Iteration final - PROBLEM_DESCRIPTION
Sequence: 5
Timestamp: 2025-07-25 22:27:13

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 1), 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: Resource_i: continuous, representing the amount of campaign resources allocated to representative i
- Operational parameters align with expected linear objective: maximize ∑(Seats_i × Resource_i)
- Business configuration includes: Total budget available for campaign resources (used for Constraint bound for total resource allocation), Minimum amount of resources that must be allocated to each representative (used for Constraint bound for minimum resource allocation), Maximum amount of resources that can be allocated to representatives in a state (used for Constraint bound for state-level resource allocation)
- 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": "election_representative",
  "iteration": 1,
  "business_context": "A political party aims to maximize the total number of seats won across multiple elections by strategically allocating campaign resources to representatives in different states, while adhering to budget constraints and state-specific resource limits.",
  "optimization_problem_description": "The objective is to maximize the total seats won by the party across all elections. The decision variables represent the amount of campaign resources allocated to each representative. Constraints include a total budget limit, minimum resource allocations per representative, and maximum resource allocations per state.",
  "optimization_formulation": {
    "objective": "maximize \u2211(Seats_i \u00d7 Resource_i)",
    "decision_variables": "Resource_i: continuous, representing the amount of campaign resources allocated to representative i",
    "constraints": [
      "\u2211(Resource_i) \u2264 Total_Budget",
      "Resource_i \u2265 Minimum_Resource_Allocation for all i",
      "\u2211(Resource_i for all i in state j) \u2264 Maximum_Resource_Allocation_State_j for all j"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "Seats_i": {
        "currently_mapped_to": "election.Seats",
        "mapping_adequacy": "good",
        "description": "Number of seats won by representative i"
      }
    },
    "constraint_bounds": {
      "Total_Budget": {
        "currently_mapped_to": "business_configuration_logic.Total_Budget",
        "mapping_adequacy": "good",
        "description": "Total budget available for campaign resources"
      },
      "Minimum_Resource_Allocation": {
        "currently_mapped_to": "business_configuration_logic.Minimum_Resource_Allocation",
        "mapping_adequacy": "good",
        "description": "Minimum amount of resources that must be allocated to each representative"
      },
      "Maximum_Resource_Allocation_State_j": {
        "currently_mapped_to": "state_resource_limits.Maximum_Resource_Allocation",
        "mapping_adequacy": "good",
        "description": "Maximum amount of resources that can be allocated to representatives in a state"
      }
    },
    "decision_variables": {
      "Resource_i": {
        "currently_mapped_to": "resource_allocation.Resource_Amount",
        "mapping_adequacy": "good",
        "description": "Amount of campaign resources allocated to representative i",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [],
  "iteration_status": {
    "complete": true,
    "confidence": "high",
    "next_focus": "Ready for convergence"
  }
}

FINAL DATABASE SCHEMA:
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for decision variables and constraint bounds, moving scalar parameters to business configuration logic, and updating the data dictionary to reflect optimization mappings.

CREATE TABLE election (
  Seats INTEGER
);

CREATE TABLE resource_allocation (
  Resource_Amount FLOAT
);

CREATE TABLE state_resource_limits (
  Maximum_Resource_Allocation INTEGER
);


```

CURRENT STORED VALUES:
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on realistic campaign budgets, resource allocation limits, and election outcomes, ensuring they align with the business context and optimization requirements.

-- Realistic data for election
INSERT INTO election (Seats) VALUES (1);
INSERT INTO election (Seats) VALUES (2);
INSERT INTO election (Seats) VALUES (3);

-- Realistic data for resource_allocation
INSERT INTO resource_allocation (Resource_Amount) VALUES (1000.0);
INSERT INTO resource_allocation (Resource_Amount) VALUES (2000.0);
INSERT INTO resource_allocation (Resource_Amount) VALUES (3000.0);

-- Realistic data for state_resource_limits
INSERT INTO state_resource_limits (Maximum_Resource_Allocation) VALUES (50000);
INSERT INTO state_resource_limits (Maximum_Resource_Allocation) VALUES (60000);
INSERT INTO state_resource_limits (Maximum_Resource_Allocation) VALUES (70000);


```

DATA DICTIONARY:
{
  "tables": {
    "election": {
      "business_purpose": "Stores election results for each representative",
      "optimization_role": "objective_coefficients",
      "columns": {
        "Seats": {
          "data_type": "INTEGER",
          "business_meaning": "Number of seats won by representative i",
          "optimization_purpose": "Coefficient in the objective function",
          "sample_values": [
            1,
            2,
            3
          ]
        }
      }
    },
    "resource_allocation": {
      "business_purpose": "Stores campaign resource allocations for each representative",
      "optimization_role": "decision_variables",
      "columns": {
        "Resource_Amount": {
          "data_type": "FLOAT",
          "business_meaning": "Amount of campaign resources allocated to representative i",
          "optimization_purpose": "Decision variable in the optimization model",
          "sample_values": [
            1000.0,
            2000.0,
            3000.0
          ]
        }
      }
    },
    "state_resource_limits": {
      "business_purpose": "Stores maximum resource allocation limits for each state",
      "optimization_role": "constraint_bounds",
      "columns": {
        "Maximum_Resource_Allocation": {
          "data_type": "INTEGER",
          "business_meaning": "Maximum amount of resources that can be allocated to representatives in a state",
          "optimization_purpose": "Constraint bound in the optimization model",
          "sample_values": [
            50000,
            60000,
            70000
          ]
        }
      }
    }
  }
}


BUSINESS CONFIGURATION:

BUSINESS CONFIGURATION:
{
  "Total_Budget": {
    "data_type": "INTEGER",
    "business_meaning": "Total budget available for campaign resources",
    "optimization_role": "Constraint bound for total resource allocation",
    "configuration_type": "scalar_parameter",
    "value": 1000000,
    "business_justification": "A realistic total budget for a national campaign, sufficient to cover minimum allocations and state limits."
  },
  "Minimum_Resource_Allocation": {
    "data_type": "INTEGER",
    "business_meaning": "Minimum amount of resources that must be allocated to each representative",
    "optimization_role": "Constraint bound for minimum resource allocation",
    "configuration_type": "scalar_parameter",
    "value": 1000,
    "business_justification": "Ensures each representative receives a baseline level of campaign support."
  },
  "Maximum_Resource_Allocation_State_j": {
    "data_type": "INTEGER",
    "business_meaning": "Maximum amount of resources that can be allocated to representatives in a state",
    "optimization_role": "Constraint bound for state-level resource allocation",
    "configuration_type": "scalar_parameter",
    "value": 50000,
    "business_justification": "Prevents over-allocation of resources to any single state, ensuring fair distribution."
  }
}

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: election_representative

## 1. Problem Context and Goals

### Context  
[Regenerate business context that naturally aligns with LINEAR optimization formulation. Ensure:]
- Business decisions match expected decision variables: Resource_i: continuous, representing the amount of campaign resources allocated to representative i
- Operational parameters align with expected linear objective: maximize ∑(Seats_i × Resource_i)
- Business configuration includes: Total budget available for campaign resources (used for Constraint bound for total resource allocation), Minimum amount of resources that must be allocated to each representative (used for Constraint bound for minimum resource allocation), Maximum amount of resources that can be allocated to representatives in a state (used for Constraint bound for state-level resource allocation)
- 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 ∑(Seats_i × Resource_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: ['∑(Resource_i) ≤ Total_Budget', 'Resource_i ≥ Minimum_Resource_Allocation for all i', '∑(Resource_i for all i in state j) ≤ Maximum_Resource_Allocation_State_j for all j'] (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 1 Database Schema
-- Objective: Schema changes include creating tables for decision variables and constraint bounds, moving scalar parameters to business configuration logic, and updating the data dictionary to reflect optimization mappings.

CREATE TABLE election (
  Seats INTEGER
);

CREATE TABLE resource_allocation (
  Resource_Amount FLOAT
);

CREATE TABLE state_resource_limits (
  Maximum_Resource_Allocation INTEGER
);


```

### 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 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on realistic campaign budgets, resource allocation limits, and election outcomes, ensuring they align with the business context and optimization requirements.

-- Realistic data for election
INSERT INTO election (Seats) VALUES (1);
INSERT INTO election (Seats) VALUES (2);
INSERT INTO election (Seats) VALUES (3);

-- Realistic data for resource_allocation
INSERT INTO resource_allocation (Resource_Amount) VALUES (1000.0);
INSERT INTO resource_allocation (Resource_Amount) VALUES (2000.0);
INSERT INTO resource_allocation (Resource_Amount) VALUES (3000.0);

-- Realistic data for state_resource_limits
INSERT INTO state_resource_limits (Maximum_Resource_Allocation) VALUES (50000);
INSERT INTO state_resource_limits (Maximum_Resource_Allocation) VALUES (60000);
INSERT INTO state_resource_limits (Maximum_Resource_Allocation) VALUES (70000);


```

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

Response:
# Complete Optimization Problem and Solution: election_representative

## 1. Problem Context and Goals

### Context  
A political party is focused on maximizing the total number of seats won across multiple elections by strategically allocating campaign resources to its representatives in different states. The party must make decisions on how much campaign resources to allocate to each representative, ensuring that these allocations adhere to a total budget limit, provide a minimum level of support to each representative, and respect state-specific resource caps. The total budget available for campaign resources is set at one million units, ensuring that the party can cover all necessary allocations without exceeding its financial capacity. Each representative must receive at least one thousand units of resources to ensure a baseline level of campaign support. Additionally, the total resources allocated to representatives within any single state cannot exceed fifty thousand units, ensuring a fair distribution of resources across states. These operational parameters are designed to support a linear optimization approach, where the relationships between resource allocations and outcomes are straightforward and proportional.

### Goals  
The primary goal of this optimization problem is to maximize the total number of seats won by the party across all elections. This is achieved by strategically allocating campaign resources to representatives in a way that directly increases the likelihood of winning seats. The success of this strategy is measured by the total seats won, which is calculated as the sum of the seats won by each representative multiplied by the amount of resources allocated to them. The optimization process ensures that the party’s resource allocation decisions are aligned with its objective of maximizing electoral success while adhering to all operational constraints.

## 2. Constraints    

The optimization problem is subject to three key constraints, each designed to ensure that resource allocations are both effective and feasible. First, the total amount of resources allocated to all representatives combined must not exceed the total budget of one million units. This ensures that the party does not overspend its available financial resources. Second, each representative must receive at least one thousand units of resources, guaranteeing that every candidate receives a minimum level of campaign support. Third, the total resources allocated to representatives within any single state must not exceed fifty thousand units, ensuring that no state receives an disproportionate share of resources. These constraints are designed to be linear and proportional, supporting a straightforward optimization approach.

## 3. Available Data  

### Database Schema  
```sql
-- Iteration 1 Database Schema
-- Objective: Schema changes include creating tables for decision variables and constraint bounds, moving scalar parameters to business configuration logic, and updating the data dictionary to reflect optimization mappings.

CREATE TABLE election (
  Seats INTEGER
);

CREATE TABLE resource_allocation (
  Resource_Amount FLOAT
);

CREATE TABLE state_resource_limits (
  Maximum_Resource_Allocation INTEGER
);
```

### Data Dictionary  
The database schema includes three key tables, each with a specific role in the optimization process. The `election` table stores the number of seats won by each representative, which serves as the coefficient in the objective function. The `resource_allocation` table tracks the amount of campaign resources allocated to each representative, representing the decision variables in the optimization model. The `state_resource_limits` table contains the maximum amount of resources that can be allocated to representatives within each state, serving as a constraint bound in the optimization model. Together, these tables provide the necessary data to support the linear optimization of campaign resource allocations.

### Current Stored Values  
```sql
-- Iteration 1 Realistic Data
-- Generated by triple expert (business + data + optimization)
-- Values were determined based on realistic campaign budgets, resource allocation limits, and election outcomes, ensuring they align with the business context and optimization requirements.

-- Realistic data for election
INSERT INTO election (Seats) VALUES (1);
INSERT INTO election (Seats) VALUES (2);
INSERT INTO election (Seats) VALUES (3);

-- Realistic data for resource_allocation
INSERT INTO resource_allocation (Resource_Amount) VALUES (1000.0);
INSERT INTO resource_allocation (Resource_Amount) VALUES (2000.0);
INSERT INTO resource_allocation (Resource_Amount) VALUES (3000.0);

-- Realistic data for state_resource_limits
INSERT INTO state_resource_limits (Maximum_Resource_Allocation) VALUES (50000);
INSERT INTO state_resource_limits (Maximum_Resource_Allocation) VALUES (60000);
INSERT INTO state_resource_limits (Maximum_Resource_Allocation) VALUES (70000);
```
