARE
ORIENTED TO USE IN
MULTIDIMENSIONAL
ANALYSIS DATA TOOLS
INDUSTRIAL DATA INFORMATION SYSTEM
161. To capitalize its expertise in mathematical optimization projects,
DW created OPCHAIN, a brand through which we have grouped
the solutions developed by DW, in different areas of application
using mathematical programming methodologies and technologies.
In 2012, OPCHAIN has accumulated the experience of more than
thirty-five (35) years in engineering problem solving and business
analytics using mathematical programming models. OPCHAIN
models are fully programmable, easy to customize for each client,
and are easily integrated with other IT solutions in organizations.
OPCHAIN
OPTIMIZING THE VALUE CHAIN
162. OPCHAIN-SCO
SUPPLY CHAIN OPTIMIZATION
OPCHAIN-TSO
TRANSPORT SYSTEMS OPTIMIZATION
OPCHAIN-RSO
RETAIL CHAIN OPTIMIZATION
OPCHAIN-RPO
REGIONAL PLANING OPTIMIZATION
OPCHAIN-ESO
ENERGY SYSTEMS OPTIMIZATION
OPCHAIN-BANK
BANK SYSTEMS OPTIMIZATION
OPCHAIN-EDO
EDUCATIONAL SYSTEMS OPTIMIZATION
OPCHAIN-MINES
MINES SYSTEMS OPTIMIZATION
163. OPTEX Mathematical Modeling System,
was developed to support
DecisionWare’s mathematical modeling
projects since 1991.
OPTEX supports the development of all
multi-model OPCHAIN-DSS developed
by
164. SERVICES
TO SELL OPTEX MATHEMATICAL MODELING MANAGEMENT SYSTEM
TO SELL OPCHAIN-MODELS IN ANY PLATFORM
(INCLUDING SOURCE CODE)
TO CONVERT MODELS FROM ANY PLATFORM TO ANY PLATFORM
TO DEVELOPMENT ON DEMAND MODELS IN ANY PLATFORM
ON DEMAND OPTIMIZATION IN THE CLOUD