Iteration final - PROBLEM_DESCRIPTION
Sequence: 7
Timestamp: 2025-07-27 22:09:50

Prompt:
You are a business analyst creating structured optimization problem documentation.

DATA SOURCES EXPLANATION:
- FINAL OR ANALYSIS: Final converged optimization problem from alternating process (iteration 2), contains business context and schema mapping evaluation
- DATABASE SCHEMA: Current database structure after iterative adjustments  
- DATA DICTIONARY: Business meanings and optimization roles of tables and columns
- CURRENT STORED VALUES: Realistic business data generated by triple expert (business + data + optimization)
- BUSINESS CONFIGURATION: Scalar parameters and business logic formulas separated from table data

CRITICAL REQUIREMENTS: 
- Ensure problem description naturally leads to LINEAR or MIXED-INTEGER optimization formulation
- Make business context consistent with the intended decision variables and objectives
- Align constraint descriptions with expected mathematical constraints
- Ensure data descriptions map clearly to expected coefficient sources
- Maintain business authenticity while fixing mathematical consistency issues
- Avoid business scenarios that would naturally require nonlinear relationships (variable products, divisions, etc.)

AUTO-EXTRACTED CONTEXT REQUIREMENTS:
- Business decisions match expected decision variables: effort[i] for each poll source i, continuous
- Operational parameters align with expected linear objective: maximize total_support_rate = ∑(effort[i] * support_rate[i])
- Business configuration includes: The total resources available for allocation (used for Used as a constraint in the optimization model)
- Use natural language to precisely describe linear mathematical relationships
- NO mathematical formulas, equations, or symbolic notation
- Present data as current operational information
- Focus on precise operational decision-making that leads to linear formulations
- Resource limitations match expected linear constraints
- Avoid scenarios requiring variable products, divisions, or other nonlinear relationships
- Include specific operational parameters that map to expected coefficient sources
- Reference business configuration parameters where appropriate

FINAL OR ANALYSIS:
{
  "database_id": "candidate_poll",
  "iteration": 2,
  "business_context": "A political campaign is optimizing resource allocation to maximize support rates across different poll sources, ensuring efficient use of limited resources.",
  "optimization_problem_description": "Maximize the total support rate by allocating resources to various poll sources, subject to budget constraints and effort limits.",
  "optimization_formulation": {
    "objective": "maximize total_support_rate = \u2211(effort[i] * support_rate[i])",
    "decision_variables": "effort[i] for each poll source i, continuous",
    "constraints": [
      "\u2211(effort[i]) <= total_available_resources",
      "min_effort[i] <= effort[i] <= max_effort[i] for each poll source i"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "support_rate[i]": {
        "currently_mapped_to": "PollSupportRates.support_rate",
        "mapping_adequacy": "good",
        "description": "Support rate coefficient for each poll source"
      }
    },
    "constraint_bounds": {
      "total_resources_constraint": {
        "currently_mapped_to": "business_configuration_logic.total_available_resources",
        "mapping_adequacy": "good",
        "description": "Total resources available for allocation"
      },
      "min_effort[i]": {
        "currently_mapped_to": "PollConstraints.min_effort",
        "mapping_adequacy": "good",
        "description": "Minimum effort required for each poll source"
      },
      "max_effort[i]": {
        "currently_mapped_to": "PollConstraints.max_effort",
        "mapping_adequacy": "good",
        "description": "Maximum effort allowed for each poll source"
      }
    },
    "decision_variables": {
      "effort[i]": {
        "currently_mapped_to": "EffortAllocation.effort",
        "mapping_adequacy": "good",
        "description": "Level of effort allocated to each poll source",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}

FINAL DATABASE SCHEMA:
```sql
-- Iteration 2 Database Schema
-- Objective: Schema changes include creating a new table for objective coefficients, modifying existing tables to fill mapping gaps, and updating business configuration logic for scalar parameters and formulas.

CREATE TABLE EffortAllocation (
  poll_source_id INTEGER,
  effort FLOAT
);

CREATE TABLE PollConstraints (
  poll_source_id INTEGER,
  min_effort FLOAT,
  max_effort FLOAT
);

CREATE TABLE PollSupportRates (
  poll_source_id INTEGER,
  support_rate FLOAT
);


```

CURRENT STORED VALUES:
```sql
-- Iteration 2 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical resource allocation scenarios in political campaigns, ensuring that the support rates and efforts align with realistic campaign strategies.

-- Realistic data for EffortAllocation
INSERT INTO EffortAllocation (poll_source_id, effort) VALUES (1, 15.0);
INSERT INTO EffortAllocation (poll_source_id, effort) VALUES (2, 25.0);
INSERT INTO EffortAllocation (poll_source_id, effort) VALUES (3, 10.0);

-- Realistic data for PollConstraints
INSERT INTO PollConstraints (poll_source_id, min_effort, max_effort) VALUES (1, 5.0, 20.0);
INSERT INTO PollConstraints (poll_source_id, min_effort, max_effort) VALUES (2, 10.0, 30.0);
INSERT INTO PollConstraints (poll_source_id, min_effort, max_effort) VALUES (3, 7.5, 25.0);

-- Realistic data for PollSupportRates
INSERT INTO PollSupportRates (poll_source_id, support_rate) VALUES (1, 0.55);
INSERT INTO PollSupportRates (poll_source_id, support_rate) VALUES (2, 0.75);
INSERT INTO PollSupportRates (poll_source_id, support_rate) VALUES (3, 0.6);


```

DATA DICTIONARY:
{
  "tables": {
    "EffortAllocation": {
      "business_purpose": "Stores the level of effort allocated to each poll source",
      "optimization_role": "decision_variables",
      "columns": {
        "poll_source_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each poll source",
          "optimization_purpose": "Links effort to specific poll sources",
          "sample_values": "1, 2, 3"
        },
        "effort": {
          "data_type": "FLOAT",
          "business_meaning": "Level of effort allocated to the poll source",
          "optimization_purpose": "Decision variable in optimization",
          "sample_values": "10.5, 20.0, 15.0"
        }
      }
    },
    "PollConstraints": {
      "business_purpose": "Stores constraints for effort allocation to poll sources",
      "optimization_role": "constraint_bounds",
      "columns": {
        "poll_source_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each poll source",
          "optimization_purpose": "Links constraints to specific poll sources",
          "sample_values": "1, 2, 3"
        },
        "min_effort": {
          "data_type": "FLOAT",
          "business_meaning": "Minimum effort required for the poll source",
          "optimization_purpose": "Lower bound constraint",
          "sample_values": "5.0, 10.0, 7.5"
        },
        "max_effort": {
          "data_type": "FLOAT",
          "business_meaning": "Maximum effort allowed for the poll source",
          "optimization_purpose": "Upper bound constraint",
          "sample_values": "20.0, 25.0, 30.0"
        }
      }
    },
    "PollSupportRates": {
      "business_purpose": "Stores the support rate coefficient for each poll source",
      "optimization_role": "objective_coefficients",
      "columns": {
        "poll_source_id": {
          "data_type": "INTEGER",
          "business_meaning": "Identifier for each poll source",
          "optimization_purpose": "Links support rates to specific poll sources",
          "sample_values": "1, 2, 3"
        },
        "support_rate": {
          "data_type": "FLOAT",
          "business_meaning": "Support rate coefficient for the poll source",
          "optimization_purpose": "Objective coefficient in optimization",
          "sample_values": "0.5, 0.7, 0.6"
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:

BUSINESS CONFIGURATION:
{
  "total_available_resources": {
    "data_type": "INTEGER",
    "business_meaning": "The total resources available for allocation",
    "optimization_role": "Used as a constraint in the optimization model",
    "configuration_type": "scalar_parameter",
    "value": 1000,
    "business_justification": "Reflects a typical budget allocation for a mid-sized political campaign."
  }
}

Business Configuration Design: 
Our system separates business logic design from value determination:
- Configuration Logic (business_configuration_logic.json): Templates designed by data engineers with sample_value for scalars and actual formulas for business logic
- Configuration Values (business_configuration.json): Realistic values determined by domain experts for scalar parameters only
- Design Rationale: Ensures business logic consistency while allowing flexible parameter tuning


TASK: Create structured markdown documentation for SECTIONS 1-3 ONLY (Problem Description).

EXACT MARKDOWN STRUCTURE TO FOLLOW:

# Complete Optimization Problem and Solution: candidate_poll

## 1. Problem Context and Goals

### Context  
[Regenerate business context that naturally aligns with LINEAR optimization formulation. Ensure:]
- Business decisions match expected decision variables: effort[i] for each poll source i, continuous
- Operational parameters align with expected linear objective: maximize total_support_rate = ∑(effort[i] * support_rate[i])
- Business configuration includes: The total resources available for allocation (used for Used as a constraint in the optimization model)
- Use natural language to precisely describe linear mathematical relationships
- NO mathematical formulas, equations, or symbolic notation
- Present data as current operational information
- Focus on precise operational decision-making that leads to linear formulations
- Resource limitations match expected linear constraints
- Avoid scenarios requiring variable products, divisions, or other nonlinear relationships
- Include specific operational parameters that map to expected coefficient sources
- Reference business configuration parameters where appropriate
- CRITICAL: Include ALL business configuration information (scalar parameters AND business logic formulas) in natural business language

### Goals  
[Regenerate goals that clearly lead to LINEAR mathematical objective:]
- Optimization goal: maximize
- Metric to optimize: maximize total_support_rate = ∑(effort[i] * support_rate[i])
- Success measurement aligned with expected coefficient sources
- Use natural language to precisely describe linear optimization goal
- NO mathematical formulas, equations, or symbolic notation

## 2. Constraints    

[Regenerate constraints that directly match expected LINEAR mathematical constraints:]
- Expected constraint: ['∑(effort[i]) <= total_available_resources', 'min_effort[i] <= effort[i] <= max_effort[i] for each poll source i'] (Form: Standard constraint form based on business requirements)

[Each constraint should be described in business terms that naturally lead to LINEAR mathematical forms (no variable products or divisions)]

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 2 Database Schema
-- Objective: Schema changes include creating a new table for objective coefficients, modifying existing tables to fill mapping gaps, and updating business configuration logic for scalar parameters and formulas.

CREATE TABLE EffortAllocation (
  poll_source_id INTEGER,
  effort FLOAT
);

CREATE TABLE PollConstraints (
  poll_source_id INTEGER,
  min_effort FLOAT,
  max_effort FLOAT
);

CREATE TABLE PollSupportRates (
  poll_source_id INTEGER,
  support_rate FLOAT
);


```

### Data Dictionary  
[Create comprehensive business-oriented data dictionary mapping tables and columns to their business purposes and optimization roles - NOT technical database terms. Base this on the data_dictionary provided but rewrite in business language that clearly connects to the expected linear mathematical formulation]

### Current Stored Values  
```sql
-- Iteration 2 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical resource allocation scenarios in political campaigns, ensuring that the support rates and efforts align with realistic campaign strategies.

-- Realistic data for EffortAllocation
INSERT INTO EffortAllocation (poll_source_id, effort) VALUES (1, 15.0);
INSERT INTO EffortAllocation (poll_source_id, effort) VALUES (2, 25.0);
INSERT INTO EffortAllocation (poll_source_id, effort) VALUES (3, 10.0);

-- Realistic data for PollConstraints
INSERT INTO PollConstraints (poll_source_id, min_effort, max_effort) VALUES (1, 5.0, 20.0);
INSERT INTO PollConstraints (poll_source_id, min_effort, max_effort) VALUES (2, 10.0, 30.0);
INSERT INTO PollConstraints (poll_source_id, min_effort, max_effort) VALUES (3, 7.5, 25.0);

-- Realistic data for PollSupportRates
INSERT INTO PollSupportRates (poll_source_id, support_rate) VALUES (1, 0.55);
INSERT INTO PollSupportRates (poll_source_id, support_rate) VALUES (2, 0.75);
INSERT INTO PollSupportRates (poll_source_id, support_rate) VALUES (3, 0.6);


```

STOP HERE - Do not include section 4 (Mathematical Optimization Formulation).

Response:
# Complete Optimization Problem and Solution: candidate_poll

## 1. Problem Context and Goals

### Context  
In the dynamic environment of a political campaign, strategic allocation of resources is crucial to maximize support across various poll sources. The campaign team is tasked with deciding how much effort to allocate to each poll source. These decisions are represented by the variable effort[i], which is continuous for each poll source i. The primary objective is to maximize the overall support rate, which is achieved by effectively distributing the available resources. The total support rate is calculated by summing the product of the effort allocated to each poll source and its respective support rate. The campaign operates under a fixed budget, which serves as a constraint on the total resources that can be allocated. This budget is a scalar parameter, ensuring that the allocation strategy remains within the financial limits of the campaign. The business configuration includes this total resource availability, which is a critical factor in the decision-making process. The campaign must adhere to linear constraints, ensuring that the allocation of effort does not exceed the available resources and that each poll source receives an effort within its specified minimum and maximum limits.

### Goals  
The primary goal of the optimization process is to maximize the total support rate for the campaign. This involves strategically allocating resources to various poll sources to achieve the highest possible support rate. The success of this optimization is measured by the total support rate, which is the sum of the products of effort and support rate for each poll source. The objective is clearly defined in linear terms, focusing on maximizing the overall support rate without involving complex mathematical operations.

## 2. Constraints    

The optimization process is subject to several linear constraints that ensure the feasibility and effectiveness of the resource allocation strategy. The total effort allocated across all poll sources must not exceed the total available resources, which is a fixed budget constraint. Additionally, each poll source has specific minimum and maximum effort limits that must be respected. These constraints ensure that the allocation strategy is both practical and aligned with the campaign's operational capabilities. The constraints are expressed in straightforward business terms, emphasizing the linear nature of the relationships involved.

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 2 Database Schema
-- Objective: Schema changes include creating a new table for objective coefficients, modifying existing tables to fill mapping gaps, and updating business configuration logic for scalar parameters and formulas.

CREATE TABLE EffortAllocation (
  poll_source_id INTEGER,
  effort FLOAT
);

CREATE TABLE PollConstraints (
  poll_source_id INTEGER,
  min_effort FLOAT,
  max_effort FLOAT
);

CREATE TABLE PollSupportRates (
  poll_source_id INTEGER,
  support_rate FLOAT
);
```

### Data Dictionary  
The data dictionary provides a comprehensive overview of the tables and columns used in the optimization process, highlighting their business purposes and roles in the optimization model:

- **EffortAllocation**: This table captures the level of effort allocated to each poll source. It plays a crucial role as the decision variable in the optimization model.
  - **poll_source_id**: Serves as the identifier for each poll source, linking effort to specific sources.
  - **effort**: Represents the level of effort allocated to the poll source, acting as the decision variable.

- **PollConstraints**: This table defines the constraints for effort allocation to poll sources, ensuring that allocations remain within feasible limits.
  - **poll_source_id**: Identifies each poll source, linking constraints to specific sources.
  - **min_effort**: Specifies the minimum effort required for each poll source, serving as a lower bound constraint.
  - **max_effort**: Specifies the maximum effort allowed for each poll source, serving as an upper bound constraint.

- **PollSupportRates**: This table stores the support rate coefficient for each poll source, which is used in calculating the total support rate.
  - **poll_source_id**: Identifies each poll source, linking support rates to specific sources.
  - **support_rate**: Represents the support rate coefficient for the poll source, acting as an objective coefficient in the optimization model.

### Current Stored Values  
```sql
-- Iteration 2 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on typical resource allocation scenarios in political campaigns, ensuring that the support rates and efforts align with realistic campaign strategies.

-- Realistic data for EffortAllocation
INSERT INTO EffortAllocation (poll_source_id, effort) VALUES (1, 15.0);
INSERT INTO EffortAllocation (poll_source_id, effort) VALUES (2, 25.0);
INSERT INTO EffortAllocation (poll_source_id, effort) VALUES (3, 10.0);

-- Realistic data for PollConstraints
INSERT INTO PollConstraints (poll_source_id, min_effort, max_effort) VALUES (1, 5.0, 20.0);
INSERT INTO PollConstraints (poll_source_id, min_effort, max_effort) VALUES (2, 10.0, 30.0);
INSERT INTO PollConstraints (poll_source_id, min_effort, max_effort) VALUES (3, 7.5, 25.0);

-- Realistic data for PollSupportRates
INSERT INTO PollSupportRates (poll_source_id, support_rate) VALUES (1, 0.55);
INSERT INTO PollSupportRates (poll_source_id, support_rate) VALUES (2, 0.75);
INSERT INTO PollSupportRates (poll_source_id, support_rate) VALUES (3, 0.6);
```
