Iteration 0 - OR_EXPERT
Sequence: 1
Timestamp: 2025-07-25 22:43:58

Prompt:
You are an Operations Research (OR) expert focused ONLY on optimization modeling. Your role is to analyze the business domain and design LINEAR optimization problems without involving database design decisions.

CRITICAL MATHEMATICAL CONSTRAINTS FOR LINEAR/MIXED-INTEGER PROGRAMMING:
- The optimization problem MUST be either Linear Programming (LP) or Mixed-Integer Programming (MIP)
- Objective function MUST be linear: minimize/maximize ∑(coefficient × variable)
- All constraints MUST be linear: ∑(coefficient × variable) ≤/≥/= constant
- Decision variables can be continuous (LP) or mixed continuous/integer (MIP)
- NO variable products, divisions, or other nonlinear relationships
- Design business scenarios that naturally lead to linear mathematical formulations
- Generate between 2 and 20 constraints for optimization feasibility

YOUR SCOPE: Focus exclusively on optimization modeling and understanding current schema-to-optimization mapping. Do NOT propose database changes.
ROW COUNT AWARENESS: Be aware that data engineer will apply 3-row minimum rule - tables unable to generate sufficient meaningful rows will be moved to business_configuration_logic.json.

CRITICAL: Respond with ONLY a valid JSON object. No explanations, no markdown, no extra text.

Database: voter_1

```sql
CREATE TABLE AREA_CODE_STATE (
  area_code NUMBER,
  state TEXT
);
```

```sql
CREATE TABLE CONTESTANTS (
  contestant_number NUMBER,
  contestant_name TEXT
);
```

```sql
CREATE TABLE VOTES (
  vote_id NUMBER,
  phone_number NUMBER,
  state TEXT,
  contestant_number NUMBER,
  created TIME
);
```



Current Business Configuration Logic: {} (initially empty)

TASK: Design a realistic LINEAR optimization problem and analyze how it maps to the current schema.

JSON STRUCTURE REQUIRED:

{
  "database_id": "voter_1",
  "iteration": 0,
  "business_context": "Describe the realistic business scenario that leads to linear optimization (avoid scenarios requiring nonlinear relationships)",
  "optimization_problem_description": "Detailed description of what needs to be optimized using linear objective functions and constraints",
  "optimization_formulation": {
    "objective": "minimize/maximize specific_linear_metric with clear definition (sum of weighted variables only)",
    "decision_variables": "What linear variables can be controlled/decided (continuous or integer)",
    "constraints": "What linear limitations must be respected (no variable products or divisions) - design 2 to 20 constraints"
  },
  
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "coefficient_name[indices]": {
        "currently_mapped_to": "table.column OR business_configuration_logic.key OR missing",
        "mapping_adequacy": "good/missing/redundant/partial/inaccurate",
        "description": "what this coefficient represents in the optimization model"
      }
    },
    "constraint_bounds": {
      "constraint_name[indices]": {
        "currently_mapped_to": "table.column OR business_configuration_logic.key OR missing", 
        "mapping_adequacy": "good/missing/redundant/partial/inaccurate",
        "description": "what this constraint bound represents"
      }
    },
    "decision_variables": {
      "variable_name[indices]": {
        "currently_mapped_to": "table.column OR business_configuration_logic.key OR missing",
        "mapping_adequacy": "good/missing/redundant/partial/inaccurate", 
        "description": "what this decision variable represents",
        "variable_type": "continuous/integer/binary"
      }
    }
  },
  
  "missing_optimization_requirements": [
    "List what data/parameters are needed for complete linear optimization model"
  ],
  
  "iteration_status": {
    "complete": false,
    "confidence": "low/medium/high",
    "next_focus": "What optimization aspects need refinement"
  }
}

Response:
{
  "database_id": "voter_1",
  "iteration": 0,
  "business_context": "A voting competition where contestants aim to maximize their votes across different states. The goal is to allocate a limited budget for promotional activities to maximize the total number of votes received.",
  "optimization_problem_description": "Maximize the total number of votes received by contestants by allocating a promotional budget across states. The budget allocation must respect state-specific constraints and ensure fairness in promotional spending.",
  "optimization_formulation": {
    "objective": "maximize \u2211(votes_received[contestant_number, state])",
    "decision_variables": "promotional_budget[contestant_number, state] (continuous)",
    "constraints": [
      "\u2211(promotional_budget[contestant_number, state]) \u2264 total_budget",
      "promotional_budget[contestant_number, state] \u2265 0 for all contestant_number, state",
      "votes_received[contestant_number, state] = conversion_rate[state] \u00d7 promotional_budget[contestant_number, state] for all contestant_number, state",
      "promotional_budget[contestant_number, state] \u2264 max_budget_per_state[state] for all contestant_number, state"
    ]
  },
  "current_optimization_to_schema_mapping": {
    "objective_coefficients": {
      "votes_received[contestant_number, state]": {
        "currently_mapped_to": "VOTES.contestant_number",
        "mapping_adequacy": "partial",
        "description": "Number of votes received by a contestant in a specific state"
      }
    },
    "constraint_bounds": {
      "total_budget": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Total available budget for promotional activities"
      },
      "max_budget_per_state[state]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Maximum promotional budget allowed per state"
      }
    },
    "decision_variables": {
      "promotional_budget[contestant_number, state]": {
        "currently_mapped_to": "missing",
        "mapping_adequacy": "missing",
        "description": "Promotional budget allocated to a contestant in a specific state",
        "variable_type": "continuous"
      }
    }
  },
  "missing_optimization_requirements": [
    "Total available budget for promotional activities",
    "Conversion rate of promotional budget to votes per state",
    "Maximum promotional budget allowed per state"
  ],
  "iteration_status": {
    "complete": false,
    "confidence": "medium",
    "next_focus": "Refine the mapping of decision variables and constraints, and gather missing data for complete optimization model"
  }
}
