OPTEX Mathematical Modeling System: The META-PLATFORM for Mathematical Programming.
Why do you choose to programming in any specific optimization technology when you can program in all tools at the same time with only one effort ?
The best way is to have the mathematical models in a meta-platform, like OPTEX, and in a second phase go to any specific commercial platform.
3. Why do you choose to
programming in any
specific optimization
technology when you
can program in all tools
at the same time with
only one effort ?
The best way is to have
the mathematical
models in a meta-
platform, like OPTEX,
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 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.
OPTEX dramatically simplify the developing and solving
of complex optimization applications by supporting :
Rapid Prototyping
Big Data Intensive Optimization
Decision-Making under Uncertainty
Integrate Multiples Optimization Technologies
15. MODELERS
REAL WORLD
ALGEBRAIC MODEL
DECISION MAKERS
OPL
FICO™
MOSEL
OPTIMIZATION TECHNOLOGY
DEVELOPING
MATHEMATICAL
MODELS
TRADITIONAL WAY
PROGRAMMERS
DSS
DATA
BASE
DATA MODEL
PROGRAMMING
17. A DECISION SUPPORT SYSTEM
IS AS A DECISION MAKING CHAIN
INTEGRATED BY A COLLECTION
OF MODELS AND DATA FLOW
18. 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
24. 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
26. ALGEBRAIC LANGUAGES OBJECTS
MATHEMATICAL DEFINITIONS
• Index, Sets, Parameters, Variables, Equations,
Objective Functions, Planning Horizons, Decision
Trees
DECISION SUPPORT SYSTEMS
• Problems = S (Equations, Variables, Objective
Functions)
• Model = S (Problems, Data Flows)
• DSS = S (Models, Data Flows)
DATA MODEL
• DSN, Data Tables, Fields, Shell Windows, Data
Windows, Menus
28. OPTEX- DATABASE ALGEBRAIC LANGUAGE
SQL
Server
Internet - Intranet
MM
Server
MATHEMATICAL
MODEL
SERVER
INFORMATION
SYSTEM
EASY DEVELOPMENT MATHEMATICAL MODELS
IN A LAN-WAN ENVIRONMENT USING THE POWER
OF THE DATABASE SERVERS
29. OPTEX- DATABASE ALGEBRAIC LANGUAGE
SQL
Server
Internet - Intranet
MM
Server
MATHEMATICAL
MODEL
SERVER
INFORMATION
SYSTEM
THE IMPLEMENTATION OF A
DECISION SUPPORT SYSTEMS IS BASED IN
A FILLING THE BLANKS PROCESS
31. JVB-08/94OPTEX
Min St Sj Sh CTt(GTjth)
sujeto a:
GDzth = SuTN(z) LDuzth
GDzth + GHAzth + DEFzth = DEMzth
ENuth - SjL1(u) GTEjuth
- SvL2(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
INDEXESINDEXES
OPTEX- DATABASE ALGEBRAIC LANGUAGE
32. JVB-08/94OPTEX
Min St Sj Sh CTt(GTjth)
sujeto a:
GDzth = SuTN(z) LDuzth
GDzth + GHAzth + DEFzth = DEMzth
ENuth - SjL1(u) GTEjuth
- SvL2(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
SETSSETS
OPTEX- DATABASE ALGEBRAIC LANGUAGE
35. JVB-08/94OPTEX
Min St Sj Sh CTt(GTjth)
sujeto a:
GDzth = SuTN(z) LDuzth
GDzth + GHAzth + DEFzth = DEMzth
ENuth - SjL1(u) GTEjuth
- SvL2(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
PARAMETERSPARAMETERS
OPTEX- DATABASE ALGEBRAIC LANGUAGE
37. TIPO DE SERIE INTERPRETACIÓN
E
ESCALÓN
(STEP)
I
IMPULSO
(PULSE)
P
POLI LÍNEA
(POLY LINE)
OPTEX- DATABASE ALGEBRAIC LANGUAGE
MULTIPLES FORMS OF
DATA INTERPRETATION
38. JVB-08/94OPTEX
Min St Sj Sh CTt(GTjth)
sujeto a:
GDzth = SuTN(z) LDuzth
GDzth + GHAzth + DEFzth = DEMzth
ENuth - SjL1(u) GTEjuth
- SvL2(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
39. JVB-08/94OPTEX
Min St Sj Sh CTt(GTjth)
sujeto a:
GDzth = SuTN(z) LDuzth
GDzth + GHAzth + DEFzth = DEMzth
ENuth - SjL1(u) GTEjuth
- SvL2(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
42. MO
IL
MO
WO MO
Tiempo
OPTEX- DATABASE ALGEBRAIC LANGUAGE
FOR DISCRETE TIME MODELS, THE
PLANNING HORIZON MAY BE IN YEARS,
MONTHS, DAY, HOURS, MINUTES, …
43. 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
44. IN OPTEX IS DIRECT THE UNION OF MATHEMATICAL PROGRAMMING
PROBLEMS TO GENERATE A NEW MODEL OR VARIATION OF AN
ALREADY EXISTING MODEL
=+
45. 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
46. 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
50. 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-1TIME
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
PROBLEMS <-> MODELS
OPTEX- LARGE SCALE METHODOLOGIES
51. HYDRAULIC SYSTEM
COORDINATOR PROBLEM: MODBENCO
CCP, CGH, CGS, COE, CSP, EQE, SQE
yk
ELECTRIC SYSTEM
SUB-PROBLEM: MODBENUNNU
DUN, NUN
pk
vk
OPTEX- BENDERS IMPLEMENTATION
52. HYDRAULIC SYSTEM
COORDINATOR PROBLEM: MODBENCO
CCP, CGH, CGS, COE, CSP, EQE, SQE
yk
ELECTRIC SYSTEM
SUB-PROBLEM: MODBENNU
DUN, NUN
pk
vk
MODEL: MODBENNU
OPTEX- BENDERS IMPLEMENTATION
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. OPTEX HAS TOOLS ORIENTED TO DEVELOP
MULTISTAGE STOCHASTIC OPTIMIZATION
INCLUDING MULTIPLES TYPES OF RISK CONSTRAINTS
Conditional Value-at-Risk (CVaR)
Cost Probability Function
Standard
Deviation
(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
56. DETERMINISTIC CASE
t = 1 t = 2
Mean
Demand
Deterministics
Decisions
Deterministics
Future Operations
Decisions
57. TWO-STAGE DECISION TREE FOR
DEMAND: UNCERTAINTY DIMENSION
t = 1 t = 2
Scenario
Demand 10
Scenario
Demand 1
Scenario
Demand 2
Deterministics
Decisions
0.10
0.10
Uncertainty
Future Operations
Decisions
58. 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
Decisions
Uncertainty
Future Operations
Decisions
TWO-STAGE DECISION TREE FOR
DEMAND: UNCERTAINTY DIMENSION 1
EXTREME EVENT: UNCERTAINTY DIMENSION 2
WITH Extrem Event
59. THE AUTOMATIC CONVERSION IMPLIES:
1. TO INCLUDE THE INDEXES RELATED WITH THE
UNCERTAINTY DIMENSIONS
1.
60. 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
3.
4.
2.
77. 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
78. 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
105. INFORMATION
SYSTEM
Min St Sj Sh CTt(GTjth)
sujeto a:
GDzth - SuTN(z) LDuzth = 0
GDzth + GHAzth + DEFzth = DEMzth
ENuth - SjL1(u) GTEjuth
- SvL2(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
SIMM: MATHEMATICAL MODEL
INFORMATION SYSTEM
SIDI: INDUSTRIAL DATA
INFORMATION SYSTEM
108. IMPLEMENTATION INDUSTRIAL DATA INFORMATION SYSTEM
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
109. 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
113. 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
114. 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.
115. 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
119. 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
Sets
Parameters
Tables
Sets
Parameters
Tables
Variables
Primal-Dual
Tables
Sets
Parameters
Tables
Variables
Primal-Dual
Scenario
No. E-X
Directory
Tables
Sets
Parameters
Tables
Variables
Primal-Dual
AUTOMATICALLY, OPTEX GENERATES A HIERARCHIC INFORMATION
SYSTEM TO STORE THE RESULTS OF THE MODELS USING THE
CONCEPTS OF SCENARIOS AND FAMILY OF SCENARIOS.
120. OPTEX STORES
THE RESULTS
IN DATA
TABLES
AND/OR IN
TEXT FILES
AND/OR IN
EXCEL FILES
INDUSTRIAL DATA INFORMATION SYSTEM
121. OPTEX STORES
THE RESULTS
IN DATA
TABLES
AND/OR IN
TEXT FILES
AND/OR IN
EXCEL FILES
INDUSTRIAL DATA INFORMATION SYSTEM
137. 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
138. 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
139. OPTEX Mathematical Modeling System,
was developed to support
DecisionWare’s mathematical modeling
projects since 1991.
OPTEX has supported the development
of all multi-model OPCHAIN-DSS
developed by
140. 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